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Thickness and electric field dependent polarizability and dielectric constant in phosphorene
Abstract
Based on extensive first principle calculations, we explore the thickness dependent effective di- electric constant and slab polarizability of few layer black phosphorene. We find that the dielectric constant in ultra-thin phosphorene is thickness dependent and it can be further tuned by applying an out of plane electric field. The decreasing dielectric constant with reducing number of layers of phosphorene, is a direct consequence of the lower permittivity of the surface layers and the in- creasing surface to volume ratio. We also show that the slab polarizability depends linearly on the number of layers, implying a nearly constant polarizability per phosphorus atom. Our calculation of the thickness and electric field dependent dielectric properties will be useful for designing and interpreting transport experiments in gated phosphorene devices, wherever electrostatic effects such as capacitance, charge screening etc. are important. (http://arxiv.org/abs/1602.09073)
... For ferroelectric device, the controlling of external fields on polarization is undoubtedly more meaningful than other tuning methods. In fact, the transport, magnetism, catalysis, and other properties of 2D materials can all be modified by an external field [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. A large number of relevant studies have been reported [23,[33][34][35][36][37][38][39]. ...
... In fact, the transport, magnetism, catalysis, and other properties of 2D materials can all be modified by an external field [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. A large number of relevant studies have been reported [23,[33][34][35][36][37][38][39]. However, the external electric field effects on the sliding ferroelectricity of 2D materials are rarely reported. ...
Recent experiments confirm that two-dimensional (2D) boron nitride (BN) films possess room-temperature out-of-plane ferroelectricity when each BN layer is sliding with respect to each other. This ferroelectricity is attributed to the interlayered orbital hybridization or interlayer charge transfer in previous work. In this work, we attempt to understand the sliding ferroelectricity from the perspective of orbital distortion of long-pair electrons. Using the maximally localized Wannier function (MLWF) method and first-principles calculations, the out-of-plane pz orbitals of BN are investigated. Our results indicate that the interlayer van der Waals interaction causes the distortion of the N pz orbitals. Based on the picture of out-of-plane orbital distortion, we propose a possible mechanism to tune the ferroelectric polarization by external fields, including electric field and stress field. It is found that both the polarization intensity and direction can be modulated under the electric field. The polarization intensity of the system can also be controlled by stress field perpendicular to the plane. This study will provide theoretical help in the device design based on sliding ferroelectrics.
... Since, its rediscovery in 2014, phosphorene and 2D-BP have gotten a lot of interest. Furthermore, because of the layer-to-layer coupling effect, B.G of 2D-BP was substantially dependent on its layer number, as has been comprehensively explored by multiple theoretical [76] and experimental [77] research. The B.G value is anticipated to be 2 eV for monolayer and 0.3 eV for bulk in all circumstances, despite the fact that it is directly tied to the approximation strategy used in various computations and the methodologies used in various measurements. ...
... Organic solvents are the most popular and widely used LE medium. For the synthesis of the phosphorene [217] several organic solvents have been used, including NMP [215], dimethyl sulfoxide (DMSO) [218,219], isopropyl alcohol (IPA) [77], dimethyl-formamide (DMF) [218], and N-cyclohexyl-2-pyrrolidone (CHP) [216]. LPE can be divided into five categories: ...
A monolayer of black phosphorus (BP), commonly known as phosphorene is a novel member of the two-dimensional (2D) materials family. In consequence of its “puckered” lattice structure, phosphorene has a larger surface to volume ratio than graphene and transition metal dichalcogenides (TMDCs), and has revealed some distinct benefits in sensing applications. Since, its first synthesis in 2014 by mechanical exfoliation has spurred a wave of material science research activity. Phosphorene's structure and anisotropic characteristics, with its applications in transistors, batteries, solar cells, disease theranostics and sensing has been the subject of several reviews. This pursuit has sparked a flurry of new areas of research, theoretical and experimental, targeted at technological breakthroughs. The target of this review is to explain current advances in phosphorene synthesis, properties, and sensing applications, such as gas sensing, humidity sensing, photo-detection, bio-sensing, and ion-sensing. Finally, we will discuss the present obstacles and potential for phosphorene synthesis, properties and sensing applications.
... A linear dependence can be observed through the image for all O 2 coverages. Relative dielectric constant (ε r ) is related to polarizability (P) by: where V cell is the effective 2D cell volume without vacuum space [49]. In the meanwhile, polarizability is proportional to layer numbers (N) by: ...
... where V bulk , ε bulk , b correspond to volume of the bulk unit cell with two layers, bulk dielectric constant, constant related to surface polarizability, respectively [49]. V cell can be approximated by: ...
Two-dimensional (2D) few-layer black phosphorus (BP) with extraordinary electronic and optical properties is an excellent candidate for optoelectronic applications. However, rapid surface oxidation under ambient environment significantly restricts its practicability. Here, we investigate excitonic effect in few-layer BP oxides via first-principle calculation and effective mass approximation. Influence of layer numbers and degree of oxidation on exciton binding energy (EBE) is discussed in detail for the first time. It is found that EBE in BP oxides decreases exponentially with increasing sample thickness and becomes almost oxygen independent over six layers with values similar to that of pristine BP. Instead, oxidation alters excitation probability of excitons in few-layer BP via a direct/indirect bandgap transition.
... Importantly, these analyses have yielded, among other things, the anisotropic effective masses of both electrons and holes. Both the static dielectric constant [40] and ML thickness of phosphorene [70] are also known, which is important for characterizing the electrostatic interaction between the electron and hole. These parameters can be inserted directly into the Schrödinger equation describing the electron-hole system, enabling a straightforward solution of the anisotropic exciton eigensystem. ...
... The phosphorene ML thickness l phos , obtained via ab initio calculations in Ref. [70], agrees well with theoretical results from other works, namely, 0.53 nm [26] and 0.6 nm [6]-we note that these last two references also measured the ML thickness using atomic force microscopy (AFM), obtaining values of 0.85 and 0.7 nm, respectively, but the authors themselves note that AFM measurements tend to overestimate ML thickness. The 2D polarizability χ 2D was calculated from first principles in Ref. [13] and agrees well with the value of 0.38 nm, also obtained from first principles in Ref. [58]. ...
We study the eigenenergies and optical properties of both direct excitons in a phosphorene monolayer in different dielectric environments and indirect excitons in heterostructures of phosphorene with hexagonal boron nitride. For these systems, we solve the 2D Schrödinger equation using the Rytova-Keldysh (RK) potential for direct and both the RK and Coulomb potentials for indirect excitons. The results show that excitons formed from charge carriers with anisotropic effective mass exhibit enhanced (suppressed) optical absorption, compared to their 2D isotropic counterparts, under linearly polarized excitations along the crystal axis with relatively smaller (larger) effective carrier masses. This anisotropy leads to dramatically different excited states than the isotropic exciton. The direct exciton binding energy depends strongly on the dielectric environment, and shows good agreement with previously published data. For indirect excitons, the oscillator strength and absorption coefficient increase as the interlayer separation increases. The choice of RK or Coulomb potential does not significantly change the indirect exciton optical properties, but leads to significant differences in the binding energy for small interlayer separation.
... The electronic band structures of BP shown in Fig. 3(a) and Fig. 3(b) [10,44] are obtained using theoretical calculations and angle-resolved photo emission spectroscopy (ARPES) [10]. Fig. 3(c) shows the monolayer BP band structure by theoretical calculation [45]. ...
... BP belongs to the D 2h point group structure of an orthogonal crystal system. The effective carriers along the longitudinal zigzag shape are 10 times greater than those along the transverse structure, which directly leads to the strong anisotropy of BP electrons in its plane [44,58]. ...
This review focuses on the structure and properties of two-dimensional black phosphorus (BP). First, the crystal and electronic structures of BP are introduced. Second, the anisotropy properties of BP including the band structure and mechanical, thermal, electric, thermoelectric, optical, optoelectronic, magnetic, and magneto-optic
properties are described. Third, the applications of BP based on the aforementioned properties are detailed. This review of the properties and applications of BP can not only promote deeper understanding of the physical structure and properties of BP, but also enable the rational design of various devices based on BP’s properties.
... It is determined that the ionic contribution is found to be~2 times greater than the electronic response. This stark contrast sets Bi 2 SeO 5 apart from most other 2D materials studied to date, including BP, InSe, MoS 2 , and others [26][27][28][29]. Furthermore, it is worth mentioning that experimental findings indicate that Bi 2 SeO 5 possesses both high dielectric constants and high breakdown field (EBD) values. ...
Bi2SeO5 has garnered considerable attention as a van der Waals (vdW) layered dielectric material featuring excellent electrical insulation properties. However, the related theoretical understanding of the dielectric properties of atomically thin films is still lacking. Here, we conducted the first-principles calculations to determine the dielectric performance of Bi2SeO5, showing a high average dielectric constant (ε) of >20 ranging from bulk to bilayer and monolayer. Besides, the conduction and valance band offsets between the monolayer Bi2SeO5 and bilayer Bi2O2Se were calculated to be greater than 1 eV, suggesting that monolayer Bi2SeO5 works well as the dielectric for atomically thin Bi2O2Se. Unlike h-BN or other two-dimensional (2D) vdW insulators, ε of Bi2SeO5 is dominated by its ionic component and remains nearly constant as the thickness decreases, demonstrating an ultralow equivalent oxide thickness (EOT) of 0.3 nm for its monolayer form. Moreover, the high ε of monolayer Bi2SeO5 survives under tensile or compressive strains up to 6%, which greatly facilitates its integration with various 2D semiconductors. Our work suggests that Bi2SeO5 ultrathin films can serve as excellent atomically flat encapsulation and dielectric layers for high-performance 2D electronic devices.
... , where G and κ are the BL energy gap and the dielectric constant in the absence of the transverse electric field, E G is the characteristic electric field, W is the BL thickness (see, for example, [38][39][40][41], and η = � C /(� C + � V ) < 1 the fraction of the BL height related to the conduction band. For the b-P BL with W = 10 nm (the number of the atomic layers N = 20 ), E G ≃ 0.7 − 0.8 ≃ V/nm. ...
We propose the terahertz (THz) detectors based on field-effect transistors (FETs) with the graphene channel (GC) and the black-Arsenic (b-As) black-Phosphorus (b-P), or black-Arsenic-Phosphorus (b-As $$_x$$ x P $$_{1-x}$$ 1 - x ) gate barrier layer. The operation of the GC-FET detectors is associated with the carrier heating in the GC by the THz electric field resonantly excited by incoming radiation leading to an increase in the rectified current between the channel and the gate over the b-As $$_x$$ x P $$_{1-x}$$ 1 - x energy barrier layer (BLs). The specific feature of the GC-FETs under consideration is relatively low energy BLs and the possibility to optimize the device characteristics by choosing the barriers containing a necessary number of the b-As $$_x$$ x P $$_{1-x}$$ 1 - x atomic layers and a proper gate voltage. The excitation of the plasma oscillations in the GC-FETs leads to the resonant reinforcement of the carrier heating and the enhancement of the detector responsivity. The room temperature responsivity can exceed the values of $$10^3$$ 10 3 A/W. The speed of the GC-FET detector’s response to the modulated THz radiation is determined by the processes of carrier heating. As shown, the modulation frequency can be in the range of several GHz at room temperatures.
... where ∆ G and κ are the BL energy gap and the dielectric constant in the absence of the transverse electric field, E G is the characteristic electric field, W is the BL thickness (see, for example, [38][39][40][41], and η = ∆ C /(∆ C + ∆ V ) < 1 the fraction of the BL height related to the conduction band. For the b-P BL with W = 10 nm (the number of the atomic layers N = 20), E G ≃ 0.7 − 0.8 ≃ V/nm. ...
We propose the terahertz (THz) detectors based on field-effect transistors (FETs) with the graphene channel (GC) and the black-Arsenic (b-As) black-Phosphorus (b-P), or black-Arsenic-Phosphorus (b-As$_x$P$_{1-x}$) gate barrier layer. The operation of the GC-FET detectors is associated with the carrier heating in the GC by the THz electric field resonantly excited by incoming radiation leading to an increase in the rectified current between the channel and the gate over the b-As$_x$P$_{1-x}$ energy barrier layer (BLs). The specific feature of the GC-FETs under consideration is relatively low energy BLs and the possibility to optimize the device characteristics by choosing the barriers containing a necessary number of the b-As$_x$P$_{1-x}$ atomic layers and a proper gate voltage. The excitation of the plasma oscillations in the GC-FETs leads to the resonant reinforcement of the carrier heating and the enhancement of the detector responsivity. The room temperature responsivity can exceed the values of $10^3$~A/W. The speed of the GC-FET detector's response to the modulated THz radiation is determined by the processes of carrier heating. As shown, the modulation frequency can be in the range of several GHz at room temperatures.
... 447 Although graphitic surfaces are prone to hydrocarbon contamination, the simulated contact angle is in good quantitative agreement with the contact angle of 62−68°r eported in the majority of recent experimental studies on pristine graphite surfaces. 532−535 All-atomistic polarizable force fields can also be used to investigate the wetting of other 2D materials, including hBN 536 and phosphorene, 537 which have polarizabilities that are similar to, or larger than, that of graphene. ...
Confined fluids and electrolyte solutions in nanopores exhibit rich and surprising physics and chemistry that impact the mass transport and energy efficiency in many important natural systems and industrial applications. Existing theories often fail to predict the exotic effects observed in the narrowest of such pores, called single-digit nanopores (SDNs), which have diameters or conduit widths of less than 10 nm, and have only recently become accessible for experimental measurements. What SDNs reveal has been surprising, including a rapidly increasing number of examples such as extraordinarily fast water transport, distorted fluid-phase boundaries, strong ion-correlation and quantum effects, and dielectric anomalies that are not observed in larger pores. Exploiting these effects presents myriad opportunities in both basic and applied research that stand to impact a host of new technologies at the water-energy nexus, from new membranes for precise separations and water purification to new gas permeable materials for water electrolyzers and energy-storage devices. SDNs also present unique opportunities to achieve ultrasensitive and selective chemical sensing at the single-ion and single-molecule limit. In this review article, we summarize the progress on nanofluidics of SDNs, with a focus on the confinement effects that arise in these extremely narrow nanopores. The recent development of precision model systems, transformative experimental tools, and multiscale theories that have played enabling roles in advancing this frontier are reviewed. We also identify new knowledge gaps in our understanding of nanofluidic transport and provide an outlook for the future challenges and opportunities at this rapidly advancing frontier.
... where q is electronic charge, W n is the depletion width along MoS 2 side, N D is intrinsic doping concentration for n-type MoS 2 , MoS 2 ∼ 7.6 is dielectric constant for multilayer MoS 2 [27], ä o is permittivity of free space and r MoS 2 ∼ 40 Å is screening length for MoS 2 [28]. Similarly, W p is depletion width along BP side, N A is intrinsic doping concentration in p-type BP, BP ∼ 8.3 is dielectric constant for multilayer BP [29] and r~23.2 Å BP is screening length for BP [30]. ...
2D van der Waals heterostructure paves a path towards next generation semiconductor junctions for nanoelectronics devices in the post silicon era. Probing the band alignment at a real condition of such 2D contacts and experimental determination of its junction parameters is necessary to comprehend the charge diffusion and transport through such 2D nano-junctions. Here, we demonstrate the formation of the p-n junction at the MoS2/Black phosphorene (BP) interface and conduct a nanoscale investigation to experimentally measure the band alignment at real conditions by means of measuring the spatial distribution of built-in potential, built-in electric field, and depletion width using the Kelvin probe force microscopy (KPFM) technique. We show that optimization of lift scan height is critical for defining the depletion region of MoS2/BP with nanoscale precision using the KPFM technique. The variations in the built-in potential and built-in electric field with varying thicknesses of MoS2 are revealed and calibrated.
... They showed that the variation is between 0.1 and 0.5 for h-BN and MoS 2 when the number of layers changes from one to five, reaching the bulk value after five layers [28]. On the other hand, Kumar et al. showed that for BP, the dielectric constant slowly increases with the number of layers towards its bulk value [29]. Since the flakes studied here have thickness larger than 5 nm, we used the dielectric constant of bulk BP. ...
Epsilon near-zero photonics and surface polariton nanophotonics have become major fields within optics, leading to unusual and enhanced light-matter interaction. Specific dielectric responses are required in both cases, which can be achieved, e.g., via operation near a material’s electronic or phononic resonance. However, this condition restricts operation to a specific, narrow frequency range. It has been shown that using a thin dielectric layer can adjust the dielectric response of a surface and, therefore, the operating frequency for achieving specific photonic excitations. Here, we show that a surface’s optical properties can be tuned via the deposition/transference of ultra-thin layered van der Waals (vdW) crystals, the thicknesses of which can easily be adjusted to provide the desired response. In particular, we experimentally and theoretically show that the surface phonon resonance of a silica surface can be tuned by ∼50 cm⁻¹ through the simple deposition of nanometer-thick exfoliated flakes of black phosphorus. The surface properties were probed by infrared nanospectroscopy, and results show a close agreement with the theory. The black phosphorus-silica layered structure effectively acts as a surface with a tunable effective dielectric constant that presents an infrared response dependent on the black phosphorus thickness. In contrast, with a lower dielectric constant, hexagonal boron nitride does not significantly tune the silica surface phonon polariton. Our approach also applies to epsilon near-zero surfaces, as theoretically shown, and to polaritonic surfaces operating at other optical ranges.
... Surprisingly, we find that Bi 2 O 2 Se has a huge inplane relative static dielectric constant of 0,xx = 195.5. This value is more than an order of magnitude higher than other layered semiconductors such as MoS 2 [24], InSe [25], and black phosphorus [26], as illustrated in Fig. 3a. The value of 0 in the out-of-plane direction, 0,zz = 117.5, is also significant. ...
We discover that, in the layered semiconductor Bi$_2$O$_2$Se, an incipient ferroelectric transition endows the material a surprisingly large dielectric permittivity, providing it with a robust protection against mobility degradation by extrinsic Coulomb scattering. Based on state-of-the-art first-principles calculations, we show that the low-temperature electron mobility of Bi$_2$O$_2$Se, taking into account both electron-phonon and ionized impurity scattering, can reach an unprecedented level of $10^5$ to $10^7$ cm$^2$V$^{-1}$s$^{-1}$ over a wide range of realistic doping levels. Moreover, a small elastic strain of 1.7% can drive Bi$_2$O$_2$Se toward the ferroelectric phase transition, which further induces a giant increase in the permittivity, enabling the strain-tuning of carrier mobility by orders of magnitude. These results open a new avenue for the discovery of high-mobility layered semiconductors via phase and dielectric engineering.
... The impact of electric field on electronic characteristics of graphene, germanene, silicene, TMDs and black phosphorus have been studied earlier in Refs. [67][68][69][70][71][72] . For electrostatically controlled and potassium doped black-P, GSE has been experimentally observed in ...
In 2004, graphene was exfoliated, for the �first time, from its bulk counterpart graphite.
Although, graphene has excellent electron mobility and thermal transport properties, but
it has zero bandgap. The zero bandgap of graphene, makes it less suitable for semiconductor applications. Hence, the semiconductor and material scientists started exploring new 2D materials, with better electronic properties. After graphene, a number of 2D materials such as, germanene, silicene, arsenene, 2D allotropes of phosphorus (e.g. black phosphorene, blue phosphorene, etc.), TMDs (Transition Metal Di-chalcogenides), and many other materials have been reported.
2D layer consisting of phosphorus atoms is known as phosphorene. Similar to graphene,
phosphorene is also governed by Van-der Waals forces. In case of phosphorene, the atoms are sp3 hybridized and, hence not in plane whereas, in graphene all carbon atoms are in the same plane. Out of all 2D allotropes of phosphorus, black phosphorene (BP) and blue phosphorene (BlP) are most important materials, due to their tunable electronic
properties. For black phosphorene, a number of experimental and computational studies
have been reported. However, for blue phosphorene, very little research literature exists.
Hence, we have carried out further exploration of the blue phosphorene properties.
The stability of graphene is due to the presence of ripples, as according to Marmin-
Wagner, any long range at 2D crystal can't be stable. Hence, it is necessary to examine the impact of ripples on properties of the materials, that can be changed by applying
strain and external electric fi�eld. Further, rotation of layers with respect to each other
while stacking them, can provide very interesting properties, such as observation of superconductivity in graphene for a set of magic angles. Presence of at bands near valence band edge (known as Van-Hove singularities), shows the possibility of magnetism in the material. Additionally, as both the �-P and silicene have similar buckled honeycomb crystal structure, hence, some new allotropes of BlP and Si with same crystal symmetry can possibly exist.
In the light of above-mentioned 2D material properties, we carried out the research
on the following topics for the BlP in this thesis:
• The impact of ripples on the electronic properties of the BlP and the e�ect of external
vertical electric fi�eld (Giant Stark E�ect), on rippled BlP monolayers.
• The magnetism and band structure engineering in the rotated bi-layers (Moire superlattices) of blue phosphorene (�-P) and grey arsenene (�-As).
• The electronic properties of new 2D materials, made with BlP and Si.
... Accounting for this difference is significant for accurate model predictions of wetting properties of graphene on the one hand, or related dielectric materials like e.g. boron-nitride,61 phosphorene,75 or saturated derivatives of graphene on the other. The self-consistent atomic polarization model of ref.39 can also describe induction effects in the latter class of 2-dimensional materials. ...
Wetting experiments show pure graphene to be weakly hydrophilic, but its contact angle (CA) also reflects the character of the supporting material. Measurements and Molecular Dynamics simulations on suspended and supported graphene often reveal a CA reduction due to the presence of the supporting substrate. A similar reduction is consistently observed when graphene is wetted from both sides. The effect has been attributed to transparency to molecular interactions across the graphene sheet, however, the possibility of substrate-induced graphene polarization has also been considered. Computer simulations of CA on graphene have so far been determined by ignoring the material’s conducting properties. We improve the graphene model by incorporating its conductivity according to the Constant Applied Potential Molecular Dynamics. Using this method, we compare the wettabilities of suspended graphene and graphene supported by water by measuring the CA of cylindrical water drops on the sheets. The inclusion of graphene conductivity and concomitant polarization effects lead to a lower CA on suspended graphene but the CA reduction is significantly bigger when the sheets are also wetted from the opposite side. The stronger adhesion is accompanied by a profound change in the correlations among water molecules across the sheet. While partial charges on water molecules interacting across an insulator sheet attract charges of the opposite sign, apparent attraction among like charges is manifested across the conducting graphene. The change is associated with graphene polarization, as the image charges inside the conductor attract equally signed partial charges of water molecules on both sides of the sheet. Additionally, by using a non-polar liquid (diiodomethane), we affirm a detectable wetting translucency when liquid-liquid forces are dominated by dispersive interactions. Our findings are important for predictive modeling toward a variety of applications including sensors, fuel cell membranes, water filtration, and graphene-based electrode materials in high-performance supercapacitors.
... [1] Due to its unique electrical properties, such as high carrier mobility of 1000 cm 2 ·V −1 ·s −1 and switching ratio of 10 4 , [2,3] BP will become a candidate for a channel semiconductor material that overcomes the shortcomings of graphene with zero bandgap and transition metal dichalcogenides (TMDs) with low mobility. [4,5] Similar to the related 2D materials, the electrical properties of BP can be modulated by means of strain, [6] electric field, [7] doping, [8] and construction of heterojunctions. [9,10] In particular, its strongly anisotropic features have great potential applications in optoelectronic and semiconductor devices. ...
We investigate the electronic and transport properties of one-dimensional armchair phosphorene nanoribbons (APNRs) containing atomic vacancies with different distributions and concentrations using ab initio density functional calculations. It is found that the atomic vacancies are easier to form and detain at the edge region rather than a random distribution through analyzing formation energy and diffusion barrier. The highly local defect states are generated at the vicinity of the Fermi level, and emerge a deep-to-shallow transformation as the width increases after introducing vacancies in APNRs. Moreover, the electrical transport of APNRs with vacancies is enhanced compared to that of the perfect counterparts. Our results provide a theoretical guidance for the further research and applications of PNRs through defect engineering.
... It is widely accepted that the PBE exchange correlation, tends to underestimate the bangap. [19][20][21] Indeed, changing the choice of E g yields different regression relation with 1/↵ k 2D , as shown in Figure 14. We see that due to the underestimation of PBE bandgap, the slope of linear regression is larger than that from HSE-bandgap. ...
The dielectric constant, which defines the polarization of the media, is a key quantity in condensed matter. It determines several electronic and optoelectronic properties important for a plethora of modern technologies from computer memory to field effect transistors and communication circuits. Moreover, the importance of the dielectric constant in describing electromagnetic interactions through screening plays a critical role in understanding fundamental molecular interactions. Here we show that despite its fundamental transcendence, the dielectric constant does not define unequivocally the dielectric properties of two-dimensional (2D) materials due to the locality of their electrostatic screening. Instead, the electronic polarizability correctly captures the dielectric nature of a 2D material which is united to other physical quantities in an atomically thin layer. We reveal a long-sought universal formalism where electronic, geometrical and dielectric properties are intrinsically correlated through the polarizability opening the door to probe quantities yet not directly measurable including the real covalent thickness of a layer. We unify the concept of dielectric properties in any material dimension finding a global dielectric anisotropy index defining their controllability through dimensionality.
... is the cavity dielectric constant for monolayer BP system [77]. Next we apply the lowest cavity mode, which is quasi-resonant to the considered cyclotron LL transition, with ...
In modern physics, the investigation of the interaction between light and matter is important from both a fundamental and an applied point of view. Cavity quantum electrodynamics (cavity QED) is the study of the interaction between light confined in a reflective cavity and atoms or other particles where the quantum nature of light photons is significant. The strong interaction between an exciton and cavity photon in a high-finesse microcavity can induce a hybrid light-matter eigenstate which is usually named as polariton in solid-state systems. This strong light-matter interaction can be achieved when this interaction is larger than all broadenings caused by other various factors e.g. electron phonon scattering and cavity loss. The polariton is now stimulating tremendous research interests due to its high potential in cavity quantum electrodynamics (QED) and the achievement of polaritonic devices. Moreover, when the interaction strength between an excitation and the cavity photon, quantified by vacuum Rabi frequency, becomes comparable to or larger than the corresponding electronic transition frequency in a cavity, the system can enter an ultrastrong coupling regime, which has been experimentally observed. In this regime, the standard rotating-wave approximation is no longer valid and the antiresonant term of the interaction Hamiltonian starts to play an important role, giving rise to exciting effects in cavity QED.
The Aharonov-Bohm (AB) effect is a fundamental quantum phenomenon that bears the significance of the nature of electromagnetic fields and potentials. Besides its fundamental significance in quantum theory, its importance for applications in interferometric devices is omnipresent. Recently, since the 2D materials have triggered immense interest, some work has been done to integrate the AB effect with the electronic and transport properties of 2D materials.
This thesis consists of two parts. In the first part, the light-matter coupling between cyclotron transition and photon is theoretically investigated in some 2-D materials such as the monolayer MoS<sub>2</sub>, graphene and monolayer black phosphorene (BP) systems. The results show that, in these 2-D materials, the ultrastrong light-matter coupling can be achieved at a high filling factor of Landau levels. Furthermore, we show that, in contrast to the case for conventional semiconductor resonators, the MoS<sub>2</sub> system shows a vacuum instability. In monolayer MoS<sub>2 </sub>resonator, the diamagnetic term can still play an important role in determining magnetopolariton dispersion which is different from monolayer graphene system. The diamagnetic term arises from electron-hole asymmetry which indicates that electron-hole asymmetry can influence the quantum phase transition. Meanwhile, we show that, similar with some other 2D materials such as graphene and MoS2, the monolayer BP system shows a vacuum instability. However, in contrast with other 2D materials, the BP system displays a large energy gap between three branches of polaritons because of its strong anisotropic behavior in the eigenstates of the band structures. For the
graphene system, we investigate the coupling of cyclotron transition and a multimode cavity described by a multimode Dicke model. This model exhibits a superradiant quantum phase transition, which we describe exactly in an effective Hamiltonian approach. The complete excitation spectrum in both the normal phase and superradiant phase regimes is given. At last, in contrast to the single mode case, multimode coupling of cavity photon and cyclotron transition can greatly reduce the critical vacuum Rabi frequency required for quantum phase transition, and dramatically enhance the superradiant emission by fast modulating the Hamiltonian. Our study provides new insights in cavity-controlled magneto-transport in these 2-D systems, which could lead to the development of polariton-based devices. The second part is a diversion from the main content of this thesis; readers who are not interested in foundational issues of physics can skip this part. For one charged quantum particle P moving in an electromagnetic vector potential Aˆµ = ( φˆ, - A ˆ ) created by some other charged particles, we can either use the framework of one particle quantum mechanics (OPQM) to calculate the evolutions of P, or we can treat this as an multi-particles problem in the framework of quantum field theory and calculate the evolution of P. These two methods need to be equivalent, i.e., they produce the same result for the evolution of P. One open question is how to describe the evolution of P within the framework of quantum field theory and show that these two methods yield the same result? In chapter 5, we are going to derive the OPQM from the quantum field theory, i.e., the quantum electrodynamics (QED) to be specific. We start with the discussions on the AB effect then raise a plausible interpretation within the QED framework. We provide a quantum treatment of the source of the electromagnetic potential and argue that the underlying mechanism in AB effect can be viewed as interactions between electrons described by QED theory where the interactions are mediated by virtual photons. On further analysis, we show that the framework of one particle quantum mechanics (OPQM) can be given, in general, as a mathematically approximated model which is reformulated from QED theory while the AB effect scheme provides a platform for our derivations. In addition, the classical Maxwell equations are derived from QED scattering process while both classical electromagnetic fields and potentials serve as mathematical tools that are constructed to approximate the interactions among elementary particles described by QED physics. This work opens up a new perspective on the nature of electromagnetic fields and potentials.
... By solving the Poisson equation d 2 V s (z)/dz 2 = e 2 ρ(z)/( 0 κ), the substrateinduced potential V s (z) can be obtained. Here κ is the dielectric constant of few-layer phosphorene which we take κ = 6 for 7-layer phosphorene, which is close to the values obtained by DFT calculations [24]. The calculation results are shown in Fig. 7. ...
Electro-optical modulators, which use an electric voltage (or an electric field) to modulate a beam of light, are essential elements in present-day telecommunication devices. Using a self-consistent tight-binding approach combined with the standard Kubo formula, we show that the optical conductivity and the linear dichroism of few-layer phosphorene can be modulated by a perpendicular electric field. We find that the field-induced charge screening plays a significant role in modulating the optical conductivity and the linear dichroism. Distinct absorption peaks are induced in the conductivity spectrum due to the strong quantum confinement along the out-of-plane direction and to the field-induced forbidden-to-allowed transitions. The field modulation of the linear dichroism becomes more pronounced with increasing number of phosphorene layers. We also show that the Faraday rotation is present in few-layer phosphorene even in the absence of an external magnetic field. This optical Hall effect is induced by the reduced lattice symmetry of few-layer phosphorene. The Faraday rotation is greatly influenced by the field-induced charge screening and is strongly dependent on the strength of perpendicular electric field and on the number of phosphorene layers.
... By solving the Poisson equation d 2 V s (z)/dz 2 = e 2 ρ(z)/( 0 κ), the substrateinduced potential V s (z) can be obtained. Here κ is the dielectric constant of few-layer phosphorene which we take κ = 6 for seven-layer phosphorene, which is close to the values obtained by DFT calculations [24]. The calculation results are shown in figure 7. ...
Electro-optical modulators, which use an electric voltage (or an electric field) to modulate a beam of light, are essential elements in present-day telecommunication devices. Using a self-consistent tight-binding approach combined with the standard Kubo formula, we show that the optical conductivity and the linear dichroism of few-layer phosphorene can be modulated by a perpendicular electric field. We find that the field-induced charge screening plays a significant role in modulating the optical conductivity and the linear dichroism. Distinct absorption peaks are induced in the conductivity spectrum due to the strong quantum confinement along the out-of-plane direction and to the field-induced forbidden-to-allowed transitions. The field modulation of the linear dichroism becomes more pronounced with increasing number of phosphorene layers. We also show that the Faraday rotation is present in few-layer phosphorene even in the absence of an external magnetic field. This optical Hall effect is induced by the reduced lattice symmetry of few-layer phosphorene. The Faraday rotation is greatly influenced by the field-induced charge screening and is strongly dependent on the strength of perpendicular electric field and on the number of phosphorene layers.
In this study, using the tight-binding model and Green's function technique, we investigate potential electronic phase transitions in bilayer P6mmm borophene under the influence of external stimuli, including a perpendicular...
Inorganic molecular crystal films, particularly α-Sb 2 O 3 , emerge as promising van der Waals (vdW) dielectrics for the large-scale integration of two-dimensional (2D) semiconductors in field-effect transistors (FETs) [ Nat . Electron . 4, 906...
Pseudo-ferroelectric transistors have attracted particular interest owing to their applications in the non-volatile memories and neuromorphic circuits; however, it remains to be explored in the limit of few-layer devices. Here we reveal a pseudo-ferroelectric phenomenon in the ultrathin graphene/black phosphorene (G/BP) heterostructure by first-principles calculations. Putting forward an excitation-assisted mechanism, the ferroelectric-like hysteresis loop can be explained by a combined effect of the external electric fields dependent bipolarity and anisotropy in the G/BP heterostructure. Considering the build-in electric field, the bipolar behavior results in the multistate effect of the G/BP heterostructure when modulating the applied electric field. The anisotropic hybridization caused by the susceptible Dirac electrons in graphene and the large in-plane anisotropy in BP provides the interfacial states, which trap excitations and stabilize the multistate. The pseudo-ferroelectric behavior should be useful for interpreting transport experiments in gated G/BP devices and exploring its applications in memories or synaptic devices.
The dielectric screening plays a critical role in determining the fundamental electronic properties in semiconductor devices. In this work, we report a noncontact and spatially resolved method, based on Kelvin probe force microscopy (KPFM), to obtain the inherent dielectric screening of black phosphorus (BP) and violet phosphorus (VP) as a function of the thickness. Interestingly, the dielectric constant of VP and BP flakes increases monotonically and then saturates to the bulk value, which is consistent with our first-principles calculations. The dielectric screening in VP has a much weaker dependence on the number of layers. This could be ascribed to a strong electron orbital overlap between two adjacent layers of VP, resulting in a strong interlayer coupling. The findings of our work are significant both for fundamental studies of dielectric screening and for more technical applications in nanoelectronic devices based on layered 2D materials.
The dielectric properties in semiconductor quantum dots are crucial for exciton formation, migration and recombination. Different from 3D bulk materials, the dielectric response is however ambiguous for the small-sized 0D dots in which the effect of outer atoms on the inner atoms is usually described qualitatively. Based on the first-principles calculated electron density, the polarizability of the core-shell CdSe@ZnS wurtzite quantum dots is decomposed into the distributional contributions among which the dipole polarizability of the core is proposed to measure the shell effect on the dielectric properties of core-shell quantum dots. The shell thickness dependence on the shell effect is then studied, which is significant for the outermost shell, but decays rapidly in the additional shells. Moreover, this model gives explicit physical origins of the core dipole polarizability in the core-shell QDs, which is determined by the intra-shell polarization and inter-core-shell charge transfer. Our study proposes a new approach for studying the dielectric properties of core-shell quantum dots, which is effective and extendable for other low-dimensional structures.
Flexible optoelectronics have attracted much attention in recent years for their potential applications in healthcare and wearable devices. Narrow bandgap (NBG) semiconductor nanomembranes (NMs) are promising candidates for flexible near-infrared...
Black phosphorus (BP) has attracted significant attention owing to its unique structure and preeminent photoelectric properties, which can be utilized to create novel junctions. Based on different BP-based junctions, versatile optoelectronic devices have been fabricated and investigated in recent years, providing a fertile library for the characteristics of BP-based junctions and their optoelectronic applications. This review summarizes diverse BP-based junctions and their optoelectronic device applications. We firstly introduce the structure and properties of BP. Then, we emphatically describe the formation, properties, and optoelectronic device applications of the BP-based junctions including heterojunctions of BP and other two-dimensional (2D) semiconductors, BP p—n homojunctions, and BP/metal Schottky junctions. Finally, the challenge and prospect of the development and application of BP-based junctions are discussed. This timely review gives a snapshot of recent research breakthroughs in BP-based junctions and optoelectronic devices based on them, which is expected to provide a comprehensive vision for the potential of BP in the optoelectronic field.
Highly crystalline few-layered tungsten disulfide (WS2) nanosheets were synthesized via a cost-effective, low-temperature hydrothermal route. X-ray diffraction and HR-TEM analysis confirmed the formation of hexagonal nanosheets with thickness of ∼6-8 nm. Raman analysis and AFM results confirmed the few-layered 2H phase of WS2 nanosheets. The UV-vis study shows absorption peaks at 219 and 271 nm with large band gap value of ∼3.12 eV for WS2 nanosheets. Surprisingly, WS2 nanosheets show a dielectric constant of approximately ε' ≈ 5245, whereas bulk WS2 material exhibits a dielectric constant of 7482373. An almost 1426-fold decrease in the value of dielectric constant for the WS2 nanosheet is observed. Such an extreme reduction in dielectric constant and observance of large band gap in WS2 nanosheet were observed for the first time. The present study reveals the excellent and unusual optical and dielectric properties for their potential application in optoelectronic, dielectric, solar, phosphor, and various nanoelectronic devices.
The prediction of the dielectric response in 2D metal–semiconductor junctions (MSJs) is challenging since the screening is inhomogeneous. Herein, a generalized model is proposed to uncover the relationship between interfacial electrostatic screening and the modulation of Schottky barrier height (ΦSB) in 2D MSJs. This model is developed based on the effective dielectric constant, interfacial distance, and van der Waals gap that sheds light on the profound difference between dielectric screening in 2D and conventional MSJs. This model can predict the variation of ΦSB for a series of 2D MSJs. Combining thermionic field emission theory with the model, several compatible 2D metals are provided for low‐dimensional electronics, among which the α‐graphyne‐based junction exhibits the largest on/off ratio.
Two-dimensional van der Waals heterostructures (vdWHs) based on transition metal dichalcogenides and gallium monochalcogenides have attracted widely attention for their distinctive physicochemical properties. Here, the GaS/MoTe2 vdWHs are constructed and their electronic structures, transport behaviors and optical properties are investigated via the first-principles calculations. The results demonstrated that the GaS/MoTe2 vdWHs are type-I semiconductors with direct bandgaps of 1.05 eV. The heterostructures have flexible tunability, compression strain and negative external electric field (Efield) can induce the conversion of type-I GaS/MoTe2 to type-II. The semiconductor-metal transition can be achieved under the control of strain and Efield. Current-voltage curves display that the current magnitude can reach the order of μA. Additionally, the absorption coefficients (∼10⁵ cm-1) and adsorption ranges of the heterostructures are far greater than GaS and MoTe2 monolayers. Especially, the absorption intensity of GaS is significantly enhanced in the visible-light region. The work provides a significant theoretical guidance for the next generation optoelectronic materials, nanodevices applications and the design of GaS/MoTe2 vdWHs.
In this paper, a model of Si atom adsorbed on black phosphorene with a coverage of 2.778% is constructed and the electronic properties of the model are calculated based on density functional theory. Moreover, the electronic properties are regulated by stress and electric field. Under the coverage of the current research, the results show that the adsorption of Si atoms results in the destruction of the black phosphorene’s geometric symmetry, which intensifies the charge transfer in the system and completes the orbital re-hybrid. The band gap of black phosphorene thus disappears and the transition from semiconductor to quasi metal is completed. The stable adsorption is at the H site in the middle of the P atomic ring. Both tensile field and electric field reduce the stability of the system. Owing to the tensile deformation, the band gap is opened by the structure of Si atom adsorbed on black phosphorene. And since the band gap is proportional to the deformation variable, it can be regulated and controlled. Under the combined action of electric field and tensile, the introduction of the electric field leads the band gap of Si adsorbed on black phosphorene system to be narrowed and the transition from the direct band gap to an indirect one to be completed. The band gap still goes up in proportion to the increase of deformation. The band gap of Si atom adsorbed on black phosphorene system is more adjustable than that of the Si atom that is not adsorbed on black phosphorene system, and the stable adjustment of the band gap is more likely to be realized.
Two-dimensional (2D) materials offer novel platforms to meet the increasing demands of next-generation miniaturized electronics. Among them, the recently emerged 2D Bi2O2Se with unique non-van der Waals interlayer interaction, high mobility, sizeable bandgap, and capability to fabricate homologous heterojunction, is of particular interest. In this Review, we introduce recent progress in preparation, transfer, mechanical and electrical properties, and electronic applications of 2D Bi2O2Se. First, we summarize methodologies to synthesize and massively produce 2D Bi2O2Se, as well as recent advances in transferring them from growth substrate to arbitrary substrates. Then, we review current understandings on the intrinsic mechanical properties of Bi2O2Se at 2D thickness limit, and its in-plane and out-of-plane electrical properties. Electronic devices including field-effect transistors, memristors, and sensors based on 2D Bi2O2Se for neuromorphic computing, memory, logic and integrated circuits are discussed. Finally, challenges and prospects for the development of 2D Bi2O2Se are proposed.
The two-dimensional (2D) materials, represented by graphene, stand out in the electrical industry applications of the future and have been widely studied. As commonly existing in electronic devices, the electric field has been extensively utilized to modulate the performance. However, how the electric field regulates thermal transport is rarely studied. Herein, we investigate the modulation of thermal transport properties by applying an external electric field ranging from 0 to 0.4 V Å-1, with bilayer graphene, monolayer silicene, and germanene as study cases. The monotonically decreasing trend of thermal conductivity in all three materials is revealed. A significant effect on the scattering rate is found to be responsible for the decreased thermal conductivity driven by the electric field. Further evidence shows that the reconstruction of internal electric field and generation of induced charges lead to increased scattering rate from strong phonon anharmonicity. Thus, the ultralow thermal conductivity emerges with the application of external electric fields. Applying an external electric field to regulate thermal conductivity illustrates a constructive idea for highly efficient thermal management.
Two-dimensional (2D) layered materials as a new class of nanomaterial are characterized by a list of exotic properties. These layered materials are investigated widely in several biomedical applications. A comprehensive understanding of the state-of-the-art developments of 2D materials designed for multiple nanoplatforms will aid researchers in various fields to broaden the scope of biomedical applications. Here, we review the advances in 2D material-based biomedical applications. First, we introduce the classification and properties of 2D materials. Next, we summarize surface and structural engineering methods of 2D materials where we discuss surface functionalization, defect, and strain engineering, and creating heterostructures based on layered materials for biomedical applications. After that, we discuss different biomedical applications. Then, we briefly introduced the emerging role of machine learning (ML) as a technological advancement to boost biomedical platforms. Finally, the current challenges, opportunities, and prospects on 2D materials in biomedical applications are discussed.
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We study direct and indirect excitons in Rydberg states in phosphorene monolayers, bilayers, and van der Waals (vdW) heterostructure in an external magnetic field within the framework of the effective-mass approximation. The magnetic field is applied perpendicular to the monolayer or heterostructure and is varied between 0 and 60 T. Binding energies of magnetoexcitons are calculated by numerical integration of the Schrödinger equation using the Rytova-Keldysh potential for direct magnetoexcitons and both the Rytova-Keldysh and Coulomb potentials for indirect magnetoexcitons. The latter aids in the understanding of the role of screening in phosphorene. We report the magnetic field energy contribution to the binding energies and diamagnetic coefficients (DMCs) for magnetoexcitons, which depend strongly on the effective anisotropic masses of electrons and holes and can be tuned by the external magnetic field. We demonstrate that the vdW phosphorene heterostructure is a novel category of two-dimensional semiconductors with magnetoexcitonic binding energies tunable by means of the external magnetic field. The binding energies and DMCs are controlled by the number of hexagonal boron nitride layers separating two phosphorene sheets. Such tunability is potentially useful for the device design.
Twist-induced moiré bands and accompanied correlated phenomena have been extensively investigated in twisted hexagonal lattices with weak interlayer coupling. However, the formation of moiré bands in strongly coupled layered materials and their controlled tuning remain largely unexplored. Here, we systematically study the moiré bands in twisted trilayer black phosphorene (TTbP) and the influences of pressure and electric field on them. Moiré states can form in various TTbPs even when the twist angle is larger than 16° similar to that of twisted bilayer bP. However, different TTbPs show different localization patterns depending on the twisting layer, leading to distinct dipolar behaviors. While these moiré states become quasi-one-dimensional (1D) as the twist angle decreases, external pressure causes the crossover of moiré states from quasi-1D to 0D with a dramatic change in localization areas and greatly reduced bandwidth. Interestingly, compared to twisted bilayer and pristine bP, TTbPs show a much larger electric-field induced Stark effect, controllable by either the twist angle or twist layer. Our work thus demonstrates TTbP as an attractive platform to explore moiré-controlled electronic and optical properties, as well as tunable optoelectronic applications.
Thermoelectric technology is very promising to the development of global sustainable energy and carbon neutrality. Understanding the thermoelectric transport, in low dimensions, may provide a potential route to achieve high thermoelectric conversion efficiency of thermoelectric materials. In the past decade, low-dimensional thermoelectric materials, including their hybrids, have gradually attracted more and more attentions due to their unique electronic structures and potentially high thermoelectric performance. They are expected to play an increasingly significant role in power generation and solid-state cooling systems. In this chapter, we briefly review recent advances in their electronic structures, thermoelectric performance, and characterization techniques.
We study direct and indirect excitons in Rydberg states in phosphorene monolayers, bilayer and van der Waals (vdW) heterostructure in an external magnetic field, applied perpendicular to the monolayer or heterostructure within the framework of the effective mass approximation. Binding energies of magnetoexcitons are calculated by a numerical integration of the Schrodinger equation using the Rytova-Keldysh potential for direct magnetoexcitons and both the Rytova-Keldysh and Coulomb potentials for indirect one. The latter allows to understand the role of screening in phosphorene. We report the magnetic field energy contribution to the binding energies and diamagnetic coefficients (DMCs) for magnetoexcitons that strongly depend on the effective mass of electron and hole and their anisotropy and can be tuned by the external magnetic field. We demonstrate theoretically that the vdW phosphorene heterostructure is a novel category of 2D semiconductor offering a tunability of the binding energies of magnetoexcitons by mean of external magnetic field and control the binding energies and DMCs by the number of hBN layers separated two phosphorene sheets. Such tunability is potentially useful for the devices design.
With the ability to alter the inherent interatomic electrostatic interactions, modulating external electric field strength is a promising approach to tune the phonon transport behavior and enhance the thermoelectric performance of two-dimensional (2D) materials. Here, by applying an electric field (Ez = 0.1 V Å-1), it is predicted that an ultralow value of the lattice thermal conductivity (0.016 W m-1 K-1) at 300 K of 2D indium selenide (InSe) is nearly three orders of magnitude lower than that under an electric field of 0 V Å-1 (27.49 W m-1 K-1). Meanwhile, we calculated the variations in the electrical conductivities, electronic thermal conductivities, Seebeck coefficients, and figure of merit (ZT) of 2D InSe along with the carrier (hole and electron doping) concentrations under some representative electric fields. Owing to the smaller total thermal conductivity along the armchair and zigzag directions, p-type doped 2D InSe at Ez = 0.1 V Å-1 exhibits a larger ZT value (∼1.6) compared to the ZT value (∼0.1) without an electric field at room temperature. The peak ZT value (∼0.53) of the n-type 2D InSe at Ez = 0.1 V Å-1 is much higher than that without an electric field (∼0.02) at the same temperature. Our results pave the way for applying an external electric field to modulate the phonon transport properties and greatly promote the thermoelectric performance of some specific 2D semiconductor materials without altering their crystal structure.
Graphene and phosphorene show a strong affinity towards DNA/RNA nucleobases, serving as promising materials to be integrated as part of bioinorganic interfaces for either self-assembly, sensing, or sequencing of DNA/RNA constituents. Here, the intermolecular driving forces determining the adsorption of DNA/RNA nucleobases and base-pairs onto graphene and phosphorene are studied with density functional theory (DFT) calculations in the gas phase and solution with a polarizable continuum model (PCM). The formed complexes are studied through binding analyses (adsorption energy, AIM, IGM), charge transfer, and energy decomposition analyses based on absolutely localized molecular orbitals (ALMO-EDA). It is found that nucleobases are adsorbed with similar stability onto graphene and phosphorene in stacked patterns. Electrostatics and dispersion effects are the primary stabilizing intermolecular forces, standing for 85% of the stabilizing energy. Dispersion is higher than electrostatic effects for nucleobase-Graphene complexes; conversely, nucleobase-Phosphorene complexes show a greater contribution from electrostatics to the stability. Moreover, solvent effects lead to energy destabilization of complexes with respect to the gas phase due to the relative difference in the solute-solvent polarity of the components, which are higher for those complexes stabilized by electrostatic forces. Consequently, the adsorption on phosphorene is more destabilized than graphene in aqueous solution; while, dispersion/electrostatic effects turn almost balanced for nucleobase-Phosphorene complexes in solution as a result of the decrease in the magnitude of electrostatic interactions. Otherwise, an extra energy lowering is reached by adsorption with phosphorene due to the high adsorbent polarizability and its response upon nucleobase adsorption; nevertheless, Pauli repulsion compensates all the stabilizing effects due to the larger electron density of the phosphorene surface compared to graphene. Finally, physical effects along the dissociation path reveal the dominant factors on the stabilization of the nucleobase-Graphene(Phosphorene) complexes during the entire adsorption process.
In this work, the geometrical structure, stability, electronic and optical properties of the GaS/AlN van der Waals heterostructure have been explored based on first principles calculations considering the effect of vertical strain, in-plane biaxial strain and the electric field. It is demonstrated that, the GaS/AlN van der Waals heterostructure possesses an intrinsic typical type-II band alignment with an indirect band gap of 1.65 eV. Due to the difference of work functions between monolayer GaS and AlN, the electrons transfer from AlN layer to GaS layer, causing a build-in electric field which facilitates the separation of free electrons and holes. The band gap value of the heterostructure is insensitive to the vertical strain, while in-plain biaxial strain is an effective way to tune the band gap. The band gap value is in the range of 0.68–1.82 eV under in-plane biaxial strain of −5%–5%. The band offsets of the heterostructure can be increased by positive electric field and decreased by negative electric field. Meanwhile, the type-II band alignment of the heterostructure is retained under vertical strain, in-plane biaxial strain and the electric field. In addition, for the heterostructure, compare to constituent layers, the optical absorption is enhanced in visible region. These results render GaS/AlN heterostructure as a good candidate for photovoltaic devices.
Phosphorene is one of the most important 2D materials, which was exfoliated from bulk black phosphorus in 2014. This 2D material features the combined properties of large band gap, high carrier mobility, and strong in-plane anisotropy, which make it well suited for future electronic and optoelectronic applications. The electronic, optical and transport properties of phosphorene tuned by gating, strain, and disorder effects are presented in this chapter. To this end, tight-binding approach, linear Kubo formula, and scattering matrix method are employed.
With the rapid development and improvement of the state of the art of modern equipment and advanced methods both in synthesis and characterization, scientists have demonstrated great ability and techniques in tuning the geometric profiles and physical properties of low‐dimensional materials to investigate and describe the desired functions and applications in both materials and physical areas. Among the various types of control measures, size effect, strain engineering, and electric field modulation have been extensively adopted especially in the field of 2D materials because of their distinct nature of great convenience, easy accessibility, and high efficiency. In this chapter, the modulation capability of size effect, strain engineering, and electric field on the electronic properties of 2D materials have been reviewed in detail.
Broadband light absorbers are highly desirable in various applications including solar-energy harvesting, thermo-photovoltaics, and photon detection. Fabry-Perot (F-P) cavity comprising metal-insulator-metal (MIM) layers has attracted enormous interest as a lithography-free structure for realizing planar super absorbers. However, typical F-P cavity exhibits a narrow absorption band, and efforts have thus been made to increase the absorption bandwidth. This study demonstrates that near-perfect absorption over a broad spectral range can be obtained from the MIM structure by using thermally evaporated Ag and Au thin films whose dielectric and optical properties are much different from bulk-state properties owing to their nanoscale features. A 55-nm-thick SiO2 spacer sandwiched between a 10-nm Ag top layer and a 100-nm Al back reflector exhibits absorption > 95% in the visible range of 400-700 nm. The broad absorption band shifts to a near-infrared range of 650-1000 nm by replacing the top layer with a 10-nm-thick Au film and increasing the SiO2 spacer thickness to 115 nm. The experimental results are supported by finite-difference time-domain simulation. The large absorption bandwidth is attributed to the lossy nature of the nanostructured top metallic layer combined with the resonant absorption of the MIM cavity.
First-principle calculations were employed to analyze the effects induced by vacancies of molybdenum (Mo) and sulfur (S) on the dielectric properties of few-layered MoS2. We explored the combined effects of vacancies and dipole interactions on the dielectric properties of few-layered MoS2. In the presence of dielectric screening, we investigated uniformly distributed Mo and S vacancies, and then considered the case of concentrated vacancies. Our results show that the dielectric screening remarkably depends on the distribution of vacancies owing to the polarization induced by the vacancies and on the interlayer distances. This conclusion was validated for a wide range of wide-gap semiconductors with different positions and distributions of vacancies, providing an effective and reliable method for calculating and predicting electrostatic screening of dimensionally reduced materials. We further provided a method for engineering the dielectric constant by changing the interlayer distance, tuning the number of vacancies and the distribution of vacancies in few-layered van der Waals materials for their application in nanodevices and supercapacitors.
Acquiring how the performance depend on structure is the most pivotal steps of material design, preparation and application. Particularly, it is extremely significant to figure out the correlation between structure and property for two-dimensional materials possessed abundant magical features due to their unique layered stacking. Here, we first reported a conceptually theoretical method to define the boundary between intralayer and interlayer of layered structures based on total electron density distribution. According to the concept, two-dimensional structures binding by the van der Waals force could be divided into layer thickness and interlayer interaction zones. Using 2D semiconductor hexagonal boron nitride (h-BN) and molybdenum disulfide (MoS2) bilayers as model systems, we successfully applied the demarcation method into revealing the intrinsic relationship between bandgap fluctuation and potential energy surface (PES) landscape induced by stacking configuration. The presented theoretical method enables the study of not only the correlation, depended on electronic redistribution, between PES and bandgap in h-BN and MoS2 but also other analogous physical issue, such as the microcontact, the sliding between surface/interface and the properties (heat conduction) depend on thickness of 2D atomic layer.
2D materials strongly drive the development of micro–nano devices, and patterned structures based on such crystals bring new opportunities. The advanced fabrication techniques of patterned 2D materials and the analysis of their electronic structures, and physical properties to provide access to diverse applications are discussed. Special attention is given to the hotspot electromagnetic functions and devices based on patterned 2D materials, including photodetectors, optoelectronic switches, modulators, polarization converters, gratings, as well as electromagnetic wave attenuation devices. Finally, a systematical outlook on the development of patterned 2D materials in micro–nano devices is presented, pointing out the current problems and exploring the most promising directions in the future.
The striking in-plane anisotropy remains one of the most intriguing properties for the newly rediscovered black phosphorus (BP) two-dimensional (2D) crystals. However, due to its rather low energy band gap, the optical anisotropy of few-layer BP has been primarily investigated in the near-infrared (NIR) regime. Moreover, the essential physics that determines the intrinsic anisotropic optical properties of few-layer BP, which is of great importance for practical applications in optical and optoelectronic devices, is still in the fancy of theory. Herein, we report the direct observation of the optical anisotropy of few-layer BP in the visible regime simply by using polarized optical microscopy. Based on the Fresnel equation, the intrinsic anisotropic complex refractive indices (n-iκ) in the visible regime (480 nm-650 nm) were experimentally obtained for the first time using the anisotropic optical contrast spectra. Our findings not only provide a convenient approach to measure the optical constants of 2D layered materials, but also suggest a possibility to design novel BP-based photonic devices, such as atomic-thick light modulator, including linear polarizer, phase plate and optical compensator in a broad spectral range extending to the visible window.
We systematically explore chemical functionalization of monolayer black
phosphorene via chemisorption of oxygen and fluorine atoms. Using the cluster
expansion technique, with vary- ing concentration of the adsorbate, we
determine the ground states considering both single- as well as double- side
chemisorption, which have novel chemical and electronic properties. The nature
of the bandgap depends on the concentration of the adsorbate: for fluorination
the direct bandgap first decreases, and then increases while becoming indirect,
with increasing fluorination, while for oxidation the bandgap first increases
and then decreases, while mostly maintaining its direct nature. Further we find
that the unique anisotropic free-carrier effective mass for both the electrons
and holes, can be changed and even rotated by 90 degrees, with controlled
chemisorption, which can be useful for exploring unusual quantum Hall effect,
and novel electronic devices based on phosphorene.
The effect of the number of stacking layers and the type of stacking on the electronic and optical properties of bilayer and trilayer black phosphorus are investigated by using first principles calculations within the framework of density functional theory. We find that inclusion of many body effects (i.e., electron-electron and electron-hole interactions) modifies strongly both the electronic and optical properties of black phosphorus. While trilayer black phosphorus with a particular stacking type is found to be a metal by using semilocal functionals, it is predicted to have an electronic band gap of 0.82 eV when many-body effects are taken into account within the G0W0 scheme. Though different stacking types result in similar energetics, the size of the band gap and the optical response of bilayer and trilayer phosphorene is very sensitive to the number of layers and the stacking type. Regardless of the number of layers and the type of stacking, bilayer and trilayer black phosphorus are direct band gap semiconductors whose band gaps vary within a range of 0.3 eV. Stacking arrangments different from the ground state structure in both bilayer and trilayer black phosphorus significantly modify valence bands along the zigzag direction and results in larger hole effective masses. The optical gap of bilayer (trilayer) black phosphorus varies by 0.4 (0.6) eV when changing the stacking type. Due to strong interlayer interaction, some stackings obstruct the observation of the optical excitation of bound excitons within the quasi-particle band gap. In other stackings, the binding energy of bound excitons hardly changes with the type of stacking and is found to be 0.44 (0.30) eV for bilayer (trilayer) phosphorous.
The electronic properties of two-dimensional monolayer and bilayer phosphorene subjected to uniaxial and biaxial strains have been investigated using first-principles calculations based on density functional theory. Strain engineering has obvious influence on the electronic properties of monolayer and bilayer phosphorene. By comparison, we find that biaxial strain is more effective in tuning the band gap than uniaxial strain. Interestingly, we observe the emergence of Dirac-like cones by the application of zigzag tensile strain in the monolayer and bilayer systems. For bilayer phosphorene, we induce the anisotropic Dirac-like dispersion by the application of appropriate armchair or biaxial compressive strain. Our results present very interesting possibilities for engineering the electronic properties of phosphorene and pave a way for tuning the band gap of future electronic and optoelectronic devices.
2D materials are well-known to exhibit interesting phenomena due to quantum
confinement. Here, we show that quantum confinement, together with structural
anisotropy, result in an electric-field-tunable Dirac cone in 2D black
phosphorus. Using density functional theory calculations, we find that an
electric field, E_ext, applied normal to a 2D black phosphorus thin film, can
reduce the direct band gap of few-layer black phosphorus, resulting in an
insulator-to-metal transition at a critical field, E_c. Increasing E_ext beyond
E_c can induce a Dirac cone in the system, provided the black phosphorus film
is sufficiently thin. The electric field strength can tune the position of the
Dirac cone and the Dirac-Fermi velocities, the latter being similar in
magnitude to that in graphene. We show that the Dirac cone arises from an
anisotropic interaction term between the frontier orbitals that are spatially
separated due to the applied field, on different halves of the 2D slab. When
this interaction term becomes vanishingly small for thicker films, the Dirac
cone can no longer be induced. Spin-orbit coupling can gap out the Dirac cone
at certain electric fields; however, a further increase in field strength
reduces the spin-orbit-induced gap, eventually resulting in a
topological-insulator-to-Dirac-semi-metal transition.
Using hybrid density functional theory combined with a semiempirical van der Waals dispersion correction, we have investigated the structural and electronic properties of vacancies and self-interstitials in defective few-layer phosphorene. We find that both a vacancy and a self-interstitial defect are more stable in the outer layer than in the inner layer. The formation energy and transition energy of both a vacancy and a self-interstitial P defect decrease with increasing film thickness, mainly due to the upward shift of the host valence band maximum in reference to the vacuum level. Consequently, both vacancies and self-interstitials could act as shallow acceptors, and this well explains the experimentally observed p-type conductivity in few-layer phosphorene. On the other hand, since these native point defects have moderate formation energies and are stable in negatively charged states, they could also serve as electron compensating centers in n-type few-layer phosphorene.
Motivated by recent interest in various 2D crystals, we investigate the
possibility of band structure engineering in the recently predicted blue
phosphorous via a transverse electric field, using density functional theory
based calculations. We consider both the monolayer and three differently
stacked bilayer structures of blue phosphorous in presence of a transverse
electric field and find that the default indirect bandgap becomes comparable to
the direct band gap at the {\Gamma} point with increasing electric field (Ez >
0.4 V/A). Additionally, we also calculate the electron and hole effective
masses along various symmetry directions in the reciprocal lattice. Our study
may be useful to explore and optimize the potential application of monolayer
and bilayer blue phosphorous in nanoelectronic and nanophotonic devices.
Semi-metallic graphene and semiconducting monolayer transition metal
dichalcogenides (TMDCs) are the two-dimensional (2D) materials most intensively
studied in recent years. Recently, black phosphorus emerged as a promising new
2D material due to its widely tunable and direct bandgap, high carrier mobility
and remarkable in-plane anisotropic electrical, optical and phonon properties.
However, current progress is primarily limited to its thin-film form, and its
unique properties at the truly 2D quantum confinement have yet to be
demonstrated. Here, we reveal highly anisotropic and tightly bound excitons in
monolayer black phosphorus using polarization-resolved photoluminescence
measurements at room temperature. We show that regardless of the excitation
laser polarization, the emitted light from the monolayer is linearly polarized
along the light effective mass direction and centers around 1.3 eV, a clear
signature of emission from highly anisotropic bright excitons. In addition,
photoluminescence excitation spectroscopy suggests a quasiparticle bandgap of
2.2 eV, from which we estimate an exciton binding energy of around 0.9 eV,
consistent with theoretical results based on first-principles. The experimental
observation of highly anisotropic, bright excitons with exceedingly large
binding energy not only opens avenues for the future explorations of
many-electron effects in this unusual 2D material, but also suggests a
promising future in optoelectronic devices such as on-chip infrared light
sources.
Using first principles calculations we showed that the electronic and optical
properties of single layer black phosphorus (BP) depend strongly on the applied
strain. Due to the strong anisotropic atomic structure of BP, its electronic
conductivity and optical response are sensitive to the magnitude and the
orientation of the applied strain. We found that the inclusion of many body
effects is essential for the correct description of the electronic properties
of monolayer BP; for example while the electronic gap of strainless BP is found
to be 0.90 eV by using semilocal functionals, it becomes 2.31 eV when many-body
effects are taken into account within the G0W0 scheme. Applied tensile strain
was shown to significantly enhances electron transport along zigzag direction
of BP. Furthermore, biaxial strain is able to tune the optical band gap of
monolayer BP from 0.38 eV (at -8% strain) to 2.07 eV (at 5.5%). The exciton
binding energy is also sensitive to the magnitude of the applied strain. It is
found to be 0.40 eV for compressive biaxial strain of -8%, and it becomes 0.83
eV for tensile strain of 4%. Our calculations demonstrate that the optical
response of BP can be significantly tuned using strain engineering which
appears as a promising way to design novel photovoltaic devices that capture a
broad range of solar spectrum.
Graphene and transition metal dichalcogenides (TMDCs) are the two major types of layered materials under intensive investigation. However, the zero-bandgap nature of graphene and the relatively low mobility in TMDCs limit their applications. Here we reintroduce black phosphorus (BP), the most stable allotrope of phosphorus with strong intrinsic in-plane anisotropy, to the layered-material family. For 15-nm-thick BP, we measure a Hall mobility of 1,000 and 600 cm(2 )V(-1 )s(-1) for holes along the light (x) and heavy (y) effective mass directions at 120 K. BP thin films also exhibit large and anisotropic in-plane optical conductivity from 2 to 5 μm. Field-effect transistors using 5 nm BP along x direction exhibit an on-off current ratio exceeding 10(5), a field-effect mobility of 205 cm(2 )V(-1 )s(-1), and good current saturation characteristics all at room temperature. BP shows great potential for thin-film electronics, infrared optoelectronics and novel devices in which anisotropic properties are desirable.
Two-dimensional crystals are emerging materials for nanoelectronics. Development of the field requires candidate systems with both a high carrier mobility and, in contrast to graphene, a sufficiently large electronic bandgap. Here we present a detailed theoretical investigation of the atomic and electronic structure of few-layer black phosphorus (BP) to predict its electrical and optical properties. This system has a direct bandgap, tunable from 1.51 eV for a monolayer to 0.59 eV for a five-layer sample. We predict that the mobilities are hole-dominated, rather high and highly anisotropic. The monolayer is exceptional in having an extremely high hole mobility (of order 10,000 cm(2) V(-1) s(-1)) and anomalous elastic properties which reverse the anisotropy. Light absorption spectra indicate linear dichroism between perpendicular in-plane directions, which allows optical determination of the crystalline orientation and optical activation of the anisotropic transport properties. These results make few-layer BP a promising candidate for future electronics.
Two-dimensional crystals have emerged as a class of materials that may impact future electronic technologies. Experimentally identifying and characterizing new functional two-dimensional materials is challenging, but also potentially rewarding. Here, we fabricate field-effect transistors based on few-layer black phosphorus crystals with thickness down to a few nanometres. Reliable transistor performance is achieved at room temperature in samples thinner than 7.5 nm, with drain current modulation on the order of 10(5) and well-developed current saturation in the I-V characteristics. The charge-carrier mobility is found to be thickness-dependent, with the highest values up to ∼1,000 cm(2) V(-1) s(-1) obtained for a thickness of ∼10 nm. Our results demonstrate the potential of black phosphorus thin crystals as a new two-dimensional material for applications in nanoelectronic devices.
Use of the non-local correlation functional vdW-DF (from 'van der Waals density functional'; Dion M et al 2004 Phys. Rev. Lett. 92 246401) has become a popular approach for including van der Waals interactions within density functional theory. In this work, we extend the vdW-DF theory and derive the corresponding stress tensor in a fashion similar to the LDA and GGA approach, which allows for a straightforward implementation in any electronic structure code. We then apply our methodology to investigate the structural evolution of amino acid crystals of glycine and l-alanine under pressure up to 10 GPa-with and without van der Waals interactions-and find that for an accurate description of intermolecular interactions and phase transitions in these systems, the inclusion of van der Waals interactions is crucial. For glycine, calculations including the vdW-DF (vdW-DF-c09x) functional are found to systematically overestimate (underestimate) the crystal lattice parameters, yet the stability ordering of the different polymorphs is determined accurately, at variance with the GGA case. In the case of l-alanine, our vdW-DF results agree with recent experiments that question the phase transition reported for this crystal at 2.3 GPa, as the a and c cell parameters happen to become equal but no phase transition is observed.
QUANTUM ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). The acronym ESPRESSO stands for opEn Source Package for Research in Electronic Structure, Simulation, and Optimization. It is freely available to researchers around the world under the terms of the GNU General Public License. QUANTUM ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively parallel architectures, and a great effort being devoted to user friendliness. QUANTUM ESPRESSO is evolving towards a distribution of independent and interoperable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.
We present an ab initio analysis of polarization of multilayer graphene systems under applied electric fields. The effects of applied electric fields are calculated using a Berry phase approach within a plane-wave density functional formalism. We have determined polarizability values for graphene films and carbon nanotubes and found that the polarizability of graphene films follows a linear relationship with the number of layers. We also examined changes in the induced charge distribution as a function of graphene layers. We focus, in particular, on the bilayer graphene system. Under applied electric fields, we found the Mexican hat band structure near the K point reported by previous groups. We found that the induced charge primarily accumulated on the B sublattice sites. This observation is supported by additional calculations with a tight-binding Green’s function model. By examining the local density of states at the Fermi energy, we found a high density of states at the B sites at the Fermi energy. In contrast, coupling between A sites in neighboring graphene layers leads to negligible density of states at the Fermi level. This high density of states at the B sites results in greater induced charge under applied electric fields. This scenario of preferential induced charge on the B sublattice sites under applied electric fields could impact the stability of atoms and molecules absorbed on bilayer graphene.
The non-local van der Waals density functional (vdW-DF) of Dion et al (2004 Phys. Rev. Lett. 92 246401) is a very promising scheme for the efficient treatment of dispersion bonded systems. We show here that the accuracy of vdW-DF can be dramatically improved both for dispersion and hydrogen bonded complexes through the judicious selection of its underlying exchange functional. New and published exchange functionals are identified that deliver much better than chemical accuracy from vdW-DF for the S22 benchmark set of weakly interacting dimers and for water clusters. Improved performance for the adsorption of water on salt is also obtained.
We present an efficient implementation of the van der Waals density functional of Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)], which expresses the nonlocal correlation energy as a double spatial integral. We factorize the integration kernel and use fast Fourier transforms to evaluate the self-consistent potential, total energy, and atomic forces, in O(NlogN) operations. The resulting overhead, for medium and large systems, is a small fraction of the total computational cost, representing a dramatic speedup over the O(N(2)) evaluation of the double integral. This opens the realm of first-principles simulations to the large systems of interest in soft matter and biomolecular problems. We apply the method to calculate the binding energies and the barriers for relative translation and rotation in double-wall carbon nanotubes.
A scheme within density functional theory is proposed that provides a practical way to generalize to unrestricted geometries the method applied with some success to layered geometries [Phys. Rev. Lett. 91, 126402 (2003)]]. It includes van der Waals forces in a seamless fashion. By expansion to second order in a carefully chosen quantity contained in the long-range part of the correlation functional, the nonlocal correlations are expressed in terms of a density-density interaction formula. It contains a relatively simple parametrized kernel, with parameters determined by the local density and its gradient. The proposed functional is applied to rare gas and benzene dimers, where it is shown to give a realistic description.
We present density-functional perturbation theory for electric field perturbations and ultra-soft pseudopotentials. Applications to benzene and anthracene molecules and surfaces are reported as examples. We point out several issues concerning the evaluation of the polarizability of molecules and slabs with periodic boundary conditions.
We derive the exchange-correlation potential corresponding to the nonlocal
van der Waals density functional [M. Dion, H. Rydberg, E. Schroder, D. C.
Langreth, and B. I. Lundqvist, Phys. Rev. Lett. 92, 246401 (2004)]. We use this
potential for a self-consistent calculation of the ground state properties of a
number of van der Waals complexes as well as crystalline silicon. For the
latter, where little or no van der Waals interaction is expected, we find that
the results are mostly determined by semilocal exchange and correlation as in
standard generalized gradient approximations (GGA), with the fully nonlocal
term giving little effect. On the other hand, our results for the van der Waals
complexes show that the self-consistency has little effect at equilibrium
separations. This finding validates previous calculations with the same
functional that treated the fully nonlocal term as a post GGA perturbation. A
comparison of our results with wave-function calculations demonstrates the
usefulness of our approach. The exchange-correlation potential also allows us
to calculate Hellmann-Feynman forces, hence providing the means for efficient
geometry relaxations as well as unleashing the potential use of other standard
techniques that depend on the self-consistent charge distribution. The nature
of the van der Waals bond is discussed in terms of the self-consistent bonding
charge.
Predicting the ground states for surface adsorption is a challenging problem because the number of degrees of freedom involved in the process is very high. Most of the studies deal with some specific arrangements of adsorbates on a given surface, but very few of them actually attempt to find the ground states for different adatom coverage. In this work, we show the effectiveness of the cluster expansion method to predict the "ground states" resulting from chemisorption of oxygen and fluorine atom on the surface of monolayer black phosphorus or phosphorene. For device applications, we find that in addition to band-gap tuning, controlled chemisorption can change the unique anisotropic carrier effective mass for both the electrons and holes and even rotate them by 90, which can be useful for exploring unusual quantum Hall effect and electronic devices based on phosphorene.
Although phosphorene has attracted much attention in electronics and optoelectronics as a new type of two-dimensional material, in-depth investigations and applications have been limited by the current synthesis techniques. Herein, a basic N-methyl-2-pyrrolidone (NMP) liquid exfoliation method is described to produce phosphorene with excellent water stability, controllable size and layer number, as well as in high yield. Phosphorene samples composed of one to four layers exhibit layer-dependent Raman scattering characteristics thus providing a fast and efficient means for the in situ determination of the thickness (layer number) of phosphorene. The linear and nonlinear ultrafast absorption behavior of the as-exfoliated phosphorene is investigated systematically by UV–vis–NIR absorption and Z-scan measurements. By taking advantage of their unique nonlinear absorption, ultrashort pulse generation applicable to optical saturable absorbers is demonstrated. In addition to a unique fabrication technique, our work also reveals the large potential of phosphorene in ultrafast photonics.
An outstanding challenge of theoretical electronic structure is the
description of van der Waals (vdW) interactions in molecules and solids.
Renewed interest in resolving this is in part motivated by the technological
promise of layered systems including graphite, transition metal
dichalcogenides, and more recently, black phosphorus, in which the interlayer
interaction is widely believed to be dominated by these types of forces. We
report a series of quantum Monte Carlo (QMC) calculations for bulk black
phosphorus and related few-layer phosphorene, which elucidate the nature of the
forces that bind these systems and provide benchmark data for the energetics of
these systems. We find a significant charge redistribution due to the
interaction between electrons on adjacent layers. Comparison to density
functional theory (DFT) calculations indicate not only wide variability even
among different vdW corrected functionals, but the failure of these functionals
to capture the trend of reorganization predicted by QMC. The delicate interplay
of steric and dispersive forces between layers indicate that few-layer
phosphorene presents an unexpected challenge for the development of vdW
corrected DFT.
When performing density-functional calculations of surfaces using a plane-wave pseudopotential code, it is necessary to embed a slab with two surfaces in a periodic supercell. In many situations, it is desirable to study an asymmetric slab with a net surface dipole density. The periodic boundary conditions imposed on the electrostatic potential then give rise to an artificial electric field across the slab. We present a dipole correction that cancels the artificial field, and show how this correction can be incorporated in the density-functional theory total-energy expression. The results are supported by total-energy calculations of water-molecule layers.
The structural and electronic properties of the bulk and ultrathin black phosphorus and the effects of in-plane strain and out-of-plane electrical field on the electronic structure of phosphorene are investigated using first-principles methods. The computed results show that the bulk and few-layer black phosphorus from monolayer to six-layer demonstrates inherent direct bandgap features ranging from 0.5 to 1.6 eV. Interestingly, the band structures of the bulk and few-layer black phosphorus from X point via A point to Y point present degenerate distribution, which shows totally different partial charge dispersions. Moreover, strong anisotropy in regard to carrier effective mass has been observed along different directions. The response of phosphorene to in-plane strain is diverse. The bandgap monotonically decreases with increasing compressive strain, and semiconductor-to-metal transition occurs for phosphorene when the biaxial compressive reaches -9%. Tensile strain first enlarges the gap until the strain reaches around 4%, after which the bandgap exhibits a descending relationship with tensile strain. The bandgaps of the pristine and deformed phosphorene can also be continuously modulated by the electrical field and finally close up at about 15 V/nm. Besides, the electron and hole effective mass along different directions exhibits different responses to the combined impact of strain and electrical field.
Phosphorene, a two-dimensional (2D) monolayer of black phosphorus, has
attracted considerable theoretical interest, although the experimental
realization of monolayer, bilayer, and few-layer flakes has been a significant
challenge. Here we systematically survey conditions for liquid exfoliation to
achieve the first large-scale production of monolayer, bilayer, and few-layer
phosphorus, with exfoliation demonstrated at the 10-gram scale. We introduce a
rapid approach for quantifying the thickness of 2D phosphorus and show that
monolayer and few-layer flakes produced by our approach are crystalline and
unoxidized, while air exposure leads to rapid oxidation and the production of
acid. With large quantities of 2D phosphorus now available, we perform the
first quantitative measurements of the material's absorption edge-which is
nearly identical to the material's band gap under our experimental
conditions-as a function of flake thickness. Our interpretation of the
absorbance spectrum relies on a new analytical method introduced in this work,
allowing the accurate determination of the absorption edge in polydisperse
samples of quantum-confined semiconductors. Using this method, we found that
the band gap of black phosphorus increased from 0.33 +/- 0.02 eV in bulk to
2.14 +/- 0.05 eV in bilayers, a range that is larger than any other 2D
material. In addition, we quantified a higher-energy optical transition (VB-1
to CB), which changes from 2.0 eV in bulk to 3.74 eV in bilayers. This work
introduces several methods for producing and analyzing 2D phosphorus while also
yielding a class of 2D materials with unprecedented optoelectronic properties.
The dielectric properties of multilayer GaS films have been investigated using a Berry phase method and a density functional perturbation theory approach. A linear relationship has been observed between the number of GaS layers and slab polarizability, which can be easily converged at a small supercell size and has a weak correlation with different stacking orders. Moreover, the intercoupling effect of the stacking pattern and applied vertical field on the electronic properties of GaS bilayers has been discussed. The band gaps of different stacking orders show various downward trends with the increasing field, which is interpreted as giant Stark effect. Our study demonstrates that the slab polarizability as the substitution of conventional dielectric constant can act as an independent and reliable parameter to elucidate the dielectric properties of low-dimensional systems and that the applied electric field is an effective method to modulate the electric properties of nanostructures.Keywords: dielectric properties; GaS layers; Berry phase; DFPT; slab polarizability; stacking orders; GSE
We study the effect of surface adsorption of 27 different adatoms on the electronic and magnetic properties of monolayer black phosphorus using density functional theory. Choosing a few representative elements from each group, ranging from alkali metals (group I) to halogens (group VII), we calculate the band structure, density of states, magnetic moment and effective mass for the energetically most stable location of the adatom on monolayer phosphorene. We predict that group I metals (Li, Na, K), and group III adatoms (Al, Ga, In) are effective in enhancing the n-type mobile carrier density, with group III adatoms resulting in lower effective mass of the electrons, and thus higher mobilities. Furthermore we find that the adatoms of transition metals Ti and Fe, produce a finite magnetic moment (1.87 and 2.31 $\mu_B$) in monolayer
phosphorene, with different band gap and electronic effective masses (and thus mobilities), which approximately differ by a factor of 10 for spin up and spin down electrons opening up the possibility for exploring spintronic applications.
The study of topological insulators has generally involved search of materials that have this property as an innate quality, distinct from normal insulators. Here we focus on the possibility of converting a normal insulator into a topological one by application of an external electric field that shifts different bands by different energies and induces a specific band inversion, which leads to a topological state. Phosphorene is a two-dimensional (2D) material that can be isolated through mechanical exfoliation from layered black phosphorus, but unlike graphene and silicene, few layers phosphorene has a large band gap (1.5 - 2.2 eV). It was thus unsuspected to exhibit band inversion and the ensuing topological insulator behavior. Using first-principles calculations with applied perpendicular electric field F⊥ we predict a continuous transition from the normal insulator to a topological insulator and eventually to a metal as a function of F⊥. The tuning of topological behavior with electric field would lead to spin-separated, gapless edge states, i.e., quantum spins Hall effect. This finding opens the possibility of converting normal insulating materials into topological ones via electric field, and making a multi-functional "field effect topological transistor" that could manipulate simultaneously both spins and charge carrier. We use our results to formulate some design principles for looking for other 2D materials that could have such an electrical-induced topological transition.
Using density functional theory calculations, we have systematically explored the effect of surface adsorption of different atoms on the electronic properties of monolayer molybdenum disulfide (MoS2). We have chosen a few representative members from each group in the periodic table, ranging from alkali metals (group I) to halogens (group VII), and calculated the electronic band structure of the adatom−MoS2 system for the most energetically stable location of the adatom adsorbed on MoS2. The calculated value of charge transfer from the adsorbed adatom to MoS2 and resultant shifting of the Fermi level to the conduction band suggest that the group I (Li, Na, K) and group II metals (Mg, Ca) are the most effective adatoms to enhance the n-type mobile carrier density in MoS2. Our calculation is in good agreement with the experimental observation for K [Nano Lett. 2013, 13, 1991].
Newly fabricated few-layer black phosphorus and its monolayer structure, phosphorene, are expected to be promising for electronic and optical applications because of their finite direct band gaps and sizable but anisotropic electronic mobility. By first-principles simulations, we show that this unique anisotropic mobility and corresponding conductance can be controlled by using simple strain conditions. With the appropriate biaxial or uniaxial strain, we can rotate the preferred conducting direction by 90 degrees. This will be of useful for exploring unusual quantum Hall effects, and exotic electronic and mechanical applications based on phosphorene.
Phosphorene, a monolayer of black phosphorus, is promising for nanoelectronic
applications not only because it is a natural p-type semiconductor but also it
possesses a layer-number dependent direct bandgap (in the range of 0.3 eV~1.5
eV). On basis of the density functional theory calculations, we investigate
electronic properties of the bilayer phosphorene with different stacking
orders. We find that the direct bandgap of the bilayers can vary from 0.78 -
1.04 eV with three different stacking orders. In addition, a vertical electric
field can further reduce the bandgap down to 0.56 eV (at the field strength 0.5
V/{\AA}). More importantly, we find that when a monolayer of MoS_2 is
superimposed with the p-type AA- or AB-stacked bilayer phosphorene, the
combined tri-layer can be an effective solar-cell material with type-II
heterojunction alignment. The power conversion efficiency is predicted to be
~18% or 16% with AA- or AB-stacked bilayer phosphorene, higher than reported
efficiencies of the state-of-the-art trilayer graphene/transition metal
dichalcogenide solar cells.
We introduce the 2D counterpart of layered black phosphorus, which we call phosphorene, as an unexplored p-type semiconducting material. Same as graphene and MoS2, single-layer phosphorene is flexible and can be mechanically exfoliated. We find phosphorene to be stable and, unlike graphene, to have an inherent, direct, and appreciable band gap. Our ab initio calculations indicate that the band gap is direct, depends on the number of layers and the in-layer strain, and is significantly larger than the bulk value of 0.31-0.36 eV. The observed photoluminescence peak of single-layer phosphorene in the visible optical range confirms that the band gap is larger than that of the bulk system. Our transport studies indicate a hole mobility that reflects the structural anisotropy of phosphorene and complements n-type MoS2. At room temperature, our few-layer phosphorene field-effect transistors with 1.0 μm channel length display a high on-current of 194 mA/mm, a high hole field-effect mobility of 286 cm(2)/V·s, and an on/off ratio of up to 10(4). We demonstrate the possibility of phosphorene integration by constructing a 2D CMOS inverter consisting of phosphorene PMOS and MoS2 NMOS transistors.
The properties of two-dimensional materials, such as molybdenum disulphide, will play an important role in the design of the next generation of electronic devices. Many of those properties are determined by the dielectric constant which is one of the fundamental quantities used to characterize conductivity, refractive index, charge screening and capacitance. We predict that the effective dielectric constant (ε) of few-layer MoS2 is tunable by an external electric field (Eext). Through first-principles electronic structure calculations, including van der Waals interactions, we show that at low fields (Eext<0.01 V/Å) ε assumes a nearly constant value ~4, but increases at higher fields to values that depend on the layer thickness. The thicker the structure the stronger is the modulation of ε with the electric field. Increasing of the external field perpendicular to the dichalcogenide layers beyond a critical value can drive the system to an unstable state where the layers are weakly coupled and can be easily separated. The observed dependence of ε on the external field is due to charge polarization driven by the bias. Implications on the optical properties as well as on the electronic excitations are also considered. Our results point to a promising way of understanding and controlling the screening properties of MoS2 through external electric fields.
Three components of dielectric constant along three principal crystal axes in black phosphorus are determined for the first time. Two of them are obtained from far-infrared interference spectra for thin cleaved samples. The remaining one is determined by analyzing far-infrared absorption peaks observed in p-type sample at 1.4 K, which are ascribed to optical transitions from the acceptor ground state to its excited states.
We develop a theory for investigating atomic-scale dielectric permittivity profiles across interfaces between insulators. A local susceptibility χ(x;ω) is introduced to describe variations of the dielectric response over length scales of the order of interatomic distances. The nonlocality of the microscopic susceptibility tensor χij(r,r′;ω) occurs at smaller distances and therefore does not intervene in our formulation. The local permittivity is obtained from the microscopic charge density induced by an applied electric field. We show that the permittivity can conveniently be analyzed in terms of maximally localized Wannier functions. In this way, we can relate variations of the microscopic dielectric response to specific features of the local bonding arrangement. In addition to a continuous description in terms of the local permittivity, we introduce an alternative scheme based on discrete polarizabilities. In the latter case, electronic polarizabilities αelec(n) are obtained in terms of the displacements of maximally localized Wannier functions, while ionic polarizabilities αion(I) are determined from the induced ionic displacements and the corresponding dynamical charges. The potential of our scheme is illustrated through applications to two systems of technological interest. First, we consider the permittivity of Si slabs of finite thickness. Our approach indicates that the local permittivity in the slab interior approaches the corresponding value for bulk Si within a few atomic layers from the surface. Therefore, the decrease of the average slab permittivity with thickness originates from the lower permittivity of the outer planes and the increasing surface-to-volume ratio. Second, we address the dielectric permittivity across the Si(100)-SiO2 interface. Using two distinct interface models, we are able to show that the dielectric transition from the silicon to the oxide occurs within a width of only a few Å. The polarizability associated to intermediate oxidation states of Si is found to be enhanced with respect to bulk SiO2, resulting in a larger permittivity of the interfacial suboxide layer with respect to the stoichiometric oxide.
A recently developed theory of atomic-scale local dielectric permittivity has been used to determine the position dependent permittivity profiles of a few nanoscale insulator surfaces and multilayers. Specifically, slabs containing single-component (Si, polymer, and SiO2) and two-component (Si-SiO2 and polymer-SiO2) systems of technological importance have been studied. The present approach indicates that the local permittivity is generally enhanced at the surfaces and/or interfaces, and that it approaches the corresponding bulk values in the interior of each component. This simple method of determining the position-dependent dielectric permittivity profiles can be used to study the impact of atomic level disorder and defects on dielectric properties.
We show the existence of topological phases of Bloch insulators with time-reversal symmetry in three dimensions. These phases are characterized by topological Z2 invariants whose stability is studied using band-touching arguments. Unlike insulators which break time-reveral symmetry, some of these topological phases are intrinsically three dimensional. The number of invariants (four) needed to specify the phase of these insulators also differs from the time-reversal-breaking case. The relation between these phases and the quantum spin Hall effect in three dimensions is investigated.
We study the phases of Bloch insulators with time-reversal symmetry on the basis of the homotopy of the ground-state wave functions in momentum space and find that there are two topological classes characterized by a Z2 invariant. The results are in agreement with a recent study based on counting the zeroes of a certain Pfaffian function related to the ground-state wave function. It is shown that there is a link between the formulation of the topological invariant presented here and the number of robust edge states. A formula is also provided which greatly simplifies the computation of the invariant in a large number of cases. The present study provides guidance for the search of systems which belong to the nontrivial topological class and also establishes a link between the quantum spin Hall effect and the integer quantum Hall effect.
The dielectric constant of a material is one of the fundamental features used to characterize its electrostatic properties such as capacitance, charge screening, and energy storage capability. Graphene is a material with unique behavior due to its gapless electronic structure and linear dispersion near the Fermi level, which can lead to tunable band gap in bilayer [1-3] and trilayer [4-6] graphene, superconducting-insulating transition in hybrid systems [7] driven by electric fields and gate-controlled surface plasmons [8,9]. All these results suggest a strong interplay between graphene properties and external electric fields. Here we address the issue of the effective dielectric constant (ε) in N-layer graphene subjected to out-of-plane (E⊥ext) and in-plane (E∥ext) external electric fields. The value of ε has attracted interest due to contradictory reports from theoretical and experimental studies. Through extensive first-principles electronic structure calculations, including van der Waals interactions, we show that both the out-of-plane (ε⊥ ) and the in-plane (ε∥) dielectric constants depend on the value of applied field. For example, ε⊥ and ε∥ are nearly constant (~3 and ~1.5, respectively) at low fields (Eext <0.01 V/Å), but increase at higher fields to values that dependent on the system size. Increase of the external field perpendicular to the graphene layers beyond a critical value can drive the system to a unstable state where the graphene layers are decoupled and can be easily separated. The observed dependence of ε⊥ and ε∥ on the external field is due to charge polarization driven by the bias. Our results point to a promising way of understanding and controlling the screening properties of few-layer graphene through external electric fields.
First, the authors calculate the frequency-dependent dielectric function of black phosphorus by using the band structure and wavefunctions obtained by the self-consistent pseudopotential calculation. Then by using these results, they discuss the optical properties of black phosphorus such as KPS, UPS, plasmon frequency and reflectance in visible, VUV and soft X-ray regions. Experimental results for all these optical properties are explained consistently using the theoretical results.
We present a simple procedure to generate first-principles norm-conserving pseudopotentials, which are designed to be smooth and therefore save computational resources when used with a plane-wave basis. We found that these pseudopotentials are extremely efficient for the cases where the plane-wave expansion has a slow convergence, in particular, for systems containing first-row elements, transition metals, and rare-earth elements. The wide applicability of the pseudopotentials are exemplified with plane-wave calculations for copper, zinc blende, diamond, alpha-quartz, rutile, and cerium.
When performing density-functional calculations of surfaces using a plane-wave pseudopotential code, it is necessary to embed a slab with two surfaces in a periodic supercell. In many situations, it is desirable to study an asymmetric slab with a net surface dipole density. The periodic boundary conditions imposed on the electrostatic potential then give rise to an artificial electric field across the slab. We present a dipole correction that cancels the artificial field, and show how this correction can be incorporated in the density-functional theory total-energy expression. The results are supported by total-energy calculations of water-molecule layers.
We consider the problem of calculating the weak and strong topological
indices in noncentrosymmetric time-reversal (T) invariant insulators. In 2D we
use a gauge corresponding to hybrid Wannier functions that are maximally
localized in one dimension. Although this gauge is not smoothly defined on the
two-torus, it respects the T symmetry of the system and allows for a definition
of the Z_2 invariant in terms of time-reversal polarization. In 3D we apply the
2D approach to T-invariant planes. We illustrate the method with
first-principles calculations on GeTe and on HgTe under [001] and [111] strain.
Our approach differs from ones used previously for noncentrosymmetric materials
and should be easier to implement in ab initio code packages.
Generalized gradient approximations (GGA{close_quote}s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. {copyright} {ital 1996 The American Physical Society.}
The quantum spin Hall (QSH) phase is a time reversal invariant electronic state with a bulk electronic band gap that supports the transport of charge and spin in gapless edge states. We show that this phase is associated with a novel Z2 topological invariant, which distinguishes it from an ordinary insulator. The Z2 classification, which is defined for time reversal invariant Hamiltonians, is analogous to the Chern number classification of the quantum Hall effect. We establish the Z2 order of the QSH phase in the two band model of graphene and propose a generalization of the formalism applicable to multiband and interacting systems.
Highly anisotropic and robust excitons in monolayer black phosphorus
- Xiaomu Wang
- M Aaron
- Kyle L Jones
- Vy Seyler
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