Moiré superlattices formed in two-dimensional semiconductor heterobilayers provide a new realization of Hubbard model physics in which the number of electrons per effective atom can be tuned at will. We report on an exact diagonalization study of the electronic properties of half-filled narrow moiré bands in which correlation strengths are varied by changing twist angles or interaction strengths. We construct a phase diagram for the bilayer, identifying where the metal-insulator phase transition occurs, estimating the sizes of the charge gaps in the insulating phase, and commenting on the nature of the transition and the importance of sub-dominant interaction parameters.
Moiré superlattice systems such as transition metal dichalcogenide heterobilayers have garnered significant recent interest due to their promising utility as tunable solid state simulators. Recent experiments on a WSe$_2$/WS$_2$ heterobilayer detected incompressible charge ordered states that one can view as generalized Wigner crystals. The tunability of the hetero-TMD Moiré system presents an opportunity to study the rich set of possible phases upon melting these charge-ordered states. Here we use Monte Carlo simulations to study these intermediate phases in between incompressible charge-orde…
We study untwisted heterobilayers of ferromagnetic and antiferromagnetic van der Waals materials, with in particular a Dzyaloshinskii-Moriya interaction in the ferromagnetic layer. A continuum low energy field theory is utilized to study such systems. We develop a phase diagram as a function of the strength of inter-layer exchange and Dzyaloshinskii-Moriya interactions, combining perturbative and strong coupling analyses with numerical simulations using Landau-Lifshitz-Gilbert equations. Various moiré-periodic commensurate phases are found, and the commensurate-incommensurate transition is dis…
Moiré heterobilayer transition metal dichalcogenides (TMDs) emerge as an ideal system for simulating the single-band Hubbard model and interesting correlated phases have been observed in these systems. Nevertheless, the moiré bands in heterobilayer TMDs were believed to be topologically trivial. Recently, it was reported that both a quantum valley Hall insulating state at filling $ν=2$ (two holes per moiré unit cell) and a valley-polarized quantum anomalous Hall state at filling $ν=1$ were observed in AB stacked moiré MoTe$_2$/WSe$_2$ heterobilayers. However, how the topologically nontrivial s…
The valence flat bands in transition metal dichalcogenide (TMD) heterobilayers are shown to exhibit strong intralayer spin-orbit coupling. This is reflected in a simple tight-binding model with spin-dependent complex hoppings based on the continuum model. A perpendicular electric field causes interlayer hybridization, such that the effective model is equivalent to the Kane-Mele model of topological insulators. The proposed model can be used as a starting point to understand interactions and the experimentally observed topological phases.
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 …
We propose a new mechanism to explain the quantum anomalous Hall (QAH) effect and the electric-field-induced topological phase transition in AB-stacked MoTe${}_2$/WSe${}_2$ moiré heterobilayers at $ν=1$ hole filling. We suggest that the Chern band of the QAH state is generated from an intrinsic band inversion composed of the highest two moiré hole bands with opposite valley numbers and a gap opening induced by two Coulomb-interaction-driven magnetic orders. These magnetic orders, including an in-plane $120^{\circ}$-Néel order and an in-plane ferromagnetic order, interact with moiré bands via c…
We theoretically consider two-dimensional moiré transition metal dichalcogenide (TMD) bilayers, which are strongly correlated in the sense that the on-site Coulomb interaction is comparable to or larger than the hopping kinetic energy between the moiré lattice sites. The system accommodates many symmetry-broken ground states both in charge and isospin sectors at various commensurate rational fillings such as 1/2, 1/3, 1/4, 2/3, etc. We investigate two complementary important aspects of the dependence of the symmetry breaking on (1) the range of the electron-electron interaction, which can in p…
Twisted van der Waals heterostructures have recently been proposed as a condensed-matter platform for realizing controllable quantum models due to the low-energy moiré bands with specific charge distributions in moiré superlattices. Here, combining angle-resolved photoemission spectroscopy with sub-micron spatial resolution (μ-ARPES) and scanning tunneling microscopy (STM), we performed a systematic investigation on the electronic structure of 5.1° twisted bilayer WSe2 that hosts correlated insulating and zero-resistance states. Interestingly, contrary to one's expectation, moiré bands were ob…
Charge separated interlayer excitons in transition metal dichalcogenide (TMDC) heterobilayers are being explored for moiré exciton lattices and exciton condensates. The presence of permanent dipole moments and the poorly screened Coulomb interaction make many body interactions particularly strong for interlayer excitons. Here we reveal two distinct phase transitions for interlayer excitons in the MoSe2/WSe2 heterobilayer using time and spatially resolved photoluminescence imaging: from trapped excitons in the moiré-potential to the modestly mobile exciton gas as exciton density increases to ne…
Twisted bilayer transition metal dichalcogenides have emerged as important model systems for the investigation of correlated electron physics because their interaction strength, carrier concentration, band structure, and inversion symmetry breaking are controllable by device fabrication, twist angle, and most importantly, gate voltage, which can be varied in situ. The low energy physics of some of these materials has been shown to be described by a "moiré Hubbard model" generalized from the usual Hubbard model by the addition of strong, tunable spin orbit coupling and inversion symmetry breaki…
Moiré materials formed in two-dimensional semiconductor heterobilayers are quantum simulators of Hubbard-like physics with unprecedented electron-density and interaction-strength tunability. Compared to atomic scale Hubbard-like systems, electrons or holes in moiré materials are less strongly attracted to their effective lattice sites because these are defined by finite-depth potential extrema. As a consequence, non-local interaction terms like interaction-assisted hopping and intersite-exchange are more relevant. We theoretically demonstrate the possibility of tuning the strength of these cou…
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…
Experimental demonstrations of tunable correlation effects in magic-angle twisted bilayer graphene have put two-dimensional moiré quantum materials at the forefront of condensed-matter research. Other twisted few-layer graphitic structures, boron-nitride, and homo- or hetero-stacks of transition metal dichalcogenides (TMDs) have further enriched the opportunities for analysis and utilization of correlations in these systems. Recently, within the latter material class, strong spin-orbit coupling or excitonic physics were experimentally explored. The observation of a Mott insulating state and ot…
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…
Small-twist-angle transition metal dichalcogenide (TMD) heterobilayers develop isolated flat moiré bands that are approximately described by triangular lattice generalized Hubbard models [PhysRevLett.121.026402]. In this article we explore the metallic and insulating states that appear under different control conditions at a density of one-electron per moiré period, and the transitions between them. By combining fully self-consistent Hartree-Fock theory calculations with strong-coupling expansions around the atomic limit, we identify four different magnetic states and one nonmagnetic state nea…
Heterobilayer transition metal dichalcogenide (TMDC) moiré systems provide an ideal framework to investigate strongly correlated physics. Here we theoretically study bosonic many-body phases of excitons in moiré TMDCs. By using two moiré models and cluster mean-field theory, we reveal that, due to non-local Coulomb interactions, moiré excitons can feature exotic supersolid phases, i.e. superfluids of broken translational invariance, and correlated insulating states. The correlated phases exist at experimentally accessible temperatures and are tunable via the twist angle and exciton density.
While transition metal dichalcogenide (TMD) based moire materials have been shown to host various correlated electronic phenomena, topological states have not been experimentally observed until now. In this work, using first principles calculations and continuum modeling, we reveal the displacement field induced topological moire bands in AB-stacked TMD heterobilayer MoTe2/WSe2. Valley contrasting Chern bands with non-trivial spin texture are formed from interlayer hybridization between MoTe2 and WSe2 bands of nominally opposite spins. Our study establishes a recipe for creating topological ba…
Spontaneous order of layer pseudospins in two-dimensional bilayers is common in quantum Hall systems, where it is responsible for hysteretic responses to gate fields in states with Ising order, and giant drag voltages in states with XY (spontaneous inter-layer phase coherence) order. In this article we predict that layer pseudospin order will also occur in double-moiré strongly correlated two-dimensional electron systems. We comment on similarities and differences in the competition between the two types of order in quantum Hall and double-moiré systems, and relate our findings to previous wor…
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…
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…
We show that the "dark condensates" that arise when excitons form a Bose-Einstein condensate in a material with an indirect bandgap are not completely dark to optical emission. Rather, such states are "leaky condensates" in which optical emission is facilitated by many-body interactions. We analyze the properties of these leaky condensates in the context of twisted bilayers of transition metal dichalcogenides, which host strongly interacting excitons and an indirect bandgap. We show that this interaction-driven "leaky" emission dominates photoluminescence at low temperatures, with distinctive …
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…
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…
Twisted multilayers of two-dimensional (2D) materials are an increasingly important platform for investigating quantum phases of matter, and in particular, strongly correlated electrons. The moiré pattern introduced by the relative twist between layers creates effective potentials of long-wavelength, leading to electron localization. However, in contrast to the abundance of 2D materials, few twisted heterostructures have been studied until now. Here we develop a first-principle continuum theory to study the electronic bands introduced by moire patterns of twisted Janus transition metal dichalc…
Moire superlattices of transition metal dichalcogenide (TMD) bilayers have been shown to host correlated electronic states, which arises from the interplay of emergent moire potential and long-range Coulomb interactions. Here we theoretically investigate structural relaxation and single-particle electronic properties in moire superlattices of transition metal dichalcogenide homobilayer and study the ground state charge orders in the effective honeycomb lattice of MX and XM region. From the large-scale density functional theory calculation and continuum model with layer degrees of freedom, we f…
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, …
