Twistronic assembly of 2D materials employs the twist angle between adjacent layers as a tuning parameter for designing the electronic and optical properties of van der Waals heterostructures. Here, we study how interlayer hybridization, weak ferroelectric charge transfer between layers, and piezoelectric response to deformations set the valence and conduction band edges across the moir{é} supercell in twistronic homobilayers of MoS$_2$, MoSe$_2$, WS$_2$ and WSe$_2$. We show that, due to the lack of inversion symmetry in the monolayer crystals, bilayers with parallel (P) and anti-parallel (AP) unit cell orientations display contrasting behaviors. For P-bilayers at small twist angles we find band edges in the middle of triangular domains of preferential stacking. In AP-bilayers at marginal twist angles ($θ_{AP} < 1^\circ$) the band edges are located in small regions around the intersections of domain walls, giving highly localized quantum dot states.
We show that moiré bands of twisted homobilayers can be topologically nontrivial, and illustrate the tendency by studying valence band states in $\pm K$ valleys of twisted bilayer transition metal dichalcogenides, in particular, bilayer MoTe$_2$. Because of the large spin-orbit splitting at the monolayer valence band maxima, the low energy valence states of the twisted bilayer MoTe$_2$ at $+K$ ($-K$) valley can be described using a two-band model with a layer-pseudospin magnetic field $\boldsymbolΔ(\boldsymbol{r})$ that has the moiré period. We show that $\boldsymbolΔ(\boldsymbol{r})$ has a to…
We predict that in a twisted homobilayer of transition-metal dichalcogenide MoS$_2$, spin-orbit coupling in the conduction band states from $\pm K$ valleys can give rise to moiré flat bands with nonzero Chern numbers in each valley. The nontrivial band topology originates from a unique combination of angular twist and local mirror symmetry breaking in each individual layer, which results in unusual skyrmionic spin textures in momentum space with skyrmion number $\mathcal{S} = \pm 2$. Our Hartree-Fock analysis further suggests that density-density interactions generically drive the system at $1…
Motivated by the recent experimental realization of twisted transition metal dichalcogenide bilayers, we study a simplified model driven by different forms of monochromatic light. As a concrete and representative example we use parameters that correspond to a twisted MoTe$_2$ homobilayer. First, we consider irradiation with circularly polarized light in free space and demonstrate that the corresponding Floquet Hamiltonian takes the same form as the static Hamiltonian, only with a constant overall shift in quasi-energy. This is in stark contrast to twisted bilayer graphene, where new terms are …
The spatial texture of internal degree of freedom of electrons has profound effects on the properties of materials. Such texture in real space can manifest as an emergent magnetic field (or Berry curvature), which is expected to induce interesting valley/spin-related transport phenomena. Moiré pattern, which emerges as a spatial variation at the interface of 2D atomic crystals, provides a natural platform for investigating such real space Berry curvature effects. Here we study moiré structures formed in homobilayer transition metal dichalcogenides (TMDs) due to twisting, various uniform strain…
Recent experiments have observed correlated insulating and possible superconducting phases in twisted homobilayer transition metal dichalcogenides (TMDs). Besides the spin-valley locked moire bands due to the intrinsic Ising spin-orbit coupling, homobilayer moire TMDs also possess either logarithmic or power-law divergent Van Hove singularities (VHS) near the Fermi surface, controllable by an external displacement field. The former and the latter are dubbed conventional and higher-order VHS, respectively. Here, we perform a perturbative renormalization group (RG) analysis to unbiasedly study t…
Moiré superlattices in twisted van der Waals materials constitute a promising platform for engineering electronic and optical properties. However, a major obstacle to fully understanding these systems and harnessing their potential is the limited ability to correlate the local moiré structure with optical properties. By using a recently developed scanning electron microscopy technique to image twisted WSe$_2$/WSe$_2$ bilayers, we directly correlate increasing moiré periodicity with the emergence of two distinct exciton species. These can be tuned individually through electrostatic gating, and …
The valence band maxima of most group-VI transition metal dichalcogenide thin films remain at the $Γ$-point all the way from bulk to bilayer. In this paper we develop a continuum theory of the moirè minibands that are formed in the valence bands of $Γ$-valley homobilayers by a small relative twist. Our effective theory is benchmarked against large-scale ab initio electronic structure calculations that account for lattice relaxation. As a consequence of an emergent $D_6$ symmetry we find that low-energy $Γ$-valley moirè holes differ qualitatively from their K-valley counterparts addressed previ…
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…
Janus dichalcogenide multilayers provide a paradigmatic platform to engineer electronic phenomena dominated by spin-orbit coupling. Their unique spin-orbit effects stem from local mirror symmetry breaking in each layer, which induces a colossal Rashba spin-orbit effect in comparison with the conventional dichalcogenide counterparts. Here we put forward twisted dichalcogenide bilayers as a simple platform to realize spin-orbit correlated states. We demonstrate the emergence of flat bands featuring strong spin-momentum locking and the emergence of non-collinear symmetry broken states when intera…
Twisted van der Waals materials have become a paradigmatic platform to realize exotic correlated states of matter. Here, we show that a twisted dichalcogenide bilayer (WSe$_2$) encapsulated between a magnetic van der Waals material (CrBr$_3$) features flat bands with tunable valley and spin flavors. We demonstrate that, when electron-electron interactions are included, spin-ferromagnetic and valley-ferromagnetic states emerge in the flat bands, stemming from the interplay between correlations, intrinsic spin-orbit coupling and exchange proximity effects. We show that the specific symmetry brok…
We present a comprehensive dynamical mean field study of the triangular lattice moiré Hubbard model, which is believed to represent the physics of moiré bilayer transition metal dichalcogenides. In these materials, important aspects of the band structure including the bandwidth and the order and location of van Hove singularities can be tuned by varying the interlayer potential. We present a magnetic and metal-insulator phase diagram and a detailed study of the dependence of the resistivity on temperature, band filling and interlayer potential. We find that transport displays Fermi liquid, str…
The crystal structure of a material creates a periodic potential that electrons move through giving rise to the electronic band structure of the material. When two-dimensional materials are stacked, the twist angle between the layers becomes an additional degree freedom for the resulting heterostructure. As this angle changes, the electronic band structure is modified leading to the possibility of flat bands with localized states and enhanced electronic correlations. In transition metal dichalcogenides, flat bands have been theoretically predicted to occur for long moiré wavelengths over a ran…
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, …
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…
We show that a sliding motion between the two layers of a \moire superlattice induces an electric current and realizes a two-dimensional version of the topological Thouless pump when the Fermi energy lies in one of the minigaps. Interestingly, a chiral charge pump, namely, a transverse current induced by the sliding motion, is possible in twisted homobilayers. This result is confirmed by a concrete calculation of the adiabatic current in twisted bilayer graphene. Our work reveals an interesting link between mechanical motion and electricity unique to \moire superlattices, and may find applicat…
We apply a multiscale modeling approach to study lattice reconstruction in marginally twisted bilayers of transition metal dichalcogenides (TMD). For this, we develop DFT-parametrized interpolation formulae for interlayer adhesion energies of MoSe$_2$, WSe$_2$, MoS$_2$, and WS$_2$, combine those with elasticity theory, and analyze the bilayer lattice relaxation into mesoscale domain structures. Paying particular attention to the inversion asymmetry of TMD monolayers, we show that 3R and 2H stacking domains, separated by a network of dislocations develop for twist angles $θ^{\circ}<θ^{\circ}_P\…
We reveal by first-principles calculations that the interlayer binding in a twisted MoS2/MoTe2 heterobilayer decreases with increasing twist angle, due to the increase of the interlayer overlapping degree, a geometric quantity describing well the interlayer steric effect. The binding energy is found to be a Gaussian-like function of twist angle. The resistance to rotation, an analogue to the interlayer sliding barrier, can also be defined accordingly. In sharp contrast to the case of MoS2 homobilayer, here the energy band gap reduces with increasing twist angle. We find a remarkable interlayer…
Using a multiscale computational approach, we probe the origin and evolution of ultraflatbands in moiré superlattices of twisted bilayer MoS$_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…
Twisted bilayer transition metal dichalcogenides are ideal platforms to study flat-band phenomena. In this paper, we investigate flat-band plasmons in the hole-doped twisted bilayer MoS$_2$ (tb-MoS$_2$) by employing a full tight-binding model and the random phase approximation. When considering lattice relaxations in tb-MoS$_2$, the flat band is not separated from remote valence bands, which makes the contribution of interband transitions in transforming the plasmon dispersion and energy significantly different. In particular, low-damped and quasi-flat plasmons emerge if we only consider intra…
A major theoretical challenge of studying twisted transition metal dichalcogenide (TMD) bilayers is that the unit cell of such structures is very large and therefore difficult to address using first-principles methods. However, twisted TMD bilayers form moiré patterns, which consist of regions of commensurate stacking, either smoothly interpolated into one another or separated by sharp domain walls. In this paper, we study twisted TMD bilayers by studying the properties of the constituent commensurate structures. Using density functional theory (DFT), we compute band structures for commensurat…
Ultraflatbands that have been theoretically and experimentally detected in a bunch of van der Waals stacked materials showing some peculiar properties, for instance, highly localized electronic states and enhanced electron-electron interactions. In this Letter, using an accurate tight-binding model, we study the formation and evolution of ultraflatbands in transition metal dichalcogenides (TMDCs) under low rotation angles. We find that, unlike in twisted bilayer graphene, ultraflatbands exist in TMDCs for almost any small twist angles and their wave function becomes more localized when the rot…
The advent of twisted moiré heterostructures as a playground for strongly correlated electron physics has led to a plethora of experimental and theoretical efforts seeking to unravel the nature of the emergent superconducting and insulating states. Amongst these layered compositions of two dimensional materials, transition metal dichalcogenides (TMDs) are by now appreciated as highly-tunable platforms to simulate reinforced electronic interactions in the presence of low-energy bands with almost negligible bandwidth. Here, we focus on the twisted homobilayer WSe$_2$ and the insulating phase at …
In bilayers of semiconducting transition metal dichalcogenides, the twist angle between layers can be used to introduce a highly regular periodic potential modulation on a length scale that is large compared to the unit cell. In such structures, correlated states can emerge, in which excitons in the heterostructure are strongly localized to the potential minima due to exciton-exciton interactions. We explore the transition between Mott and extended exciton phases in terms of a moiré-Bose-Hubbard Hamiltonian. Hopping and on-site interaction parameters are obtained from a Wannier representation …
In moiré heterostructures, gate-tunable insulating phases driven by electronic correlations have been recently discovered. Here, we use transport measurements to characterize the gate-driven metal-insulator transitions and the metallic phase in twisted WSe$_2$ near half filling of the first moiré subband. We find that the metal-insulator transition as a function of both density and displacement field is continuous. At the metal-insulator boundary, the resistivity displays strange metal behaviour at low temperature with dissipation comparable to the Planckian limit. Further into the metallic ph…
