Twisted Transition Metal Dichalcogenides Research Articles

Giant resistance switch in twisted transition metal dichalcogenide tunnel junctions

Abstract Resistance switching in multilayer structures are typically based on materials possessing ferroic orders. Here we predict an extremely large resistance switching based on the relative spin-orbit splitting in twisted transition metal dichalcogenide (TMD) monolayers tunnel junctions. Because of the valence band spin splitting which depends on the valley index in the Brillouin zone, the perpendicular electronic transport through the junction depends on the relative reciprocal space overlap of the spin-dependent Fermi surfaces of both layers, which can be tuned by twisting one layer. Our quantum transport calculations reveal a switching resistance larger than 106% when the relative alignment of TMDs goes from 0º to 60º and when the angle is kept fixed at 60º and the Fermi level is varied. By creating vacancies, we evaluate how inter-valley scattering affects the efficiency and find that the resistance switching remains large (104%) for typical values of vacancy concentration. Not only should this resistance switching be observed at room temperature due to the large spin splitting, but our results also show how twist angle engineering and control of van der Waals heterostructures could be used for next-generation memory and electronic applications.

Twist Angle-Dependent Phonon Hybridization in WSe2/WSe2 Homobilayer.

The emerging moiré superstructure of twisted transition metal dichalcogenides (TMDs) leads to various correlated electronic and optical properties compared to those of twisted bilayer graphene. In such a versatile architecture, phonons can also be renormalized and evolve due to atomic reconstruction, which, in turn, depends on the twist angle. However, observing this reconstruction and its relationship to phonon behavior with conventional, cost-effective imaging methods remains challenging. Here, we used noninvasive Raman spectroscopy on twisted WSe2/WSe2 (t-WSe2) homobilayers to examine the evolution of phonon modes due to interlayer coupling and atomic reconstruction. Unlike in the natural bilayer (NB), ∼0° as well as ∼60° t-WSe2 samples, the nearly degenerate A1g/E2g mode in the twisted samples (1-7°) split into a doublet in addition to the nondegenerate B2g mode, and the maximum splitting is observed around 2-3°. Our detailed theoretical calculations qualitatively capture the splitting and its dependence as a function of the twist angle and highlight the role of the moiré potential in phonon hybridization. Additionally, we found that around the 2° twist angle, the anharmonic phonon-phonon interaction is higher than the natural bilayer and decreases for larger twist angles. Interestingly, we observed anomalous Raman frequency softening and line-width increase with the decreasing temperature below 50 K, pointing to the combined effect of enhanced electron-phonon coupling and cubic anharmonic interactions in moiré superlattice.

Multiferroicity and Topology in Twisted Transition Metal Dichalcogenides.

Van der Waals heterostructures have recently emerged as an exciting platform for investigating the effects of strong electronic correlations, including various forms of magnetic or electrical orders. Here, we perform an unbiased exact diagonalization study of the effects of interactions on topological flat bands of twisted transition metal dichalcogenides (TMDs) at odd integer fillings. For hole-filling ν_{h}=1, we find that the Chern insulator phase, expected from interaction-induced spin-valley polarization of the bare bands, is quite fragile, and gives way to spontaneous multiferroic order-coexisting ferroelectricity and ferromagnetism, in the presence of long-range Coulomb repulsion. We provide a simple real-space picture to understand the phase diagram as a function of interaction range and strength. Our findings establish twisted TMDs as a novel and highly tunable platform for multiferroicity, and we outline a potential route towards electrical control of magnetism in the multiferroic phase.

Chiral limit and origin of topological flat bands in twisted transition metal dichalcogenide homobilayers

The observation of zero field fractional quantum Hall analogs in twisted transition metal dichalcogenides (TMDs) asks for a deeper understanding of what mechanisms lead to topological flat bands in two-dimensional heterostructures, and what makes TMDs an excellent platform for topologically ordered phases, surpassing twisted bilayer graphene. To this aim, we explore the chiral limits of massive Dirac theories applicable to C3-symmetric moiré materials, and show their relevance for both bilayer graphene and TMD homobilayers. In the latter, the Berry curvature of valence bands leads to relativistic corrections of the moiré potential that promote band flattening, and permit a limit with exactly flat bands with nonzero Chern number. The relativistic corrections enter as a layer-orbit coupling, analogous to spin-orbit coupling for relativistic Dirac fermions, which we show is non-negligible on the moiré scale. The Berry curvature of the TMD monolayers therefore plays an essential role in the flattening of moiré Chern bands in these heterostructures.

Optical signatures of moiré trapped biexcitons

Atomically thin heterostructures formed by twisted transition metal dichalcogenides can be used to create periodic moiré patterns. The emerging moiré potential can trap interlayer excitons into arrays of strongly interacting bosons, which form a unique platform to study strongly correlated many-body states. In order to create and manipulate these exotic phases of matter, a microscopic understanding of exciton–exciton interactions and their manifestation in these systems becomes indispensable. Recent density-dependent photoluminescence (PL) measurements have revealed novel spectral features indicating the formation of trapped multi-exciton states providing important information about the interaction strength. In this work, we develop a microscopic theory to model the PL spectrum of trapped multi-exciton complexes focusing on the emission from moiré trapped single- and biexcitons. Based on an excitonic Hamiltonian we determine the properties of trapped biexcitons as function of twist angle and use these insights to predict the luminescence spectrum of moiré excitons for different densities. We demonstrate how side peaks resulting from transitions to excited states and a life time analysis can be utilized as indicators for moiré trapped biexcitons and provide crucial information about the excitonic interaction strength.

Terahertz linear/non-linear anomalous Hall conductivity of moiré TMD hetero-nanoribbons as topological valleytronics materials

Twisted moiré van der Waals heterostructures hold promise to provide a robust quantum simulation platform for strongly correlated materials and realize elusive states of matter such as topological states in the laboratory. We demonstrated that the moiré bands of twisted transition metal dichalcogenide (TMD) hetero-nanoribbons exhibit non-trivial topological order due to the tendency of valence and conduction band states in K valleys to form giant band gaps when spin-orbit coupling (SOC) is taken into account. Among the features of twisted WS2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}/MoS2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document} and WSe2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}/MoSe2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}, we found that the heavy fermions associated with the topological flat bands and the presence of strongly correlated states, enhance anomalous Hall conductivity (AHC) away from the magic angle. By band analysis, we showed that the topmost conduction bands from the ± K-valleys are perfectly flat and carry a spin/valley Chern number. Moreover, we showed that the non-linear anomalous Hall effect in moiré TMD hetero-nanoribbons can be used to manipulate terahertz (THz) radiation. Our findings establish twisted heterostructures of group-VI TMD nanoribbons as a tunable platform for engineering topological valley quantum phases and THz non-linear Hall conductivity.

Polaron-induced changes in moiré exciton propagation in twisted van der Waals heterostructures.

Twisted transition metal dichalcogenides (TMDs) present an intriguing platform for exploring excitons and their transport properties. By introducing a twist angle, a moiré superlattice forms, providing a spatially dependent exciton energy landscape. Based on a microscopic many-particle theory, we investigate in this work polaron-induced changes in exciton transport properties in the exemplary MoSe2/WSe2 heterostructure. We demonstrate that polaron formation and the associated enhancement of the moiré exciton mass lead to a significant band flattening. As a result, the moiré inter-cell tunneling and the propagation velocity undergo noticeable temperature and twist-angle dependent changes. We predict a reduction of the hopping strength ranging from 80% at a twist angle of 1° to 30% at 3° at room temperature. The provided microscopic insights into the spatio-temporal exciton dynamics in presence of a moiré potential further expand the possibilities to tune charge and energy transport in 2D materials.

Probing the Twist-Controlled Interlayer Coupling in Artificially Stacked Transition Metal Dichalcogenide Bilayers by Second-Harmonic Generation.

Interlayer coupling plays a critical role in the electronic band structures and optoelectronic properties of van der Waals (vdW) materials and heterostructures. Here, we utilize optical second-harmonic generation (SHG) measurements to probe the twist-controlled interlayer coupling in artificially stacked WSe2/WSe2 homobilayers and WSe2/WS2 and WSe2/MoS2 heterobilayers with a postannealing procedure. In the large angle twisted WSe2/WSe2 and WSe2/WS2, the angular dependence of the SHG intensity follows the interference relations up to angles above 10°. For lower angles, the SHG is significantly suppressed. Furthermore, for the twisted WSe2/MoS2 the SHG intensity largely deviates from the coherent superposition model and shows consistent quenching for all the stacking angles. The suppressed SHG in twisted transition metal dichalcogenide (TMDC) bilayers is predominantly attributed to the interlayer coupling between the two adjacent monolayers. The evolution of the interlayer Raman mode in WSe2 demonstrates that the interlayer coupling in the twisted WSe2/WSe2 and WSe2/WS2 is highly angle-dependent. Alternatively, the interlayer coupling generally exists in the twisted WSe2/MoS2, regardless of the different angles. The interlayer coupling is further confirmed by the quenching and red-shift of the photoluminescence of WSe2 in the twisted TMDC bilayers. Combined with density functional theory calculations, we reveal that the stacking-angle-modulated interlayer coupling originates from the variation of the interlayer spacing and the binding energy in the twisted TMDC bilayers.

Twist-Induced Modification in the Electronic Structure of Bilayer WSe2.

The recent discovery of strongly correlated phases in twisted transition-metal dichalcogenides (TMDs) highlights the significant impact of twist-induced modifications on electronic structures. In this study, we employed angle-resolved photoemission spectroscopy with submicrometer spatial resolution (μ-ARPES) to investigate these modifications by comparing valence band structures of twisted (5.3°) and nontwisted (AB-stacked) bilayer regions within the same WSe2 device. Relative to the nontwisted region, the twisted area exhibits pronounced moiré bands and ∼90 meV renormalization at the Γ-valley, substantial momentum separation between different layers, and an absence of flat bands at the K-valley. We further simulated the effects of lattice relaxation, which can flatten the Γ-valley edge but not the K-valley edge. Our results provide a direct visualization of twist-induced modifications in the electronic structures of twisted TMDs and elucidate their valley-dependent responses to lattice relaxation.

Mott-moiré excitons

We develop a systematic theory for excitons subject to Fermi-Hubbard physics in moir\'e twisted transition metal dichalcogenides (TMDs). Specifically, we consider excitons in moir\'e systems for which the valence band is in the Mott-insulating regime. These "Mott-moir\'e excitons", which are achievable in twisted TMD heterobilayers, are bound states of a magnetic polaron in the valence band and a free electron in the conduction band. We find significantly narrower exciton bandwidths in the presence of Hubbard physics, serving as a potential experimental signature of strong correlations. We also demonstrate the high tunability of Mott-moir\'e excitons through the dependence of their binding energies, diameters, and bandwidths on the moir\'e period. Our work provides guidelines for future exploration of strongly correlated excitons in twisted TMD heterobilayers.

Staggered pseudo magnetic field in twisted transition metal dichalcogenides: Physical origin and experimental consequences

In systems comprised of two layers of certain semiconductors stacked with a certain twist angle, the quantum mechanics of electron transfer between layers is believed to give rise to a ``staggered flux'' physics in which electrons move as though exposed to an extremely strong, but rapidly spatially varying, magnetic field. This staggered flux, heretofore thought of as a theoretical construct, is shown to give rise to dramatic, observable behavior, including ``Hofstadter butterfly'' structures in the electron spectrum, sign reversals in the Hall effect, and edge currents in systems with junctions or spatially varying interlayer potentials.

Light driven magnetic transitions in transition metal dichalcogenide heterobilayers

Motivated by the recent excitement around the physics of twisted transition metal dichalcogenide (TMD) multilayer systems, we study strongly correlated phases of TMD heterobilayers under the influence of light. We consider both waveguide light and circularly polarized light. The former allows for longitudinally polarized light, which in the high frequency limit can be used to selectively modify interlayer hoppings in a tight-binding model. We argue based on quasi-degenerate perturbation theory that changes to the interlayer hoppings can be captured as a modulation to the strength of the moiré potential in a continuum model. As a consequence, waveguide light can be used to drive transitions between a myriad of different magnetic phases, including a transition from a 120∘ Neel phase to a stripe ordered magnetic phase, or from a spin density wave phase to a paramagnetic phase, among others. When the system is subjected to circularly polarized light we find that the effective mass of the active TMD layer is modified by an applied electromagnetic field. By simultaneously applying waveguide light and circularly polarized light to a system, one has a high level of control in moving through the phase diagram in-situ. Lastly, we comment on the experimental feasibility of Floquet state preparation and argue that it is within reach of available techniques when the system is coupled to a judiciously chosen bath.

Observation of Γ -Valley Moiré Bands and Emergent Hexagonal Lattice in Twisted Transition Metal Dichalcogenides

Twisted van der Waals heterostructures have recently been proposed as a condensed-matter platform for realizing controllable quantum models due to the low-energy moir\'e bands with specific charge distributions in moir\'e superlattices. Here, combining angle-resolved photoemission spectroscopy with sub-micron spatial resolution ({\mu}-ARPES) and scanning tunneling microscopy (STM), we performed a systematic investigation on the electronic structure of 5.1{\deg} twisted bilayer WSe2 that hosts correlated insulating and zero-resistance states. Interestingly, contrary to one's expectation, moir\'e bands were observed only at {\Gamma}-valley but not K-valley in {\mu}-ARPES measurements; and correspondingly, our STM measurements clearly identified the real-space honeycomb- and Kagome-shaped charge distributions at the moir\'e length scale associated with the {\Gamma}-valley moir\'e bands. These results not only reveal the unsual valley dependent moir\'e-modified electronic structure in twisted transition metal dichalcogenides, but also highlight the {\Gamma}-valley moir\'e bands as a promising platform for exploring strongly correlated physics in emergent honeycomb and Kagome lattices at different energy scales.

Evidence for moiré intralayer excitons in twisted WSe2/WSe2 homobilayer superlattices

Recent advances in twisted van der Waals heterostructure superlattices have emerged as a powerful and attractive platform for exploring novel condensed matter physics due to the interplay between the moiré potential and Coulomb interactions. The moiré superlattices act as a periodic confinement potential in space to capture interlayer excitons (IXs), resulting in moiré exciton arrays, which provide opportunities for quantum emitters and many-body physics. The observation of moiré IXs in twisted transition-metal dichalcogenide (TMD) heterostructures has recently been widely reported. However, the capture and study of the moiré intralayer excitons based on TMD twisted homobilayer (T-HB) remain elusive. Here, we report the observation of moiré intralayer excitons in a WSe2/WSe2 T-HB with a small twist angle by measuring PL spectrum. The multiple split peaks with an energy range of 1.55–1.73 eV are different from that of the monolayer WSe2 exciton peaks. The split peaks were caused by the trapping of intralayer excitons via the moiré potential. The confinement effect of the moiré potential on the moiré intralayer excitons was further demonstrated by the changing of temperature, laser power, and valley polarization. Our findings provide a new avenue for exploring new correlated quantum phenomena and their applications.

Multifaceted moiré superlattice physics in twisted WSe2 bilayers

Lattice reconstruction in twisted transition-metal dichalcogenide (TMD) bilayers gives rise to piezo- and ferroelectric moir\'e potentials for electrons and holes, as well as a modulation of the hybridisation across the bilayer. Here, we develop hybrid $\mathbf{k}\cdot \mathbf{p}$ tight-binding models to describe electrons and holes in the relevant valleys of twisted TMD homobilayers with parallel (P) and anti-parallel (AP) orientations of the monolayer unit cells. We apply these models to describe moir\'e superlattice effects in twisted WSe${}_2$ bilayers, in conjunction with microscopic \emph{ab initio} calculations, and considering the influence of encapsulation, pressure and an electric displacement field. Our analysis takes into account mesoscale lattice relaxation, interlayer hybridisation, piezopotentials, and a weak ferroelectric charge transfer between the layers, and describes a multitude of possibilities offered by this system, depending on the choices of P or AP orientation, twist angle magnitude, and electron/hole valley.

Spin liquid in twisted homobilayers of group-VI dichalcogenides

Twisted transition metal dichalcogenide (TMD) homobilayers have recently emerged as a powerful platform for studying correlated insulating states. In the strongly correlated limit, we construct an effective spin Hamiltonian on a honeycomb lattice that includes the Heisenberg interaction and nonsymmetric interactions such as a Dzyaloshinskii-Moriya interaction and a Kane-Mele coupling for the Mott-insulating phase at half-filling. For the twisted TMD homobilayers, the spin-orbit coupling in the Hubbard model, which is expected to induce the antisymmetric exchange couplings in the effective spin Hamiltonian, is a highly tunable and experimentally accessible quantity that can be tuned by an applied electric field. In this study, we investigate classical and quantum phase diagrams of the effective spin Hamiltonian using analytical and numerical methods. We show that the model exhibits a rich classical phase diagram including an antiferromagnetic (AFM) phase, a planar spiral ordered phase with high classical degeneracy, a $z$-AFM phase, a noncoplanar phase, a noncollinear phase, and a 120$^{\circ}$-AFM phase. In the quantum treatment, we calculate low-energy magnon excitation spectrum, ground state energy, and static spin structure factor using linear spin-wave theory and density matrix renormalization group methods to compose the quantum phase diagram of the effective spin Hamiltonian. Beyond the Heisenberg interaction, we find that the existence of these antisymmetric couplings is responsible for the quantum spin liquid, $z$-AFM, noncoplanar, and 120$^{\circ}$ phases. Twisted TMD homobilayers, therefore, offer rich platforms for realizing rich phases of matter such as quantum spin liquid, noncoplanar, and 120$^{\circ}$, resulting from the spin-orbit coupling.

Generalized Wigner crystallization in moiré materials

Recent experiments on the twisted transition metal dichalcogenide (TMD) material, $\rm WSe_2/WS_2$, have observed insulating states at fractional occupancy of the moir\'e bands. Such states were conceived as generalized Wigner crystals (GWCs). In this article, we investigate the problem of Wigner crystallization in the presence of an underlying (moir\'e) lattice. Based on the best estimates of the system parameters, we find a variety of homobilayer and heterobilayer TMDs to be excellent candidates for realizing GWCs. In particular, our analysis based on $r_{s}$ indicates that $\rm MoSe_{2}$ (among the homobilayers) and $\rm MoSe_2/WSe_2$ or $\rm MoS_2/ WS_2$ (among the heterobilayers) are the best candidates for realizing GWCs. We also establish that due to larger effective mass of the valence bands, in general, hole-crystals are easier to realize that electron-crystals as seen experimentally. For completeness, we show that satisfying the Mott criterion $n_{\rm Mott}^{1/2} a_{\ast} = 1$ requires densities nearly three orders of magnitude larger than the maximal density for GWC formation. This indicates that for the typical density of operation, HoM or HeM systems are far from the Mott insulating regime. These crystals realized on a moir\'e lattice, unlike the conventional Wigner crystals, are incompressible due the gap arising from pinning with the lattice. Finally, we capture this many-body gap by variationally renormalizing the dispersion of the vibration modes. We show these low-energy modes, arising from coupling of the WC with the moir\'e lattice, can be effectively modeled as a Sine-Gordon theory of fluctuations.

Unveiling Atomic-Scale Moiré Features and Atomic Reconstructions in High-Angle Commensurately Twisted Transition Metal Dichalcogenide Homobilayers.

Twisting the angle between van der Waals stacked 2D layers has recently sparked great interest as a new strategy to tune the physical properties of the materials. The twist angle and associated strain profiles govern the electrical and optical properties of the twisted 2D materials, but their detailed atomic structures remain elusive. Herein, using combined atomic-resolution electron microscopy and density functional theory (DFT) calculations, we identified five unique types of moiré features in commensurately twisted transition metal dichalcogenide (TMD) bilayers. These stacking variants are distinguishable only when the moiré wavelength is short. Periodic lattice strain is observed in various commensurately twisted TMD bilayers. Assisted by Zernike polynomial as a hierarchical active-learning framework, a hexagon-shaped strain soliton network has been atomically unveiled in nearly commensurate twisted TMD bilayers. Unlike stacking-polytype-dependent properties in untwisted structures, the stacking variants have the same electronic structures that suggest twisted bilayer systems are invariant against interlayer gliding.

Spin-valley density wave in moiré materials

We introduce and study a minimum two-orbital Hubbard model on a triangular lattice, which captures the key features of both the trilayer ABC-stacked graphene-boron nitride heterostructure and twisted transition metal dichalcogenides in a broad parameter range. Our model comprises first- and second-nearest neighbor hoppings with valley-contrasting flux that accounts for trigonal warping in the band structure. For the strong-coupling regime with one electron per site, we derive a spin-orbital exchange Hamiltonian and find the semiclassical ground state to be a spin-valley density wave. We show that a relatively small second-neighbor exchange interaction is sufficient to stabilize the ordered state against quantum fluctuations. Effects of spin- and valley Zeeman fields as well as thermal fluctuations are also examined.