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(Color online) (a) Bandgap (E g ) and (b) the energy gap (DE K ) at the K point of graphene as a function of the external electric field strength. The black solid circles and red open circles correspond to Bernal bilayer graphene and TLG. The solid green squares correspond to rhombohedral TLG.
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Bandgaps play a central role in modern device physics, and a tunable bandgap can provide great flexibility in device design. Herein, an investigation of trilayer graphene modulated using an external electric field is presented. The calculations for trilayer graphene with hexagonal, Bernal, and rhombohedral stacking have been carried out. It was fou...
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... Charge carriers, electrons or holes can be introduced into graphene through the perpendicular electric field, which generates an interlayer potential asymmetry and can induce an energy gap in the electronic spectrum, modifying the electronic structure near the K point, as illustrated in Fig. 1(b). Theoretical and experimental studies have shown that the band structure is tunable with the perpendicular electric field in bilayer graphene [18][19][20], ABC-TLG [21][22][23] and multilayer graphene [24][25][26][27], which offers the exciting opportunity to investigate the richer electronic structure and widen the range of application for graphene systems in electronics. ...
By using the constrained-phase quantum Monte Carlo method, we performed a systematic study of the ground state of the half-filled Hubbard model for a trilayer honeycomb lattice. We analyse the effect of the perpendicular electric field on the electronic structure, magnetic property and pairing correlations. It is found that antiferromagnetic fluctuations emerge with the perpendicular electric field, and the electronic correlation drives a $d+id$ superconducting pairing to be dominant over other pairing patterns among various electric fields and interaction strengths. We also found that the $d+id$ pairing correlation is greatly enhanced as the on-site Coulomb interaction is increased. Our intensive numerical results may unveil the nature of the recently observed superconductivity in rhombohedral trilayer graphene under an electric field.
... The low-energy electronic structure near the K (or K ′ ) point considering γ 0 and γ 1 couplings and different values of the gate potential 0 ≤ V g ∼ 2γ 1 is presented in Fig. 2a. Due to the structural symmetry, the Dirac points K, K ′ are degenerate, where around each one of them there are three pairs of linear branches creating a diamond structure with Dirac cones throughout the energy-momentum space 44 . At the Fermi level E F = 0 and www.nature.com/scientificreports/ ...
... The DOS increases at these crossing-band energies and presents a pair of local sharp peaks, providing states to the EC effect when the temperature is T ≫ 300 K. When V g is turned on, an energy gap between the lower electron (conduction band) and higher hole branch (valence band) opens at the K point as well as in their vicinity because of the potential energy difference between the bottom and top graphene layers 22,25,33,37,44,48 . The gaps nonlinearly increase as V g increases 30,44 , the DOS vanishes for the gap energies as expected, and shows two high symmetric peaks (van Hove singularities) near the valence and conduction band edges, whose states are mainly contributed by the carbon atoms of the top and bottom graphene layers 30 . ...
... When V g is turned on, an energy gap between the lower electron (conduction band) and higher hole branch (valence band) opens at the K point as well as in their vicinity because of the potential energy difference between the bottom and top graphene layers 22,25,33,37,44,48 . The gaps nonlinearly increase as V g increases 30,44 , the DOS vanishes for the gap energies as expected, and shows two high symmetric peaks (van Hove singularities) near the valence and conduction band edges, whose states are mainly contributed by the carbon atoms of the top and bottom graphene layers 30 . The bandgap edges for lowgate potential V g = 0.05 eV ( V g = 0.1 eV) provide states to the EC effect for temperatures starting from ∼ 80 K (140 K), while when moderate gate fields V g = 0.2, 0.4 eV are applied, the electronic states start to contribute to the EC response when T > 240 K. Figure 5a shows the EC effect for ABC-TLG structure. ...
The electrocaloric (EC) effect is the change in temperature and entropy of a material driven by the application of an electric field. Our tight-binding calculations linked to Fermi statistics, show that the EC effect can be produced in trilayer graphene (TLG) structures connected to a heat source, triggered by changes in the electronic density of states (DOS) at the Fermi level when external gate fields are applied on the outer graphene layers. We demonstrate that entropy changes are sensitive to the stacking arrangement in TLG systems. The AAA-stacked TLG presents an inverse EC response (cooling) regardless of the temperature value and gate field potential strength, whereas the EC effect in ABC-stacked TLG remains direct (heating) above room temperature. We reveal otherwise the TLG with Bernal-ABA stacking generates both the direct and inverse EC response within the same sample, associated with gate-dependent electronic transitions of thermally excited charge carriers from the valence band to the conduction band in the band structure. The novel charge carrier electrocaloric effect we propose in quantum layered systems may bring a wide variety of prototype van der Waals materials that could be used as versatile platforms to controlling the thermal response in nanodevices.
... The AAA-stacked TLG has been recently exfoliated 36 , preserves metallic character in the presence of external electric fields 44 as in the monolayer graphene case, and possesses mirror reflection symmetry with respect to the central layer. In this structure the {Ai,Bi} sublattices match to the nearest-neighbor layer carbon sites {Ai + 1,Bi + 1} with vertical hopping γ 1 . ...
... The low-energy electronic structure near the K (or K ′ ) point for different values of the gate potential 0 ≤ V g ∼ 2γ 1 is presented in Fig. 2(a). Due to the structural symmetry, the Dirac points K,K ′ are degenerate, where around each one of them there are three pairs of linear branches creating a diamond structure with Dirac cones throughout the energy-momentum space 44 . At the Fermi level E F = 0 and momentum K, or at the charge neutrality point (CNP), one of the Dirac cones remains constant regardless of the V g strength, resembling the monolayer graphene modes. ...
... The DOS increases at these crossing-band energies and presents a pair of local sharp peaks, providing states to the EC effect when the temperature is T ≫ 300 K. When V g is turned on, an energy gap between the lower electron (conduction band) and higher hole branch (valence band) opens at the K point as well as in their vicinity because of the potential energy difference between the bottom and top graphene layers 22,25,33,37,44,48 . The gaps nonlinearly increase as V g increases 30,44 , the DOS vanishes for the gap energies as expected, and shows two high symmetric peaks (van Hove singularities) near the valence and conduction band edges, whose states are mainly contributed by the carbon atoms of the top and bottom graphene layers 30 . ...
The electrocaloric (EC) effect is the change in temperature and entropy of a material driven by the application of an electric field. Our tight-binding calculations linked to Fermi statistics, show that the EC effect can be produced in trilayer graphene (TLG) structures connected to a heat source, triggered by changes in the electronic density of states (DOS) at the Fermi level when external gate fields are applied on the outer graphene layers. We demonstrate that entropy changes are sensitive to the stacking arrangement in TLG systems. The AAA-stacked TLG presents an inverse EC response (cooling) regardless of the temperature value and gate field potential strength, whereas the EC effect in ABC-stacked TLG remains direct (heating) above room temperature. We reveal otherwise the TLG with Bernal-ABA stacking generates both the direct and inverse EC response within the same sample, associated with gate-dependent electronic transitions of thermally excited charge carriers from the valence band to the conduction band in the band structure. The novel charge carrier electrocaloric effect we propose in quantum layered systems may bring a wide variety of prototype van der Waals materials that could be used as versatile platforms to controlling the thermal response in nanodevices.
... A. AAA-stacked TLG AAA-stacked TLG has been recently exfoliated [39], preserves metallic character in the presence of external electric fields [44] as in the monolayer graphene case, and possesses mirror reflection symmetry with respect to the central layer. In this structure the {Ai,Bi} sublattices match to the nearest-neighbor layer carbon sites {Ai + 1,Bi + 1} with vertical hopping γ 1 . ...
... Figure 2(a) shows the low-energy electronic structure given by Eqs. 8 near the K point for different values of the gate potential 0 ≤ V g ∼ 2γ 1 . Due to the structural symmetry, the Dirac points K,K are degenerate, where around each one of them there are three pairs of linear branches creating a diamond structure with Dirac cones throughout energy-momentum space [44]. At the Fermi level E F = 0 and momentum K, or charge neutrality point (CNP), one of the Dirac cones remains constant regardless of the V g strength, resembling the monolayer graphene modes [Eq. ...
... The DOS increases at these crossing-band energies and presents a pair of local sharp peaks, not providing states to the EC effect for T > 900 K. When V g is turned on, an energy gap between the lower electron (conduction band) and higher hole branch (valence band) opens at the K point as well as in their vicinity because of the potential energy difference between the bottom and top graphene layers [19,22,36,44,47,48]. The gaps non-linearly increase as V g increases [27,44], the DOS vanishes for the gap energies as expected, and shows two high symmetric peaks (van Hove singularities) near the valence and conduction band edges, whose states are mainly contributed by the carbon atoms of the top and bottom graphene layers [27]. ...
The electrocaloric (EC) effect is the reversible change in temperature and/or entropy of a material when it is subjected to an adiabatic electric field change. Our tight-binding calculations linked to Fermi statistics, show that the EC effect is sensitive to the stacking arrangement in trilayer graphene (TLG) structures connected to a heat source, and is produced by changes of the electronic density of states (DOS) near the Fermi level when external gate fields are applied on the outer graphene layers. We demonstrate the AAA-stacked TLG presents an inverse EC response (cooling), whereas the EC effect in ABC-stacked TLG remains direct (heating) regardless of the applied gate field potential strength. We reveal otherwise the TLG with Bernal-ABA stacking geometry generates both the inverse and direct EC response in the same sample, associated with a gate-dependent electronic entropy transition at finite temperature. By varying the chemical potential to different Fermi levels, we find maxima and minima of the DOS are located near the extremes of the electronic entropy, which are correlated with sign changes in the differential entropy per particle, giving a particular experimentally measurable electronic entropy spectrum for each TLG geometry. The EC effect in quantum two-dimensional layered systems may bring a wide variety of prototype van der Waals materials that could be used as versatile platforms to controlling the temperature in nanoscale electronic devices required in modern portable on-chip technologies.
... It was predicted by many groups that an external field induces opening of a band gap. [108][109][110][111][112][113] Approximately two years after the first prediction, experimental research proved this. Lui et al. monitored the band gap opening of ABC-TLG through infrared conductivity measurements, and they found that a large band gap of ∼ 120 meV was induced by a gate voltage of 1.2 V. [114] Bao et al. measured the relationship between the conductance and back gate voltage via standard lock-in techniques, and they found that an insulating state emerges in ABC-TLG near the charge neutrality point at low temperatures ∼ 1.5 K. [115] They attributed the appearance of the insulating phase to the strong electronic interactions that give rise to spontaneous symmetry breaking. ...
We review the recent discoveries of exotic phenomena in graphene, especially superconductivity. It has been theoretically suggested for more than one decade that superconductivity may emerge in doped graphene-based materials. For single-layer pristine graphene, there are theoretical predictions that spin-singlet d + id pairing superconductivity is present when the filling is around the Dirac point. If the Fermi level is doped to the Van Hove singularity where the density of states diverges, then unconventional superconductivity with other pairing symmetry would appear. However, the experimental perspective was a bit disappointing. Despite extensive experimental efforts, superconductivity was not found in monolayer graphene. Recently, unconventional superconductivity was found in magic-angle twisted bilayer graphene. Superconductivity was also found in ABC stacked trilayer graphene and other systems. In this article, we review the unique properties of superconducting states in graphene, experimentally controlling the superconductivity in twisted bilayer graphene, as well as a gate-tunable Mott insulator, and the superconductivity in trilayer graphene. These discoveries have attracted the attention of a large number of physicists. The study of the electronic correlated states in twisted multilayer graphene serves as a smoking gun in recent condensed matter physics.
... The band structure can also be changed by applying a perpendicular electric field. Theoretical [9][10][11][12][13] and experimental [14,15] research have proved that the band gap of ABC-TLG is tunable with the external electric field, which is similar to the phenomenon reported in bilayer graphene (BLG) [16][17][18][19]. ...
Motivated by the recently experimental reported signatures of tunable Mott insulating state and superconductivity in an ABC-trilayer graphene, we investigate the charge compressibility, the spin correlation and the superconducting instability within the Hubbard model on a three layer honeycomb superlattice. It is found that an antiferromagnetically ordered Mott insulator emerges beyond a critical $U_c$ at half filling, and the electronic correlation drives a $d+id$ superconducting pairing to be dominant over other pairing patterns in a wide doped region. The effective pairing interaction with $d+id$ pairing symmetry is strongly enhanced with the increasing of on-site Coulomb interaction, and suppressed as the interlayer coupling strength increases. Our intensive numerical results demonstrate that the insulating state and superconductivity reported in ABC trilayer graphene supperlattice are driven by strong electric correlation, and it may offer an attractive systems to explore rich correlated behaviours.
... ABC-TLG has more practical properties compared with ABA-TLG. It was predicted by many groups that an external field induces opening of a band gap [91][92][93][94][95][96]. Approximately two years after the first prediction, experimental research proved this. ...
In this article, we review the recent discoveries of exotic phenomena in graphene, especially superconductivity. It has been theoretically suggested for more than one decade that superconductivity may emerge in doped graphene-based materials. For single-layer graphene, there are theoretical predictions that spin-singlet $d+id$ pairing superconductivity is present when the filling is around the Dirac point. If the Fermi level is doped to the Van Hove singularity where the density of states diverges, then unconventional superconductivity with other pairing symmetry would appear. However, the experimental perspective was a bit disappointing. Despite extensive experimental efforts, superconductivity was not found in monolayer graphene. Recently, unconventional superconductivity was found in "magic-angle" twisted bilayer graphene. Superconductivity was also found in ABC stacked trilayer graphene and other systems. In this article, we review the unique properties of superconducting states in graphene, experimentally controlling the superconductivity in twisted bilayer graphene, as well as a gate-tunable Mott insulator, and the superconductivity in trilayer graphene. These discoveries have attracted the attention of a large number of physicists. The study of the electronic correlated states in twisted multilayer graphene serves as a smoking gun in recent condensed matter physics.
... a possible explanation, which should be thoroughly studied, in order to explain the bad results obtained in the properties of the composites sintered by microwave radiation, is the change in the crystal structure of graphene when a perpendicular electric field was applied [37]. Some authors argue that applying a perpendicular electric field breaks the sublattice symmetry differently depending on the stacking configuration, and thus it is capable of re-ordering the energy hierarchy of the stacking configurations [38,39]. As a consequence, multilayer graphene exhibits the rare behaviour of crystal structure modification, and hence modification of electronic properties, through the application of an external electric field. ...
The choice of the right material is essential in microwave processing. The carbon materials are good microwave absorbers, which allows them to be transformed by microwave heating into new carbon materials with adapted properties, capable of heating other materials indirectly. In this paper, the microwave heating of graphene as reinforcement of the lithium aluminosilicate (LAS) ceramics has been explored. LAS ceramics have a near-zero coefficient of thermal expansion and exhibit an effective and efficient heating by microwave. Nevertheless, we have found that the graphene did not show any significant response to the microwave radiation and, hence, the interaction as mechanical reinforcement with the LAS material is harmful. The possible benefits of graphene materials to microwave technology are widely known; however, the mechanism involved in the interaction of microwave radiation with ceramic-graphene composites with high dielectric loss factors has not been addressed earlier.
... In contrast, although a band gap is induced in the graphene trilayer by applying an electric field, it is not stable; the band gap opens up to its maximum at an electric field of 0.5 Â 10 9 V m À1 and then begins to close with an increase in the electric field. 47,48 A similar result has also been observed for the BN/graphene/BN heterostructure, where opening of the band gap of graphene is only 57 meV for the electric field of 1 Â 10 9 V m À1 . 30 Our calculations find that application of an external electric field from bottom to top leads to an upward shift of VBM of the top SnO layer while lowering that of the bottom SnO layer in SnO/graphene/SnO. ...
Graphene’s applicability in nanoscale devices is somewhat limited because of the absence of a finite band gap. To overcome this limitation of zero band gap, we consider the vertically-stacked heterostructures consisted of graphene and SnO knowing that two-dimensional SnO films were synthesized recently. Calculations based on density functional theory find that the oxide monolayer can induce a noticeable band gap in graphene; the gap is 45 meV in graphene/SnO/graphene and 115 meV in SnO/graphene/SnO heterostructures. Additionally, graphene’s band gap can be maintained under a relatively high electric field (≈109 V/m) applied to the heterostructures because of the electrostatic screening effect of the oxide layer. The calculated results suggest relative superiority of the graphene/oxide heterostructures over graphene/BN heterostructures for the nanoscale devices based on graphene.
... Their responses to the electric field are also different. A band gap will be opened by an external electric field in r-TLG, while there is an electric field induced band overlap in the b-TLG [29][30][31][32][33][34][35][36][37] . Stimulated by the recent experimental progress and considering the novel electronic properties of TLG, in this work, we systematically examine the behaviors of the adatoms on TLG systems by studying the Anderson impurity model via self-consistent mean field method. ...
Recently, the existence of local magnetic moment in a hydrogen adatom on graphene has been confirmed experimentally [Gonz\'{a}lez-Herrero et al., Science, 2016, 352, 437]. Inspired by this breakthrough, we theoretically investigate the top-site adatom on trilayer graphene (TLG) by solving the Anderson impurity model via self-consistent mean field method. The influence of the stacking order, the adsorption site and external electric field are carefully considered. We find that, due to its unique electronic structure, the situation of the TLG is drastically different from that of the monolayer graphene. Firstly, the adatom on rhombohedral stacked TLG (r-TLG) can have a Fano-shaped impurity spectral density, instead of the normal Lorentzian-like one, when the impurity level is around the Fermi level. Secondly, the impurity level of the adatom on r-TLG can be tuned into an in-gap state by an external electric field, which strongly depends on the direction of the applied electric field and can significantly affect the local magnetic moment formation. Finally, we systematically calculate the impurity magnetic phase diagrams, considering various stacking orders, adsorption sites, doping and electric field. We show that, because of the in-gap state, the impurity magnetic phase of r-TLG will obviously depend on the direction of the applied electric field as well. All our theoretical results can be readily tested in experiment, and may give a comprehensive understanding about the local magnetic moment of adatom on TLG.
