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![Upper panel: Out-of-plane dependence of in-plane averaged electron potential energy of XM′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$'$$\end{document} bilayer WSe2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {WSe}_2$$\end{document} (including ionic and Hartree contributions), relative to the vacuum potential on the Se side of the vertical W–Se pair, Uvac(Se)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_{vac}(Se)$$\end{document}, which is set to 0 eV. The calculation is for a double-bilayer supercell, with the structure shown as a schematic inset. The charge transfer between the layers gives each bilayer a finite dipole moment, with a consequent difference (ΔP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta ^P$$\end{document}) between the vacuum levels on either side of a bilayer. Left-hand lower panel: potentials with isolated monolayer contributions subtracted, to better show the potential drop and other features. Three calculation methods are shown: black line—first 30 Å of the upper panel, red line—using only a single bilayer supercell, showing how the mismatched vacuum levels give a finite displacement field as necessitated by the periodic boundary conditions, blue line—a single bilayer supercell, but with a compensating dipole correction applied. The right-hand lower panel shows the same quantities, calculated using the LDA for comparison. 0 meV is set to the double-supercell vacuum level on the Se side of the vertical W–Se pair.](publication/352788507/figure/fig6/AS:1039911478112279@1624945625671/Upper-panel-Out-of-plane-dependence-of-in-plane-averaged-electron-potential-energy-of.png)
Upper panel: Out-of-plane dependence of in-plane averaged electron potential energy of XM′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$'$$\end{document} bilayer WSe2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {WSe}_2$$\end{document} (including ionic and Hartree contributions), relative to the vacuum potential on the Se side of the vertical W–Se pair, Uvac(Se)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_{vac}(Se)$$\end{document}, which is set to 0 eV. The calculation is for a double-bilayer supercell, with the structure shown as a schematic inset. The charge transfer between the layers gives each bilayer a finite dipole moment, with a consequent difference (ΔP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta ^P$$\end{document}) between the vacuum levels on either side of a bilayer. Left-hand lower panel: potentials with isolated monolayer contributions subtracted, to better show the potential drop and other features. Three calculation methods are shown: black line—first 30 Å of the upper panel, red line—using only a single bilayer supercell, showing how the mismatched vacuum levels give a finite displacement field as necessitated by the periodic boundary conditions, blue line—a single bilayer supercell, but with a compensating dipole correction applied. The right-hand lower panel shows the same quantities, calculated using the LDA for comparison. 0 meV is set to the double-supercell vacuum level on the Se side of the vertical W–Se pair.
Source publication
In bilayers of two-dimensional semiconductors with stacking arrangements which lack inversion symmetry charge transfer between the layers due to layer-asymmetric interband hybridisation can generate a potential difference between the layers. We analyse bilayers of transition metal dichalcogenides (TMDs)—in particular, WSe2—for which we find a subst...
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Twisted heterostructures of two-dimensional crystals offer almost unlimited scope for the design of new metamaterials. Here we demonstrate a room temperature ferroelectric semiconductor that is assembled using mono- or few-layer MoS 2 . These van der Waals heterostructures feature broken inversion symmetry, which, together with the asymmetry of ato...
Citations
... Here, the conduction band of the MoS 2 bilayer is U MoS ≈ 0.3 eV above the Fermi level of graphite 31 , while the valence band of the hBN layer is U BN ≈ −2.66 eV below the Dirac point of graphene as determined from complementary ARPES experiments (see SI Section 2). Due to the equal potentials initially set on the source and the drain, a small carrier density emerges in graphene and graphite to compensate for the contact potential difference (0.26 eV 32 ) between them, and to negate the FE potential from the rhombohedral MoS 2 bilayer (Δ FE ≈ 63 meV 33,34 ). This results in a corresponding electric field so that the potential profile across the dielectric stack has an additional linear contribution equalising the electrochemical potentials μ 1 and μ 2 . ...
Van der Waals heterostructures have opened new opportunities to develop atomically thin (opto)electronic devices with a wide range of functionalities. The recent focus on manipulating the interlayer twist angle has led to the observation of out-of-plane room temperature ferroelectricity in twisted rhombohedral bilayers of transition metal dichalcogenides. Here we explore the switching behaviour of sliding ferroelectricity using scanning probe microscopy domain mapping and tunnelling transport measurements. We observe well-pronounced ambipolar switching behaviour in ferroelectric tunnelling junctions with composite ferroelectric/non-polar insulator barriers and support our experimental results with complementary theoretical modelling. Furthermore, we show that the switching behaviour is strongly influenced by the underlying domain structure, allowing the fabrication of diverse ferroelectric tunnelling junction devices with various functionalities. We show that to observe the polarisation reversal, at least one partial dislocation must be present in the device area. This behaviour is drastically different from that of conventional ferroelectric materials, and its understanding is an important milestone for the future development of optoelectronic devices based on sliding ferroelectricity.
... Non-collinear spin-orbit coupling (SOC) was incorporated into all band structure calculations via ultra-soft fully relativistic pseudo-potentials [25]. In particular, this gives us the layer-resolved potentials across the studied structures (examples shown in Extended Data Fig. 1), consistent with the individual 'double-charge-layer' potential steps found in bilayers [2,26] and few-layer mixed-stacking crystals [27]. ...
... We calculate the ferroelectric field inside twins by approximating the staircase of interlayer potential steps for 6, 9 and 12 layer domains (see Fig. 1) as U = eE FE z. This gives us a value of E FE ≈ 11.5 mV/Å for MoS 2 , and E FE ≈ 11 mV/Å for WS 2 , in agreement with the earlier calculated double layer potentials in bilayers [26]. ...
Semiconducting transition metal dichalcogenides (MX$_2$) occur in 2H and rhombohedral polytypes, respectively distinguished by anti-parallel and parallel orientation of consecutive monolayer lattices. In its bulk form, rhombohedral MX$_2$ is ferroelectric, hosting an out-of-plane electric polarization, the direction of which is dictated by stacking. Here, we predict that twin boundaries, separating adjacent polarization domains with reversed built-in electric fields, are able to host two-dimensional electrons and holes with an areal density reaching $\sim 10^{13} {\rm cm}^{-2}$. Our modelling suggests that n-doped twin boundaries have a more promising binding energy than p-doped ones, whereas hole accumulation is stable at external surfaces of a twinned film. We also propose that the introduction of a twist at the twinned interface, with a `magic' angle $\theta^* \approx 3^{\circ}$, should promote a regime of strongly correlated states of electrons, such as Wigner crystals, due to commensurability between the moir\'e pattern at the interface and the accumulated carrier density.
... While many bulk, layered vdW crystals are naturally centrosymmetric and therefore non-polar, layer-by-layer assembly of individual vdW layers has been used to build non-centrosymmetric 2D heterostructures possessing an out-of-plane, interfacial polarization that can be switched via sliding of one layer. This bottom-up approach greatly expands the number of potential 2D ferroelectric candidates and has been both predicted and experimentally demonstrated for various common vdW materials, including hexagonal boron nitride (hBN) [3][4][5][6] and transition metal dichalcogenides 3,[6][7][8][9][10][11][12][13] . ...
In conventional ferroelectric materials, polarization is an intrinsic property limited by bulk crystallographic structure and symmetry. Recently, it has been demonstrated that polar order can also be accessed using inherently non-polar van der Waals materials through layer-by-layer assembly into heterostructures, wherein interfacial interactions can generate spontaneous, switchable polarization. Here we show that deliberate interlayer rotations in multilayer van der Waals heterostructures modulate both the spatial ordering and switching dynamics of polar domains. The engendered tunability is unparalleled in conventional bulk ferroelectrics or polar bilayers. By means of operando transmission electron microscopy we show how alterations of the relative rotations of three WSe2 layers produce structural polytypes with distinct arrangements of polar domains with either a global or localized switching response. Furthermore, the presence of uniaxial strain generates structural anisotropy that yields a range of switching behaviours, coercivities and even tunable biased responses. We also provide evidence of mechanical coupling between the two interfaces of the trilayer, a key consideration for the control of switching dynamics in polar multilayer structures more broadly.
... In a multilayer flake, each of the interfaces may have either XM (polarization pointing upward) or MX (downward) stacking order creating a potential ladder either going upwards or downwards, respectively. 7,14 The difference in the total number of upward-and downward-pointing polarized interfaces decides the cumulative polarization state, hence the surface potential. 7 Therefore, different ferroelectric domains in a given thickness would be visible in a V KP map. ...
... It has been shown that in bilayer 3R-TMDs, states at the Γ point of the valence band (VB) or Q point of conduction band (CB) are fully delocalized due to strong interlayer hybridization. 7,14,17 In contrast, the wavefunctions at the K points are almost entirely layer-localized. The ferroelectricity-induced builtin potential manifests as a local electrostatic perturbation and introduces a shift between the layer-projected energy levels at K points, leading to a type-II band alignment at the interfaces, 17 with the energy decreasing from layer X to layer M. By the same token, in a multilayer sample, the spatial profile of K-point band extrema along the out-of-plane direction follows the underlying ferroelectric potential and is, therefore, susceptible to the stacking order, as depicted schematically in Fig1e (cf. ...
Interfacial ferroelectricity is a phenomenon arising in a plethora of parallel-stacked layered materials, ¹⁻¹¹ in which out-of-plane ferroelectric order is switched by in-plane sliding of adjacent layers. ⁴ Unlike conventional ferroelectrics, interfacial ferroelectricity is stable against doping, ⁷ potentially enabling next-generation devices with storage and computational capabilities. ¹² However, the field has been limited to indirect sensing or visualizing the ferroelectricity in basic bilayer units employing surface-sensitive probes. In the case of transition metal dichalcogenides, this leaves a void of in-depth knowledge about the influence of ferroelectric order on their intrinsic valley and excitonic properties. Here, we report direct far-field probing of ferroelectricity in few-layer 3R-MoS 2 using reflectance contrast spectroscopy. Contrary to a simple electrostatic perception, the intralayer excitons with strictly in-plane dipole orientation are sensitive to out-of-plane ferroelectric ordering. On the other hand, despite possessing an out-of-plane electric dipole component, ¹³ layer-hybridized momentum-indirect excitons remain decoupled from such ordering. Ab initio calculations elucidate the microscopic origin of the correspondence between ferroelectric order and optical response. Using a field-effect device, we demonstrate room temperature control and optical readout of multi-state polarization and its hysteretic switching. Time-resolved Kerr ellipticity measured in different ferroelectric domains reveals a direct correspondence between spin-valley dynamics and ferroelectric order.
... In contrast, broken centrosymmetry of the P bilayers leads to four Fermi lines, which are essentially a pair of layer-hybridized copies of the monolayer bands. DFT calculations in mirror-reflected supercells also demonstrate the presence of a ferroelectric charge transfer, resulting in an ≈ 11 meV potential energy drop between the layers (see Appendix A 3), which is notably smaller than for semiconducting TMDs [52]. We note that this charge transfer in principle allows for a layer-dependent potential contribution to interlayer band splitting of P bilayers; however, explicit incorporation of this term does not have a significant effect on interlayer hybridization due to the small degree of charge transfer between the layers (see comparison between Fermi surface fitting with and without an explicit layer-polarization term in Appendix A 4). ...
The creation of moiré superlattices in twisted bilayers of two-dimensional crystals has been utilized to engineer quantum material properties in graphene and transition metal dichalcogenide semiconductors. Here, we examine the structural relaxation and electronic properties in small-angle twisted bilayers of metallic NbSe2. Reconstruction appears to be particularly strong for misalignment angles θP<2.9∘ and θAP<1.2∘ for parallel (P) and antiparallel (AP) orientations of monolayers' unit cells, respectively. Multiscale modeling reveals the formation of domains and domain walls with distinct stacking, for which density functional theory calculations are used to map the shape of the bilayer Fermi surface and the relative phase of the charge density wave (CDW) order in adjacent layers. We find a significant modulation of interlayer coupling across the moiré superstructure and the existence of preferred interlayer orientations of the CDW phase, necessitating the nucleation of CDW discommensurations at superlattice domain walls.
... In particular, for an almost perfectly aligned AP bilayer (θ < 0.15 • ), corresponding to that (θ[rad] < δ ≈ 3 × 10 −3 , a relative lattice mismatch between MoX 2 and WX 2 ), we find that electrons and holes are localized at quantum dots at the opposite corners of hexagonal DWNs, with binding energies of both s-and p-like orbitals in the range of 200−300 meV, as shown in Fig. 1 P-MoSe 2 /WSe 2 , where, for θ < 0.45 • , the lowest energy states for both electrons and holes appear to be at the XX nodes of the triangular DWN network. The right hand side panels in Fig. 1 indicate that, while for the larger angles the 'XX quantum dots' persist for the conduction band electrons (bound states only 10−20 meV below the lowest 1D band inside the domain wall 'wires'), the valence band holes get deconfined into the XW stacking domain areas, where the band edge is promoted by the interlayer charge transfer [16,[28][29][30][31][32], as compared to MoX domains. As discussed in detail in the rest of the paper, similar scenarios also appear in MoS 2 /WS 2 . ...
Twisted bilayers of two-dimensional semiconductors offer a versatile platform to engineer quantum states for charge carriers using moiré superlattice effects. Among the systems of recent interest are twistronic MoSe2/WSe2 and MoS2/WS2 heterostructures, which undergo reconstruction into preferential stacking domains and highly strained domain wall networks, determining the electron/hole localization across moiré superlattices. Here, we present a catalogue of options for the formation of self-organized quantum dots and wires in lattice-reconstructed marginally twisted MoSe2/WSe2 and MoS2/WS2 bilayers, fine tuned by the twist angle between the monolayers from perfect alignment to θ ∼ 1◦, and by choosing parallel or anti-parallel orientation of their unit cells. The proposed
scenarios of the quantum dots and wires formation are found using multi-scale modelling that takes into account the features of strain textures caused by twirling of domain wall networks.
... With the moiré-averaged Fermi energy at charge neutrality, this doping density shifts the Fermi energy (Fig. 1b), measured with respect to the Dirac point in the two ferroelectric domains, by ± 71 meV . This value is about four times higher than the theoretically predicted 16 meV, based on a linear screening model with a ferroelectric potential of 56 mV (Supplementary Note 5) 39,42 . The unexpected high doping implies that the ferroelectric potential is not the sole mechanism responsible for generating the carrier density in graphene. ...
Ferroelectricity, a spontaneous and reversible electric polarization, is found in certain classes of van der Waals (vdW) materials. The discovery of ferroelectricity in twisted vdW layers provides new opportunities to engineer spatially dependent electric and optical properties associated with the configuration of moiré superlattice domains and the network of domain walls. Here, we employ near-field infrared nano-imaging and nano-photocurrent measurements to study ferroelectricity in minimally twisted WSe2. The ferroelectric domains are visualized through the imaging of the plasmonic response in a graphene monolayer adjacent to the moiré WSe2 bilayers. Specifically, we find that the ferroelectric polarization in moiré domains is imprinted on the plasmonic response of the graphene. Complementary nano-photocurrent measurements demonstrate that the optoelectronic properties of graphene are also modulated by the proximal ferroelectric domains. Our approach represents an alternative strategy for studying moiré ferroelectricity at native length scales and opens promising prospects for (opto)electronic devices.
... Moreover, hBN and TMDs have recently emerged as ferroelectric 2D materials, in which switching between two twin stacking orders by mutual sliding of the layers and electrical manipulation produces room-temperature stable outof-plane polarization. [1][2][3][4][5][6][7][8] Semiconducting ferroelectrics with low energy barrier polarization switching are of interest, as they enable ferroelectric field-effect transistors, devices that combine memory storage and logic processing into a single device. [9] The possibility of assembling vertical stacks of designer sequences from atomically thin planes of layered van der Waal materials allows for unprecedented flexibility in engineering novel electronic devices. ...
Semiconducting ferroelectric materials with low energy polarisation switching offer a platform for next-generation electronics such as ferroelectric field-effect transistors. Recently discovered interfacial ferroelectricity in bilayers of transition metal dichalcogenide films provide an opportunity to combine the potential of semiconducting ferroelectrics with the design flexibility of two-dimensional material devices. Here, local control of ferroelectric domains in a marginally twisted WS2 bilayer is demonstrated with a scanning tunneling microscope at room temperature, and their observed reversible evolution understood using a string-like model of the domain wall network (DWN). We identify two characteristic regimes of DWN evolution: (i) elastic bending of partial screw dislocations separating smaller domains with twin stackings due to mutual sliding of monolayers at domain boundaries and (ii) merging of primary domain walls into perfect screw dislocations, which become the seeds for the recovery of the initial domain structure upon reversing electric field. These results open the possibility to achieve full control over atomically thin semiconducting ferroelectric domains using local electric fields, which is a critical step towards their technological use. This article is protected by copyright. All rights reserved.
... Starting from the 2D building block of monolayer transition metal dichalcogenides (TMDs) with trigonal prismatic coordination (point group D 3h ), one can fabricate an artificial bilayer that has either a non-centrosymmetric polar structure (point group C 3v ) or a centrosymmetric non-polar structure (point group D 3d ) by controlling the stacking angle (Supplementary Section 1.1). In the untwisted TMD bilayer without inversion symmetry (Fig. 1a), electric charges can transfer from one layer to the other, thereby exhibiting spontaneous polarization in the out-of-plane direction [2][3][4][5][6][7][8][9] . Depending on the in-plane shifting direction between the two layers, the charge transfers TEM device structure, a temporal resolution of 200 ms in real-time imaging was achieved, which can be further improved by optimizing the DF imaging condition or modifying the device structure. ...
Conventional antiferroelectric materials with atomic-scale anti-aligned dipoles undergo a transition to a ferroelectric (FE) phase under strong electric fields. The moiré superlattice formed in the twisted stacks of van der Waals crystals exhibits polar domains alternating in moiré length with anti-aligned dipoles. In this moiré domain antiferroelectic (MDAF) arrangement, the distribution of electric dipoles is distinguished from that of two-dimensional FEs, suggesting dissimilar domain dynamics. Here we performed an operando transmission electron microscopy investigation on twisted bilayer WSe2 to observe the polar domain dynamics in real time. We find that the topological protection, provided by the domain wall network, prevents the MDAF-to-FE transition. As one decreases the twist angle, however, this transition occurs as the domain wall network disappears. Exploiting stroboscopic operando transmission electron microscopy on the FE phase, we measure a maximum domain wall velocity of 300 μm s–1. Domain wall pinnings by various disorders limit the domain wall velocity and cause Barkhausen noises in the polarization hysteresis loop. Atomic-scale analysis of the pinning disorders provides structural insight on how to improve the switching speed of van der Waals FEs.
... In the BA stacking, the polarization and depolarization field are reversed, giving rise to a lower surface potential ( Figure 1B). Assuming the SiO2 layer is sufficiently thin so the bottom layer in the entire flake has the same electric potential as the substrate 40 , we find the total difference in the surface potential between the two domains is twice the interlayer potential, ∆ = 2 0 / 0 , where is the polarization strength, 0 and are the thickness and dielectric constant of monolayer MoS2, 0 is the free-space permittivity. As the surface potential can induce an electrostatic force on an adjacent atomic force microscope (AFM) probe, the surface potential contrast between two types of domains can be visualized in the EFM mode. ...
Slip avalanches are ubiquitous phenomena occurring in 3D materials under shear strain and their study contributes immensely to our understanding of plastic deformation, fragmentation, and earthquakes. So far, little is known about the role of shear strain in 2D materials. Here we show some evidence of two-dimensional slip avalanches in exfoliated rhombohedral MoS2, triggered by shear strain near the threshold level. Utilizing interfacial polarization in 3R-MoS2, we directly probe the stacking order in multilayer flakes and discover a wide variety of polarization domains with sizes following a power-law distribution. These findings suggest slip avalanches can occur during the exfoliation of 2D materials, and the stacking orders can be changed via shear strain. Our observation has far-reaching implications for developing new materials and technologies, where precise control over the atomic structure of these materials is essential for optimizing their properties as well as for our understanding of fundamental physical phenomena.
