Manipulating the valley degree of freedom to encode information for potential valleytronic devices has ignited a new direction in solid-state physics. A significant, fundamental challenge in the field of valleytronics is how to generate and regulate valley-polarized currents by practical ways. Here, we discover a new mechanism of producing valley polarization in a monolayer transition metal dichalcogenides superlattice, in which valley-resolved gaps are formed at the supercell Brillouin zone boundaries and centers due to the intervalley scattering. When the energy of the incident electron is in the gaps, the available states are valley polarized, thus providing a valley-polarized current from the superlattice. We show that the direction and strength of the valley polarization may further be tuned by varying the potential applied the superlattice. The transmission can have a net valley polarization of 55% for a 4-period heterojunction. Moreover, such two valley filters in series may function as an electrostatically controlled giant valleyresistance device, representing a zero magnetic field counterpart to the familiar giant magnetoresistance device.
Recent experimental progresses have demonstrated the great potential of electronic and excitonic moiré superlattices in transition metal dichalcogenides (TMDs) for quantum many-body simulations and quantum optics applications. Here we reveal that the moiré potential landscapes in the TMDs heterostructures have an electrostatic origin from the spontaneous charge transfer across the heterointerfaces dependent on the atomic registry. This allows engineering tunable multi-chromatic superlattices through the interference of moiré potentials from independently configurable heterointerfaces in multil…
Moir{é} superlattice realized in two-dimensional heterostructures offers an exciting platform to access strongly-correlated electronic states. In this work, we study transition metal dichalcogenides (TMD) Moir{é} superlattices with time-reversal-symmetry and nontrivial spin{/valley}-Chern numbers. Utilizing realistic material parameters and the method of exact diagonalization, we find that at a certain twisting angle and fractional filling, gapped fractional topological states, i.e., fractional Chern insulators, are naturally {stabilized} by simply introducing the Coulomb repulsion. In contras…
Transition metal dichalcogenide (TMD) bilayers have recently emerged as a robust and tunable moiré system for studying and designing correlated electron physics. In this work, by combining large-scale first principle calculation and continuum model approach, we provide an electronic structure theory that maps long-period heterobilayer TMD superlattices onto diatomic crystals with cations and anions. We find that the interplay between moiré potential and Coulomb interaction leads to filling-dependent charge transfer between MM and MX regions several nanometers apart. We show that the insulating…
Geometrical moiré patterns, generic for almost aligned bilayers of two-dimensional (2D) crystals with similar lattice structure but slightly different lattice constants, lead to zone folding and miniband formation for electronic states. Here, we show that moiré superlattice (mSL) effects in $\mathrm{MoSe}_2/\mathrm{WS}_2$ and $\mathrm{MoTe}_2/\mathrm{MoSe}_2$ heterobilayers that feature alignment of the band edges are enhanced by resonant interlayer hybridization, and anticipate similar features in twisted homobilayers of TMDs, including examples of narrow minibands close to the actual band ed…
Emergent inhomogeneity and non-locality in a graphene field-effect transistor on a near-parallel moire superlattice of transition metal dichalcogenides
Flexible long period moir\' e superlattices form in two-dimensional van der Waals crystals containing layers that differ slightly in lattice constant or orientation. In this Letter we show theoretically that isolated flat moir\' e bands described by generalized triangular lattice Hubbard models are present in twisted transition metal dichalcogenide heterobilayers. The hopping and interaction strength parameters of the Hubbard model can be tuned by varying the twist angle and the three-dimensional dielectric environment. When the flat moiré bands are partially filled, candidate many-body ground…
In twisted homobilayer transition metal dichalcogenides, intra- and inter-layer valley excitons hybridize with the layer configurations spatially varying in the moiré. The ground state valley excitons are trapped at two high-symmetry points with opposite electric dipoles in a moiré supercell, forming a honeycomb superlattice of nearest-neighbor dipolar attraction. We find that the spatial texture of layer configuration results in a luminescence anomaly of the moiré trapped excitons, where a tiny displacement by interactions dramatically increases the brightness and changes polarization from ci…
Using a multiscale computational approach, we probe the origin and evolution of ultraflatbands in moiré superlattices of twisted bilayer MoS$_2$, a prototypical transition metal dichalcogenide. Unlike twisted bilayer graphene, we find no unique magic angles in twisted bilayer MoS$_2$ for flatband formation. Ultraflatbands form at the valence band edge for twist angles ($θ$) close to 0$^\circ$ and at both the valence and conduction band edges for $θ$ close to 60$^\circ$, and have distinct origins. For$ θ$ close to 0$^\circ$, inhomogeneous hybridization in the reconstructed moiré superlattice is…
In a number of widely-studied materials, such as Si, AlAs, Bi, graphene, MoS2, and many transition metal dichalcogenide monolayers, electrons acquire an additional, spin-like degree of freedom at the degenerate conduction band minima, also known as "valleys". External symmetry breaking fields such as mechanical strain, or electric or magnetic fields, can tune the valley-polarization of these materials making them suitable candidates for "valleytronics". Here we study a quantum well of AlAs, where the two-dimensional electrons reside in two energetically degenerate valleys. By fabricating a str…
Moiré superlattices serve as a playground for emerging phenomena, such as localization of band states, superconductivity, and localization of excitons. These superlattices are large and are often modeled in the zero angle limit, which obscures the effect of finite twist angles. Here, by means of first-principles calculations we quantify the twist-angle dependence of the moiré potential in the MoS$_2$ homobilayer and identify the contributions from the constituent elements of the moiré potential. Furthermore, by considering the zero-angle limit configurations, we show that the moiré potential i…
Using the tight-binding approach, we analyze the effect of a one-dimensional superlattice (1DSL) potential on the electronic structure of black phosphorene and transition metal dichalcogenides. We observe that the 1DSL potential results in a decrease of the energy band gap of the two-dimensional (2D) materials. An analytical model is presented to relate the decrease in the direct-band gap to the different orbital characters between the valence band top and conduction band bottom of the 2D materials. The direct-to-indirect gap transition, which occurs under a 1DSL potential with an unequal barr…
Moiré patterns with a superlattice potential can be formed by vertically stacking two layered materials with a relative twist or lattice constant mismatch. The moiré superlattice can generate flat bands that result in new correlated insulating, superconducting, and topological states. Strong electron correlations, tunable by the fractional filling, have been observed in both graphene and transition metal dichalcogenide (TMD) based systems. In addition, in TMD based systems, the moiré potential landscape can trap interlayer excitons (IX) at specific atomic registries. Here we report that spatia…
Although there is strong theoretical and experimental evidence for electron-hole superfluidity in separated sheets of electrons and holes at low $T$, extending superfluidity to high $T$ is limited by strong 2D fluctuations and Kosterlitz-Thouless effects. We show this limitation can be overcome using a superlattice of alternating electron- and hole-doped semiconductor monolayers. The superfluid transition in a 3D superlattice is not topological, and for strong electron-hole pair coupling, the transition temperature $T_c$ can be at room temperature. As a quantitative illustration, we show $T_c$…
We perform a comprehensive first-principles study of the electronic properties of van der Waals (vdW) trilayers via intercalating a two-dimensional (2D) monolayer (ML = BN, MoSe2, WS2, or WSe2) between MoS2 bilayer to form various MoS2/ML/MoS2 sandwich trilayers. We find that the BN monolayer is the most effective sheet to decouple the interlayer vdW coupling of the MoS2 bilayer, and the resulting sandwich trilayer can recover the electronic structures of the MoS2 monolayer, particularly the direct-gap character. Further study of the MoS2/BN superlattices confirms the effectiveness of the BN m…
Lateral superlattices in 2D materials are emerging as a powerful platform for exploring novel quantum phenomena, which can be realized through the proximity coupling in forming moiré pattern with another layer. This approach, however, is invasive, material-specific, and requires small lattice mismatch and suitable band alignment, largely limited to graphene and transition metal dichalcogenides (TMDs). Hexagonal boron nitride (h-BN) of anti-parallel (AA') stacking order has been an indispensable building block, as dielectric substrates and capping layers for realizing high quality van der Waals…
Heterostructure materials form the basis of much of modern electronics, from transistors to lasers and light-emitting diodes. Recent years have seen a renewed focus on creating heterostructures through the vertical integration of two-dimensional materials, including graphene, hexagonal boron nitride, and transition metal dichalcogenides (TMDCs). However, fundamental challenges associated with materials processing have limited material quality and impeded scalability. We demonstrate a method to convert sub-nanometer metal films deposited on silicon and sapphire into TMDC heterostructures throug…
Fabricating van der Waals (vdW) bilayer heterostructures (BL-HS) by stacking the same or different two-dimensional (2D) layers, offers a unique physical system with rich electronic and optical properties. Twist-angle between component layers has emerged as a remarkable parameter that can control the period of lateral confinement, and nature of the exciton (Coulomb bound electron-hole pair) in reciprocal space thus creating exotic physical states including moiré excitons. In this review article, we focus on opto-electronic properties of excitons in transition metal dichalcogenide (TMD) semicond…
Moiré superlattices from stacks of van der Waals materials offer an exciting arena in the fields of condensed matter physics and materials science. Typically, these moiré superlattices consist of materials with identical or similar structures, and the long moiré period arises from a small twist angle or lattice mismatch. In this article, we discuss that long moiré period appears in a new moiré system by stacking two dissimilar van der Waals layers with large lattice mismatch, resulting in couplings between moiré bands from remote valleys in the momentum space. In this system, the first layer i…
We propose to engineer time-reversal-invariant topological insulators in two-dimensional (2D) crystals of transition metal dichalcogenides (TMDCs). We note that, at low doping, semiconducting TMDCs under shear strain will develop spin-polarized Landau levels residing in different valleys. We argue that gaps between Landau levels in the range of $10-100$ Kelvin are within experimental reach. In addition, we point out that a superlattice arising from a Moiré pattern can lead to topologically non-trivial subbands. As a result, the edge transport becomes quantized, which can be probed in multi-ter…
We demonstrate a generic mechanism to realize topological flat minibands by confining massive Dirac fermions in a periodic moiré potential, which can be achieved in a heterobilayer of transition metal dichalcogenides. We show that the topological phase can be protected by the symmetry of moiré potential and survive to arbitrarily large Dirac band gap. We take the MoTe$_2$/WSe$_2$ heterobilayer as an example and find that the topological phase can be driven by a vertical electric field. By projecting the Coulomb interaction onto the topological fat minibands, we identify a correlated Chern insu…
We investigate the optical properties of interlayer excitons in heterobilayer transition metal dichalcogenides where moiré pattern is introduced by heterostrain, in comparison with that introduced by twisting (and/or lattice mismatch). Besides being a cause of the moiré texture, strain also effectively introduces a constant gauge potential on either electron or hole, which shifts the dispersion of kinetic energy with respect to the excitonic crystal momenta in the moiré superlattices.This leads to distinct exciton mini-band dispersions and light coupling properties from the twisting induced mo…
Twisted Van der Waals systems offer the unprecedented possibility to tune different states of correlated quantum matter with an external non-invasive electrostatic doping. The nature of the superconducting order presents a recurring open question in this context. In this work, we quantitatively assess the case of spin-fluctuation-mediated pairing for $Γ$-valley twisted transition metal dichalcogenide homobilayers. We self-consistently and dynamically calculate the doping dependent superconducting transition temperature $T_{\mathrm{c}}$ revealing a superconducting dome with a maximal $T_{\mathr…
Kekulé phases are Peierls-like lattice distortions in graphene that are predicted to host novel electronic states beyond graphene (1-8). Although the Kekulé phases are realized in graphene through introducing electron-electron interactions at high magnetic fields (9-11) or adatom superlattices (12-15), it is still an extremely challenge to obtain large-area graphene Kekulé phases in experiment. Here we demonstrate that sample-wide Kekulé distortions in graphene can be stabilized by using transition metal dichalcogenides (TMDs) as substrates and the induced Kekulé orders are quite robust in the…
The long wavelength moiré superlattices in twisted 2D structures have emerged as a highly tunable platform for strongly correlated electron physics. We study the moiré bands in twisted transition metal dichalcogenide homobilayers, focusing on WSe$_2$, at small twist angles using a combination of first principles density functional theory, continuum modeling, and Hartree-Fock approximation. We reveal the rich physics at small twist angles $θ<4^\circ$, and identify a particular magic angle at which the top valence moiré band achieves almost perfect flatness. In the vicinity of this magic angle, …
Stacking monolayers of transition metal dichalcogenides into a heterostructure with a finite twist-angle gives rise to artificial moiré superlattices with a tunable periodicity. As a consequence, excitons experience a periodic potential, which can be exploited to tailor optoelectronic properties of these materials. While recent experimental studies have confirmed twist-angle dependent optical spectra, the microscopic origin of moiré exciton resonances has not been fully clarified yet. Here, we combine first principle calculations with the excitonic density matrix formalism to study transitions…
Layered van der Waals materials have risen as powerful platforms to artificially engineer correlated states of matter. Here we show the emergence of a multiferroic order in a twisted dichalcogenide bilayer superlattice at quarter-filling. We show that the competition between Coulomb interactions leads to the simultaneous emergence of ferrimagnetic and ferroelectric orders. We derive the magnetoelectric coupling for this system, which leads to a direct strong coupling between the charge and spin orders. We show that, due to intrinsic spin-orbit coupling effects, the electronic structure shows a…
The formation of interfacial moiré patterns from angular and/or lattice mismatch has become a powerful approach to engineer a range of quantum phenomena in van der Waals heterostructures. For long-lived and valley-polarized interlayer excitons in transition-metal dichalcogenide (TMDC) heterobilayers, signatures of quantum confinement by the moiré landscape have been reported in recent experimental studies. Such moiré confinement has offered the exciting possibility to tailor new excitonic systems, such as ordered arrays of zero-dimensional (0D) quantum emitters and their coupling into topologi…
The predicted formation of moire superlattices leading to confined excitonic states in heterostructures formed by stacking two lattice mismatched transition metal dichalcogenide (TMD) monolayers was recently experimentally confirmed. Such periodic potential in TMD heterostructure functions as a diffusion barrier that affects the energy transport and dynamics of interlayer excitons (electron and hole spatially concentrated in different monolayers). Understanding the transport of excitons under such condition is essential to establish the material system as a next generation device platform. In …
The properties of van der Waals (vdW) heterostructures are drastically altered by a tunable moiré superlattice arising from periodic variations of atomic alignment between the layers. Exciton diffusion represents an important channel of energy transport in semiconducting transition metal dichalcogenides (TMDs). While early studies performed on TMD heterobilayers have suggested that carriers and excitons exhibit long diffusion lengths, a rich variety of scenarios can exist. In a moiré crystal with a large supercell size and deep potential, interlayer excitons may be completely localized. As the…
Moiré superlattices of van der Waals heterostructures provide a powerful new way to engineer the electronic structures of two-dimensional (2D) materials. Many novel quantum phenomena have emerged in different moiré heterostructures, such as correlated insulators, superconductors, and Chern insulators in graphene systems and moiré excitons in transition metal dichalcogenide (TMDC) systems. Twisted phosphorene offers another attractive system to explore moiré physics because phosphorene features an anisotropic rectangular lattice, different from the isotropic hexagonal lattice in graphene and TM…
In monolayers of the semiconducting transition metal dichalcogenides, the electron-hole exchange interaction splits the exciton dispersion into a massive transverse branch, and a longitudinal branch that has very light or even zero mass depending on the form of screened Coulomb interaction. The group velocity of the longitudinal branch is sensitive to the strength of electron-hole exchange, which can be engineered through the dielectric environment. Here we show that dielectric patterning of the substrate can be exploited to realize waveguide of the exciton in the longitudinal branch in a homo…
