Continuous Mott transition in semiconductor moiré superlattices

Correlated states controlled by a tunable van Hove singularity in moiré WSe2 bilayers

Twisted transition metal dichalcogenide (TMD) bilayers have enabled the discovery of superconductivity, ferromagnetism, correlated insulators, and a series of new topological phases of matter. However, the connection between these electronic phases of matter and the underlying band structure singularities has remained largely unexplored. Here, combining magnetic circular dichroism and exciton sensing measurements, we investigate the influence of a van Hove singularity (vHS) on the correlated phases in bilayer WSe2 with twist angle between 2 and 3 degrees. By tuning the vHS across the Fermi level using electric and magnetic fields, we observe Stoner ferromagnetism below moiré lattice filling one and Chern insulators at filling one. The experimental observations are supported by the continuum model band structure calculations. Our results highlight the prospect of engineering electronic phases of matter in moiré materials by tunable van Hove singularities.

Theory of correlated insulators and superconductor at ν = 1 in twisted WSe2

The observation of a superconducting phase, an intertwined insulating phase, and a continuous transition between the two at a commensurate filling of ν = 1 in bilayers of twisted WSe2 at θ = 3.650 raises a number of intriguing questions about the origin of this phenomenology. Here we report the possibility of a displacement-field induced continuous transition between a superconductor and a quantum spin-liquid Mott insulator at ν = 1, starting with a simplified three-orbital model of twisted WSe2, including on-site, nearest-neighbor density-density interactions, and a chiral-exchange interaction, respectively. By employing parton mean-field theory, we discuss the nature of these correlated insulators, their expected evolution with the displacement-field, and their phenomenological properties.

Multiple Chern Bands in Twisted MoTe_{2} and Possible Non-Abelian States

We investigate the moiré band structures and a possible even-denominator fractional quantum Hall state in small angle twisted bilayer MoTe_{2}, using combined large-scale local basis density functional theory calculation and continuum model exact diagonalization. Via large-scale first-principles calculations at θ=1.89°, we find a sequence of C=1 (Chern number in the K valley) moiré Chern bands in analogy to Landau levels. By constructing the continuum model with multiple Chern bands, we undertake a band-projected exact diagonalization using an unscreened Coulomb repulsion to identify possible non-Abelian states near twist angle θ=1.89° at the half filling of second moiré band.

Ultraviolet-Complete Local Field Theory of Persistent Symmetry Breaking in 2+1 Dimensions

Spontaneous symmetry breaking can persist at all temperatures in certain biconical O(N)×Z_{2} vector models when the underlying field theories are ultraviolet complete. So far, the existence of such theories has been established in fractional dimensions for local but nonunitary models or in 2+1 dimensions but for nonlocal models. Here, we study local models at zero and finite temperature directly in 2+1 dimensions employing functional methods. At zero temperature, we establish that our approach describes the quantum critical behavior with good accuracy for all N≥2. We then exhibit the mechanism of discrete symmetry breaking from O(N)×Z_{2}→O(N) for increasing temperature near the biconical critical point when N is finite but large. We calculate the corresponding finite-temperature phase diagram and further show that the Hohenberg-Mermin-Wagner theorem is fully respected within this approach, i.e., symmetry breaking only occurs in the Z_{2} sector. Finally, we determine the critical N above which this phenomenon can be observed to be N_{c}≈15.

Valley charge-transfer insulator in twisted double bilayer WSe2

In flat-band systems, emergent physics can be substantially modified by the presence of another nearby electronic band. For example, a Mott˘Hubbard insulator can turn into a charge transfer insulator if other electronic states enter between the upper and lower Hubbard bands. Here, we introduce twisted double bilayer (TDB) WSe2, with twist angles near 60°, as a controllable platform in which the K-valley band can be tuned to close vicinity of the Γ-valley moiré flat band. At half-filling, correlations split the Γ-valley flat band into upper and lower Hubbard bands and a charge-transfer insulator forms between the Γ-valley upper Hubbard band and K-valley band. Using gate control, we continuously move the K-valley band across the Γ-valley Hubbard bands, and observe a tunable charge-transfer insulator gap and subsequently a continuous phase transition to a metal. The tuning of Mott˘Hubbard to charge-transfer insulator establishes valley degree of freedom as a suitable knob for transitions between exotic correlated phases.

Rotation symmetry mismatch and interlayer hybridization in MoS2-black phosphorus van der Waals heterostructures

Interlayer coupling in 2D heterostructures can result in a reduction of the rotation symmetry and the generation of quantum phenomena. Although these effects have been demonstrated in transition metal dichalcogenides (TMDs) with mismatched interfaces, the role of band hybridization remains unclear. In addition, the creation of flat bands at the valence band maximum (VBM) of TMDs is still an open challenge. In this work, we investigate the electronic structure of monolayer MoS2-black phosphorus heterojunctions with a combined experimental and theoretical approach. The disruption of the rotational symmetry of the MoS2 bands, the creation of anisotropic minigaps and the appearance of flat bands at the Γ valley, accompanied by the switch of VBM from K to Γ, are clearly observed with micro-ARPES. Unfolded band structures obtained from first principles simulations precisely describe these multiple effects - all independent of the twist angle - and demonstrates that they arise from strong band hybridization between Mod z 2 and Pp x orbitals. The underlying physics revealed by our results paves the way for innovative electronics and optoelectronics based on TMDs superlattices, adding further flexibility to the approaches adopted in twisted hexagonal superlattices.

Time-domain signatures of distinct correlated insulators in a moiré superlattice

Among expanding discoveries of quantum phases in moiré superlattices, correlated insulators stand out as both the most stable and most commonly observed. Despite the central importance of these states in moiré physics, little is known about their underlying nature. Here, we use pump-probe spectroscopy to show distinct time-domain signatures of correlated insulators at fillings of one (ν = -1) and two (ν = -2) holes per moiré unit cell in the angle-aligned WSe2/WS2 system. Following photo-doping, we find that the disordering time of the ν = -1 state is independent of excitation density (nex), as expected from the characteristic phonon response time associated with a polaronic state. In contrast, the disordering time of the ν = -2 state scales with 1 / n ex , in agreement with plasmonic screening from free holons and doublons. These states display disparate reordering behavior dominated either by first order (ν = -1) or second order (ν = -2) recombination, suggesting the presence of Hubbard excitons and free carrier-like holons/doublons, respectively. Our work delineates the roles of electron-phonon (e-ph) versus electron-electron (e-e) interactions in correlated insulators on the moiré landscape and establishes non-equilibrium responses as mechanistic signatures for distinguishing and discovering quantum phases.

Superconductivity in twisted bilayer WSe2

Moiré materials have enabled the realization of flat electron bands and quantum phases that are driven by the strong correlations associated with flat bands1-4. Superconductivity has been observed, but only in graphene moiré materials5-9. The absence of robust superconductivity in moiré materials beyond graphene, such as semiconductor moiré materials4, has remained a mystery and challenged our current understanding of superconductivity in flat bands. Here we report the observation of robust superconductivity in both 3.5° and 3.65° twisted bilayer tungsten diselenide (WSe2), which hosts a hexagonal moiré lattice10,11. Superconductivity emerges near half-band filling and zero external displacement fields. The optimal superconducting transition temperature is about 200 mK in both cases and constitutes about 1-2% of the effective Fermi temperature; the latter is comparable to the value in high-temperature cuprate superconductors12 and suggests strong pairing. The superconductor borders on two distinct metals below and above half-band filling; it undergoes a continuous transition to a correlated insulator by tuning the external displacement field. The observed superconductivity on the verge of Coulomb-induced charge localization suggests roots in strong electron correlations12,13.

Possible Sliding Regimes in Twisted Bilayer WTe_{2}

Inspired by the observation of increasingly one-dimensional (1D) behavior with decreasing temperature in small-angle twisted bilayers of WTe_{2} (tWTe_{2}), we theoretically explore the exotic sliding regimes that could be realized in tWTe_{2}. At zero displacement field, while hole-doped tWTe_{2} can be thought of as an array of weakly coupled conventional two-flavor 1D electron gases (1DEGs), the electron-doped regime is equivalent to coupled four-flavor 1DEGs, due to the presence of an additional "valley" degree of freedom. In the decoupled limit, the electron-doped system can thus realize phases with a range of interesting ordering tendencies, including 4k_{F} charge-density-wave and charge-4e superconductivity. Dimensional crossovers and cross-wire transport due to interwire couplings of various kinds are also discussed. We find that a sliding Luther-Emery liquid with small interwire couplings is probably most consistent with current experiments on hole-doped tWTe_{2}.

Spin transport of a doped Mott insulator in moiré heterostructures

Moiré superlattices of semiconducting transition metal dichalcogenide heterobilayers are model systems for investigating strongly correlated electronic phenomena. Specifically, WSe2/WS2 moiré superlattices have emerged as a quantum simulator for the two-dimensional extended Hubbard model. Experimental studies of charge transport have revealed correlated Mott insulator and generalized Wigner crystal states, but spin transport of the moiré heterostructure has not yet been sufficiently explored. Here, we use spatially and temporally resolved circular dichroism spectroscopy to directly image the spin transport as a function of carrier doping and temperature in WSe2/WS2 moiré heterostructures. We observe diffusive spin transport at all hole concentrations at 11 Kelvin - including the Mott insulator at one hole per moiré unit cell - where charge transport is strongly suppressed. At elevated temperatures the spin diffusion constant remains unchanged in the Mott insulator state, but it increases significantly at finite doping away from the Mott state. The doping- and temperature-dependent spin transport can be qualitatively understood using a t-J model, where spins can move via the hopping of spin-carrying charges and via the exchange interaction.

Suppression of symmetry-breaking correlated insulators in a rhombohedral trilayer graphene superlattice

Counterintuitive temperature dependence of isospin flavor polarization has recently been found in twisted bilayer graphene, where unpolarized electrons in a Fermi liquid become a spin-valley polarized insulator upon heating. So far, the effect has been limited to v = +/-1 (one electron/hole per superlattice cell), leaving open questions such as whether it is a general property of symmetry-breaking electronic phases. Here, by studying a rhombohedral trilayer graphene/boron nitride moiré superlattice, we report that at v = -3 a resistive peak emerges at elevated temperatures or in parallel magnetic fields. Concomitantly, the Hall carrier density tends to reset at the integer filling, signaling spin-valley flavor symmetry breaking. These phenomena can also be observed at v = -1 and -2 when the displacement field is large enough to suppress correlated insulators at low temperatures. Our results greatly expand the scope for observing the counterintuitive temperature dependence of flavor polarization, i.e., the regimes proximal to symmetry-breaking phases where the flavor polarization order strongly fluctuates, encouraging more experimental and theoretical exploration of isospin flavor polarization dynamics in flat-band moiré systems.

Tunable Out-of-Plane Reconstructions in Moiré Superlattices of Transition Metal Dichalcogenide Heterobilayers

The reconstructed moiré superlattices of the transition metal chalcogenide (TMD), formed by the combined effects of interlayer coupling and intralayer strain, provide a platform for exploring quantum physics. Here, using scanning tunneling microscopy/spectroscopy, we observe that the strained WSe2/WS2 moiré superlattices undergo various out-of-plane atomically buckled configurations, a phenomenon termed out-of-plane reconstruction. This evolution is attributed to the differentiated response of intralayer strain in high-symmetry stacking regions to external strain. Notably, in larger out-of-plane reconstructions, there is a significant alteration in the local density of states (LDOS) near the Γ point in the valence band, exceeding 300%, with the moiré potential in the valence band surpassing 200 meV. Further, we confirm that the variation in interlayer coupling within high-symmetry stacking regions is the main factor affecting the moiré electronic states rather than the intralayer strain. Our study unveils intrinsic regulating mechanisms of out-of-plane reconstructed moiré superlattices and contributes to the study of reconstructed moiré physics.

Long-Lived Topological Flatband Excitons in Semiconductor Moiré Heterostructures: A Bosonic Kane-Mele Model Platform

Moiré superlattices based on two-dimensional transition metal dichalcogenides (TMDs) have emerged as a highly versatile and fruitful platform for exploring correlated topological electronic phases. One of the most remarkable examples is the recently discovered fractional quantum anomalous Hall effect (FQAHE) under zero magnetic field. Here, we propose a minimal structure that hosts long-lived excitons-a ubiquitous bosonic excitation in TMD semiconductors-with narrow topological bosonic bands. The nontrivial exciton topology originates from hybridization of moiré interlayer excitons and is tunable by controlling twist angle and electric field. At small twist angle, the lowest exciton bands are isolated from higher energy bands and provide a solid-state realization of the bosonic Kane-Mele model with topological flatbands, which could potentially support the bosonic version of FQAHE.

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.

Strong-Coupling Phases of Trions and Excitons in Electron-Hole Bilayers at Commensurate Densities

We introduce density imbalanced electron-hole bilayers at a commensurate 2:1 density ratio as a platform for realizing novel phases of electrons, excitons, and trions. Through the independently tunable carrier densities and interlayer spacing, competition between kinetic energy, intralayer repulsion, and interlayer attraction yields a rich phase diagram. By a combination of theoretical analysis and numerical calculation, we find a variety of strong-coupling phases in different parameter regions, including quantum crystals of electrons, excitons, and trions. We also propose an "electron-exciton supersolid" phase that features electron crystallization and exciton superfluidity simultaneously. The material realization and experimental signature of these phases are discussed in the context of semiconductor transition metal dichalcogenide bilayers.

Link between T-Linear Resistivity and Quantum Criticality in Ambipolar Black Phosphorus

The interplay between strong Coulomb interactions and kinetic energy leads to intricate many-body competing ground states owing to quantum fluctuations in 2D electron and hole gases. However, the simultaneous observation of quantum critical phenomena in both electron and hole regimes remains elusive. Here, we utilize anisotropic black phosphorus (BP) to show density-driven metal-insulator transition with a critical conductance ∼e2/h which highlights the significant role of quantum fluctuations in both hole and electron regimes. We observe a T-linear resistivity from the deep metallic phase to the metal-insulator boundary at moderate temperatures, while it turns to Fermi liquid behavior in the deep metallic phase at low temperatures in both regimes. An analysis of the resistivity suggests that disorder-dominated transport leads to T-linear behavior in the hole regime, while in the electron regime, the T-linear resistivity results from strong Coulomb interactions, suggestive of strange-metal behavior. Successful scaling collapse of the resistivity in the T-linear region demonstrates the link between quantum criticality and the T-linear resistivity in both regimes. Our study provides compelling evidence that ambipolar BP could serve as an exciting testbed for investigating exotic states and quantum critical phenomena in hole and electron regimes of 2D semiconductors.

Resonant Band Hybridization in Alloyed Transition Metal Dichalcogenide Heterobilayers

Bandstructure engineering using alloying is widely utilized for achieving optimized performance in modern semiconductor devices. While alloying has been studied in monolayer transition metal dichalcogenides, its application in van der Waals heterostructures built from atomically thin layers is largely unexplored. Here, heterobilayers made from monolayers of WSe2 (or MoSe2) and MoxW1 - xSe2 alloy are fabricated and nontrivial tuning of the resultant bandstructure is observed as a function of concentration x. This evolution is monitored by measuring the energy of photoluminescence (PL) of the interlayer exciton (IX) composed of an electron and hole residing in different monolayers. In MoxW1 - xSe2/WSe2, a strong IX energy shift of ≈100 meV is observed for x varied from 1 to 0.6. However, for x < 0.6 this shift saturates and the IX PL energy asymptotically approaches that of the indirect bandgap in bilayer WSe2. This observation is theoretically interpreted as the strong variation of the conduction band K valley for x > 0.6, with IX PL arising from the K - K transition, while for x < 0.6, the bandstructure hybridization becomes prevalent leading to the dominating momentum-indirect K - Q transition. This bandstructure hybridization is accompanied with strong modification of IX PL dynamics and nonlinear exciton properties. This work provides foundation for bandstructure engineering in van der Waals heterostructures highlighting the importance of hybridization effects and opening a way to devices with accurately tailored electronic properties.

Quantum critical phase of FeO spans conditions of Earth's lower mantle

Seismic and mineralogical studies have suggested regions at Earth's core-mantle boundary may be highly enriched in FeO, reported to exhibit metallic behavior at extreme pressure-temperature (P-T) conditions. However, underlying electronic processes in FeO remain poorly understood. Here we explore the electronic structure of B1-FeO at extreme conditions with large-scale theoretical modeling using state-of-the-art embedded dynamical mean field theory (eDMFT). Fine sampling of the phase diagram reveals that, instead of sharp metallization, compression of FeO at high temperatures induces a gradual orbitally selective insulator-metal transition. Specifically, at P-T conditions of the lower mantle, FeO exists in an intermediate quantum critical state, characteristic of strongly correlated electronic matter. Transport in this regime, distinct from insulating or metallic behavior, is marked by incoherent diffusion of electrons in the conducting t2g orbital and a band gap in the eg orbital, resulting in moderate electrical conductivity (~105 S/m) with modest P-T dependence as observed in experiments. Enrichment of solid FeO can thus provide a unifying explanation for independent observations of low seismic velocities and elevated electrical conductivities in heterogeneities at Earth's mantle base.

Mapping twist-tuned multiband topology in bilayer WSe2

Semiconductor moiré superlattices have been shown to host a wide array of interaction-driven ground states. However, twisted homobilayers have been difficult to study in the limit of large moiré wavelengths, where interactions are most dominant. In this study, we conducted local electronic compressibility measurements of twisted bilayer WSe2 (tWSe2) at small twist angles. We demonstrated multiple topological bands that host a series of Chern insulators at zero magnetic field near a "magic angle" around 1.23°. Using a locally applied electric field, we induced a topological quantum-phase transition at one hole per moiré unit cell. Our work establishes the topological phase diagram of a generalized Kane-Mele-Hubbard model in tWSe2, demonstrating a tunable platform for strongly correlated topological phases.

Excitonic Thermalization Bottleneck in Twisted TMD Heterostructures

Twisted van der Waals heterostructures show intriguing interface exciton physics, including hybridization effects and emergence of moiré potentials. Recent experiments have revealed that moiré-trapped excitons exhibit remarkable dynamics, where excited states show lifetimes that are several orders of magnitude longer than in monolayers. The origin of this behavior is still under debate. Based on a microscopic many-particle approach, we investigate the phonon-driven relaxation cascade of nonequilibrium moiré excitons in the exemplary MoSe2-WSe2 heterostructure. We track exciton relaxation pathways across different moiré mini-bands and identify the phonon-scattering channels assisting the spatial redistribution of excitons into low-energy pockets of the moiré potential. We unravel a phonon bottleneck in the flat band structure at low twist angles preventing excitons from fully thermalizing into the lowest state, explaining the measured enhanced emission intensity and lifetime of excited moiré excitons. Overall, our work provides important insights into exciton relaxation dynamics in flat-band exciton materials.

Linear resistivity at van Hove singularities in twisted bilayer WSe2

Different mechanisms driving a linear temperature dependence of the resistivity ρ ∼ T at van Hove singularities (VHSs) or metal-insulator transitions when doping a Mott insulator are being debated intensively with competing theoretical proposals. We experimentally investigate this using the exceptional tunability of twisted bilayer (TB) WSe2 by tracking the parameter regions where linear-in-T resistivity is found in dependency of displacement fields, filling, and magnetic fields. We find that even when the VHSs are tuned rather far away from the half-filling point and the Mott insulating transition is absent, the T-linear resistivity persists at the VHSs. When doping away from the VHSs, the T-linear behavior quickly transitions into a Fermi liquid behavior with a T2 relation. No apparent dependency of the linear-in-T resistivity, besides a rather strong change of prefactor, is found when applying displacement fields as long as the filling is tuned to the VHSs, including D ∼ 0.28 V/nm where a high-order VHS is expected. Intriguingly, such non-Fermi liquid linear-in-T resistivity persists even when magnetic fields break the spin-degeneracy of the VHSs at which point two linear in T regions emerge, for each of the split VHSs separately. This points to a mechanism of enhanced scattering at generic VHSs rather than only at high-order VHSs or by a quantum critical point during a Mott transition. Our findings provide insights into the many-body consequences arising out of VHSs, especially the non-Fermi liquid behavior found in moiré materials.

Gate-Tunable Antiferromagnetic Chern Insulator in Twisted Bilayer Transition Metal Dichalcogenides

A series of recent experimental works on twisted MoTe_{2} homobilayers have unveiled an abundance of exotic states in this system. Valley-polarized quantum anomalous Hall states have been identified at hole doping of ν=-1, and the fractional quantum anomalous Hall effect is observed at ν=-2/3 and ν=-3/5. In this Letter, we investigate the electronic properties of AA-stacked twisted bilayer MoTe_{2} at ν=-2 by k-space Hartree-Fock calculations. We identify a series of phases, among which a noteworthy phase is the antiferromagnetic Chern insulator, stabilized by an external electric field. We attribute the existence of this Chern insulator to an antiferromagnetic instability at a topological phase transition between the quantum spin hall phase and a band insulator phase. Our research proposes the potential of realizing a Chern insulator beyond ν=-1, and contributes fresh perspectives on the interplay between band topology and electron-electron correlations in moiré superlattices.

Excitonic Mott insulator in a Bose-Fermi-Hubbard system of moiré WS2/WSe2 heterobilayer

Understanding the Hubbard model is crucial for investigating various quantum many-body states and its fermionic and bosonic versions have been largely realized separately. Recently, transition metal dichalcogenides heterobilayers have emerged as a promising platform for simulating the rich physics of the Hubbard model. In this work, we explore the interplay between fermionic and bosonic populations, using a WS2/WSe2 heterobilayer device that hosts this hybrid particle density. We independently tune the fermionic and bosonic populations by electronic doping and optical injection of electron-hole pairs, respectively. This enables us to form strongly interacting excitons that are manifested in a large energy gap in the photoluminescence spectrum. The incompressibility of excitons is further corroborated by observing a suppression of exciton diffusion with increasing pump intensity, as opposed to the expected behavior of a weakly interacting gas of bosons, suggesting the formation of a bosonic Mott insulator. We explain our observations using a two-band model including phase space filling. Our system provides a controllable approach to the exploration of quantum many-body effects in the generalized Bose-Fermi-Hubbard model.

Maximally localized Wannier functions, interaction models, and fractional quantum anomalous Hall effect in twisted bilayer MoTe2

We investigate the moiré band structures and the strong correlation effects in twisted bilayer MoTe[Formula: see text] for a wide range of twist angles, employing a combination of various techniques. Using large-scale first-principles calculations, we pinpoint realistic continuum modeling parameters, subsequently deriving the maximally localized Wannier functions for the top three moiré bands. Simplifying our model with reasonable assumptions, we obtain a minimal two-band model, encompassing Coulomb repulsion, correlated hopping, and spin exchange. Our minimal interaction models pave the way for further exploration of the rich many-body physics in twisted MoTe[Formula: see text]. Furthermore, we explore the phase diagrams of the system through Hartree-Fock approximation and exact diagonalization (ED). Our two-band ED analysis underscores significant band-mixing effects in this system, which enlarge the optimal twist angle for fractional quantum anomalous Hall states.

Metal-Insulator Transition in a Semiconductor Heterobilayer Model

Transition metal dichalcogenide superlattices provide an exciting new platform for exploring and understanding a variety of phases of matter. The moiré continuum Hamiltonian, of two-dimensional jellium in a modulating potential, provides a fundamental model for such systems. Accurate computations with this model are essential for interpreting experimental observations and making predictions for future explorations. In this work, we combine two complementary quantum Monte Carlo (QMC) methods, phaseless auxiliary field quantum Monte Carlo and fixed-phase diffusion Monte Carlo, to study the ground state of this Hamiltonian. We observe a metal-insulator transition between a paramagnet and a 120° Néel ordered state as the moiré potential depth and the interaction strength are varied. We find significant differences from existing results by Hartree-Fock and exact diagonalization studies. In addition, we benchmark density-functional theory, and suggest an optimal hybrid functional which best approximates our QMC results.

Field-Induced Hybridization of Moiré Excitons in MoSe_{2}/WS_{2} Heterobilayers

We study experimentally and theoretically the hybridization among intralayer and interlayer moiré excitons in a MoSe_{2}/WS_{2} heterostructure with antiparallel alignment. Using a dual-gate device and cryogenic white light reflectance and narrow-band laser modulation spectroscopy, we subject the moiré excitons in the MoSe_{2}/WS_{2} heterostack to a perpendicular electric field, monitor the field-induced dispersion and hybridization of intralayer and interlayer moiré exciton states, and induce a crossover from type I to type II band alignment. Moreover, we employ perpendicular magnetic fields to map out the dependence of the corresponding exciton Landé g factors on the electric field. Finally, we develop an effective theoretical model combining resonant and nonresonant contributions to moiré potentials to explain the observed phenomenology, and highlight the relevance of interlayer coupling for structures with close energetic band alignment as in MoSe_{2}/WS_{2}.

Optical properties and plasmons in moiré structures

The discoveries of numerous exciting phenomena in twisted bilayer graphene (TBG) are stimulating significant investigations on moiré structures that possess a tunable moiré potential. Optical response can provide insights into the electronic structures and transport phenomena of non-twisted and twisted moiré structures. In this article, we review both experimental and theoretical studies of optical properties such as optical conductivity, dielectric function, non-linear optical response, and plasmons in moiré structures composed of graphene, hexagonal boron nitride (hBN), and/or transition metal dichalcogenides. Firstly, a comprehensive introduction to the widely employed methodology on optical properties is presented. After, moiré potential induced optical conductivity and plasmons in non-twisted structures are reviewed, such as single layer graphene-hBN, bilayer graphene-hBN and graphene-metal moiré heterostructures. Next, recent investigations of twist-angle dependent optical response and plasmons are addressed in twisted moiré structures. Additionally, we discuss how optical properties and plasmons could contribute to the understanding of the many-body effects and superconductivity observed in moiré structures.

Magnetotransport and Fermi surface segmentation in Pauli limited superconductors

We report the first theoretical investigation of the spectroscopic, electrical and optical transport signatures ofd-wave Pauli limited superconductors, based on a non perturbative numerical approach. We demonstrate that the high magnetic field low temperature regime of these materials host a finite momentum paired superconducting phase. Multi-branched dispersion spectra with finite energy superconducting gaps, anisotropic segmentation of the Fermi surface and spatial modulations of the superconducting order characterizes this finite momentum paired phase and should be readily accessible through angle resolved photo emission spectroscopy, quasiparticle interference and differential conductance measurements. Based on the electrical and optical transport properties we capture the non Fermi liquid behavior of these systems at high temperatures, dominated by local superconducting correlations and characterized by resilient quasiparticles which survive the breakdown of the Fermi liquid description. We map out the generic thermal phase diagram of thed-wave Pauli limited superconductors and provide for the first time the accurate estimates of the thermal scales corresponding to the: (a) loss of (quasi) long range superconducting phase coherence (Tc), (b) loss of local pair correlations (Tpg), (c) breakdown of the Fermi liquid theory (Tmax) and cross-over from the non Fermi liquid to the bad metallic phase (TBR). Our thermal phase diagram mapped out on the basis of the spectroscopic and transport properties are found to be in qualitative agreement with the experimental observations on CeCoIn5andκ-BEDT, in terms of the thermodynamic phases and the phase transitions. The results presented in this paper are expected to initiate important transport and spectroscopic experiments on the Pauli limitedd-wave superconductors, providing sharp signatures of the finite momentum Cooper paired state in these materials.

Magnetism and metallicity in moiré transition metal dichalcogenides

The ability to control the properties of twisted bilayer transition metal dichalcogenides in situ makes them an ideal platform for investigating the interplay of strong correlations and geometric frustration. Of particular interest are the low energy scales, which make it possible to experimentally access both temperature and magnetic fields that are of the order of the bandwidth or the correlation scale. In this manuscript, we analyze the moiré Hubbard model, believed to describe the low energy physics of an important subclass of the twisted bilayer compounds. We establish its magnetic and the metal-insulator phase diagram for the full range of magnetic fields up to the fully spin-polarized state. We find a rich phase diagram including fully and partially polarized insulating and metallic phases of which we determine the interplay of magnetic order, Zeeman-field, and metallicity, and make connection to recent experiments.

Giant Correlated Gap and Possible Room-Temperature Correlated States in Twisted Bilayer MoS_{2}

Moiré superlattices have emerged as an exciting condensed-matter quantum simulator for exploring the exotic physics of strong electronic correlations. Notable progress has been witnessed, but such correlated states are achievable usually at low temperatures. Here, we report evidence of possible room-temperature correlated electronic states and layer-hybridized SU(4) model simulator in AB-stacked MoS_{2} homobilayer moiré superlattices. Correlated insulating states at moiré band filling factors v=1, 2, 3 are unambiguously established in twisted bilayer MoS_{2}. Remarkably, the correlated electronic state at v=1 shows a giant correlated gap of ∼126  meV and may persist up to a record-high critical temperature over 285 K. The realization of a possible room-temperature correlated state with a large correlated gap in twisted bilayer MoS_{2} can be understood as the cooperation effects of the stacking-specific atomic reconstruction and the resonantly enhanced interlayer hybridization, which largely amplify the moiré superlattice effects on electronic correlations. Furthermore, extreme large nonlinear Hall responses up to room temperature are uncovered near correlated electronic states, demonstrating the quantum geometry of moiré flat conduction band.

Universal Scaling near Band-Tuned Metal-Insulator Phase Transitions

We present a theory for band-tuned metal-insulator transitions based on the Kubo formalism. Such a transition exhibits scaling of the resistivity curves in the regime where Tτ>1 or μτ>1, where τ is the scattering time and μ the chemical potential. At the critical value of the chemical potential, the resistivity diverges as a power law, R_{c}∼1/T. Consequently, on the metallic side there is a regime with negative dR/dT, which is often misinterpreted as insulating. We show that scaling and this "fake insulator" regime are observed in a wide range of experimental systems. In particular, we show that Mooij correlations in high-temperature metals with negative dR/dT can be quantitatively understood with our scaling theory in the presence of T-linear scattering.

Phase Engineering of 2D Materials

Polymorphic 2D materials allow structural and electronic phase engineering, which can be used to realize energy-efficient, cost-effective, and scalable device applications. The phase engineering covers not only conventional structural and metal-insulator transitions but also magnetic states, strongly correlated band structures, and topological phases in rich 2D materials. The methods used for the local phase engineering of 2D materials include various optical, geometrical, and chemical processes as well as traditional thermodynamic approaches. In this Review, we survey the precise manipulation of local phases and phase patterning of 2D materials, particularly with ideal and versatile phase interfaces for electronic and energy device applications. Polymorphic 2D materials and diverse quantum materials with their layered, vertical, and lateral geometries are discussed with an emphasis on the role and use of their phase interfaces. Various phase interfaces have demonstrated superior and unique performance in electronic and energy devices. The phase patterning leads to novel homo- and heterojunction structures of 2D materials with low-dimensional phase boundaries, which highlights their potential for technological breakthroughs in future electronic, quantum, and energy devices. Accordingly, we encourage researchers to investigate and exploit phase patterning in emerging 2D materials.

Zero-Field Composite Fermi Liquid in Twisted Semiconductor Bilayers

Recent experiments have produced evidence for fractional quantum anomalous Hall (FQAH) states at zero magnetic field in the semiconductor moiré superlattice system tMoTe_{2}. Here, we argue that a composite fermion description, already a unifying framework for the phenomenology of 2D electron gases at high magnetic fields, provides a similarly powerful perspective in this new context. To this end, we present exact diagonalization evidence for composite Fermi liquid states at zero magnetic field in tMoTe_{2} at fillings n=1/2 and n=3/4. We dub these non-Fermi liquid metals anomalous composite Fermi liquids (ACFLs), and we argue that they play a central organizing role in the FQAH phase diagram. We proceed to develop a long wavelength theory for this ACFL state that offers concrete experimental predictions upon doping the composite Fermi sea, including a Jain sequence of FQAH states and a new type of commensurability oscillations originating from the superlattice potential intrinsic to the system.

Composite Fermi Liquid at Zero Magnetic Field in Twisted MoTe_{2}

The pursuit of exotic phases of matter outside of the extreme conditions of a quantizing magnetic field is a long-standing quest of solid state physics. Recent experiments have observed spontaneous valley polarization and fractional Chern insulators in zero magnetic field in twisted bilayers of MoTe_{2}, at partial filling of the topological valence band (ν=-2/3 and -3/5). We study the topological valence band at half filling, using exact diagonalization and density matrix renormalization group calculations. We discover a composite Fermi liquid (CFL) phase even at zero magnetic field that covers a large portion of the phase diagram near twist angle ∼3.6°. The CFL is a non-Fermi liquid phase with metallic behavior despite the absence of Landau quasiparticles. We discuss experimental implications including the competition between the CFL and a Fermi liquid, which can be tuned with a displacement field. The topological valence band has excellent quantum geometry over a wide range of twist angles and a small bandwidth that is, remarkably, reduced by interactions. These key properties stabilize the exotic zero field quantum Hall phases. Finally, we present an optical signature involving "extinguished" optical responses that detects Chern bands with ideal quantum geometry.

An anisotropic van der Waals dielectric for symmetry engineering in functionalized heterointerfaces

Van der Waals dielectrics are fundamental materials for condensed matter physics and advanced electronic applications. Most dielectrics host isotropic structures in crystalline or amorphous forms, and only a few studies have considered the role of anisotropic crystal symmetry in dielectrics as a delicate way to tune electronic properties of channel materials. Here, we demonstrate a layered anisotropic dielectric, SiP2, with non-symmorphic twofold-rotational C2 symmetry as a gate medium which can break the original threefold-rotational C3 symmetry of MoS2 to achieve unexpected linearly-polarized photoluminescence and anisotropic second harmonic generation at SiP2/MoS2 interfaces. In contrast to the isotropic behavior of pristine MoS2, a large conductance anisotropy with an anisotropy index up to 1000 can be achieved and modulated in SiP2-gated MoS2 transistors. Theoretical calculations reveal that the anisotropic moiré potential at such interfaces is responsible for the giant anisotropic conductance and optical response. Our results provide a strategy for generating exotic functionalities at dielectric/semiconductor interfaces via symmetry engineering.

Moiré-Pattern Modulated Electronic Structures of GaSe/HOPG Heterostructure

Conventional two-dimensional electron gas (2DEG) typically occurs at the interface of semiconductor heterostructures and noble metal surfaces, but it is scarcely observed in individual 2D semiconductors. In this study, few-layer gallium selenide (GaSe) grown on highly ordered pyrolytic graphite (HOPG) is demonstrated using scanning tunneling microscopy and spectroscopy (STM/STS), revealing that the coexistence of quantum well states (QWS) and 2DEG. The QWS are located in the valence bands and exhibit a peak feature, with the number of quantum wells being equal to the number of atomic layers. Meanwhile, the 2DEG is located in the conduction bands and exhibits a standing-wave feature. Additionally, monolayer GaSe/HOPG heterostructures with different stacking angles (0°, 33°, 8°) form distinct moiré patterns that arise from lattice mismatch and angular rotation between adjacent atomic layers in 2D materials, which effectively modulate the electron effective mass, charge redistribution, and band gap of GaSe. Overall, this work reveals a paradigm of band engineering based on layer numbers and moiré patterns that can modulate the electronic properties of 2D materials.

Observation and Modulation of High-Temperature Moiré-Locale Excitons in van der Waals Heterobilayers

Transition metal dichalcogenide heterobilayers feature strong moiré potentials with multiple local minima, which can spatially trap interlayer excitons at different locations within one moiré unit cell (dubbed moiré locales). However, current studies mainly focus on moiré excitons trapped at a single moiré locale. Exploring interlayer excitons trapped at different moiré locales is highly desirable for building polarized light-emitter arrays and studying multiorbital correlated and topological physics. Here, via enhancing the interlayer coupling and engineering the heterointerface, we report the observation and modulation of high-temperature interlayer excitons trapped at separate moiré locales in WS2/WSe2 heterobilayers. These moiré-locale excitons are identified by two emission peaks with an energy separation of ∼60 meV, exhibiting opposite circular polarizations due to their distinct local stacking registries. With the increase of temperature, two momentum-indirect moiré-locale excitons are observed, which show a distinct strain dependence with the momentum-direct one. The emission of these moiré-locale excitons can be controlled via engineering the heterointerface with different phonon scattering, while their emission energy can be further modulated via strain engineering. Our reported highly tunable interlayer excitons provide important information on understanding moiré excitonic physics, with possible applications in building high-temperature excitonic devices.

Quantum Noise Spectroscopy of Dynamical Critical Phenomena

The transition between distinct phases of matter is characterized by the nature of fluctuations near the critical point. We demonstrate that noise spectroscopy can not only diagnose the presence of a phase transition, but can also determine fundamental properties of its criticality. In particular, by analyzing a scaling collapse of the decoherence profile, one can directly extract the critical exponents of the transition and identify its universality class. Our approach naturally captures the presence of conservation laws and distinguishes between classical and quantum phase transitions. In the context of quantum magnetism, our proposal complements existing techniques and provides a novel toolset optimized for interrogating two-dimensional magnetic materials.

Giant spin Hall effect in AB-stacked MoTe2/WSe2 bilayers

The spin Hall effect (SHE), in which an electrical current generates a transverse spin current, plays an important role in spintronics for the generation and manipulation of spin-polarized electrons. The phenomenon originates from spin-orbit coupling. In general, stronger spin-orbit coupling favours larger SHEs but shorter spin relaxation times and diffusion lengths. However, correlated magnetic materials often do not support large SHEs. Achieving large SHEs, long-range spin transport and magnetism simultaneously in a single material is attractive for spintronics applications but has remained a challenge. Here we demonstrate a giant intrinsic SHE coexisting with ferromagnetism in AB-stacked MoTe2/WSe2 moiré bilayers by direct magneto-optical imaging. Under moderate electrical currents with density <1 A m-1, we observe spin accumulation on transverse sample edges that nearly saturates the spin density. We also demonstrate long-range spin Hall transport and efficient non-local spin accumulation that is limited only by the device size (about 10 µm). The gate dependence shows that the giant SHE occurs only near the interaction-driven Chern insulating state. At low temperatures, it emerges after the quantum anomalous Hall breakdown. Our results demonstrate moiré engineering of Berry curvature and electronic correlation for potential spintronics applications.

Layer-Dependent Interaction Effects in the Electronic Structure of Twisted Bilayer Graphene Devices

Near the magic angle, strong correlations drive many intriguing phases in twisted bilayer graphene (tBG) including unconventional superconductivity and chern insulation. Whether correlations can tune symmetry breaking phases in tBG at intermediate (≳ 2°) twist angles remains an open fundamental question. Here, using ARPES, we study the effects of many-body interactions and displacement field on the band structure of tBG devices at an intermediate (3°) twist angle. We observe a layer- and doping-dependent renormalization of bands at the K points that is qualitatively consistent with moiré models of the Hartree-Fock interaction. We provide evidence of correlation-enhanced inversion symmetry-breaking, manifested by gaps at the Dirac points that are tunable with doping. These results suggest that electronic interactions play a significant role in the physics of tBG even at intermediate twist angles and present a new pathway toward engineering band structure and symmetry-breaking phases in moiré heterostructures.

Nematic Excitonic Insulator in Transition Metal Dichalcogenide Moiré Heterobilayers

We study the effect of interelectron Coulomb interactions on the displacement field induced topological phase transition in transition metal dichalcogenide moiré heterobilayers. We find a nematic excitonic insulator phase that breaks the moiré superlattice's threefold rotational symmetry and preempts the topological phase transition in both AA and AB stacked heterobilayers when the interlayer tunneling is weak, or when the Coulomb interaction is not strongly screened. The nematicity originates from the frustration between the nontrivial spatial structure of the interlayer tunneling, which is crucial to the existence of the topological Chern band, and the interlayer coherence induced by the Coulomb interaction that favors uniformity in layer pseudospin orientations. We construct a unified effective two-band model that captures the physics near the band inversion and applies to both AA and AB stacked heterobilayers. Within the two-band model the competition between the nematic excitonic insulator phase and the Chern insulator phase can be understood as the switching of the energetic order between the s-wave and the p-wave excitons upon increasing the interlayer tunneling.

Flat Γ Moiré Bands in Twisted Bilayer WSe_{2}

The recent observation of correlated phases in transition metal dichalcogenide moiré systems at integer and fractional filling promises new insight into metal-insulator transitions and the unusual states of matter that can emerge near such transitions. Here, we combine real- and momentum-space mapping techniques to study moiré superlattice effects in 57.4° twisted WSe_{2} (tWSe_{2}). Our data reveal a split-off flat band that derives from the monolayer Γ states. Using advanced data analysis, we directly quantify the moiré potential from our data. We further demonstrate that the global valence band maximum in tWSe_{2} is close in energy to this flat band but derives from the monolayer K states which show weaker superlattice effects. These results constrain theoretical models and open the perspective that Γ-valley flat bands might be involved in the correlated physics of twisted WSe_{2}.

Excitons in mesoscopically reconstructed moiré heterostructures

Moiré effects in vertical stacks of two-dimensional crystals give rise to new quantum materials with rich transport and optical phenomena that originate from modulations of atomic registries within moiré supercells. Due to finite elasticity, however, the superlattices can transform from moiré-type to periodically reconstructed patterns. Here we expand the notion of such nanoscale lattice reconstruction to the mesoscopic scale of laterally extended samples and demonstrate rich consequences in optical studies of excitons in MoSe₂-WSe₂ heterostructures with parallel and antiparallel alignments. Our results provide a unified perspective on moiré excitons in near-commensurate semiconductor heterostructures with small twist angles by identifying domains with exciton properties of distinct effective dimensionality, and establish mesoscopic reconstruction as a compelling feature of real samples and devices with inherent finite size effects and disorder. Generalized to stacks of other two-dimensional materials, this notion of mesoscale domain formation with emergent topological defects and percolation networks will instructively expand the understanding of fundamental electronic, optical and magnetic properties of van der Waals heterostructures.

Tunable spin and valley excitations of correlated insulators in Γ-valley moiré bands

Moiré superlattices formed from transition metal dichalcogenides support a variety of quantum electronic phases that are highly tunable using applied electromagnetic fields. While the valley degree of freedom affects optoelectronic properties in the constituent transition metal dichalcogenides, it has yet to be fully explored in moiré systems. Here we establish twisted double-bilayer WSe₂ as an experimental platform to study electronic correlations within Γ-valley moiré bands. Through local and global electronic compressibility measurements, we identify charge-ordered phases at multiple integer and fractional moiré fillings. By measuring the magnetic field dependence of their energy gaps and the chemical potential upon doping, we reveal spin-polarized ground states with spin-polaron quasiparticle excitations. In addition, an applied displacement field induces a metal-insulator transition driven by tuning between Γ- and K-valley moiré bands. Our results demonstrate control over the spin and valley character of the correlated ground and excited states in this system.

Bosonic Delocalization of Dipolar Moiré Excitons

In superlattices of twisted semiconductor monolayers, tunable moiré potentials emerge, trapping excitons into periodic arrays. In particular, spatially separated interlayer excitons are subject to a deep potential landscape and they exhibit a permanent dipole providing a unique opportunity to study interacting bosonic lattices. Recent experiments have demonstrated density-dependent transport properties of moiré excitons, which could play a key role for technological applications. However, the intriguing interplay between exciton-exciton interactions and moiré trapping has not been well understood yet. In this work, we develop a microscopic theory of interacting excitons in external potentials allowing us to tackle this highly challenging problem. We find that interactions between moiré excitons lead to a delocalization at intermediate densities, and we show how this transition can be tuned via twist angle and temperature. The delocalization is accompanied by a modification of optical moiré resonances, which gradually merge into a single free exciton peak.

Correlated insulator of excitons in WSe2/WS2 moiré superlattices

A panoply of unconventional electronic states has been observed in moiré superlattices. Engineering similar bosonic phases remains, however, largely unexplored. We report the observation of a bosonic correlated insulator in WSe₂/WS₂ moiré superlattices composed of excitons, i.e., tightly bound electron-hole pairs. We develop a pump probe spectroscopy method that we use to observe an exciton incompressible state at exciton filling ν_ex = 1 and charge neutrality, indicating a correlated insulator of excitons. With varying charge density, the bosonic correlated insulator continuously transitions into an electron correlated insulator at charge filling ν_e = 1, suggesting a mixed correlated insulating state between the two limits. Our studies establish semiconducting moiré superlattices as an intriguing platform for engineering bosonic phases.

Layer-dependent correlated phases in WSe2/MoS2 moiré superlattice

Electron correlation plays an essential role in the macroscopic quantum phenomena in the moiré heterostructure, such as antiferromagnetism and correlated insulating phases. Unlike the phenomena where the interaction involves only electrons in one layer, the interaction of distinct phases in two or more layers represents a new horizon forward, such as the one in the Kondo lattice model. Here, using interlayer excitons as a probe, we show that the interlayer interactions in heterobilayers of tungsten diselenide and molybdenum disulfide (WSe₂/MoS₂) can be electrically switched on and off, resulting in a layer-dependent correlated phase diagram, including single-layer, layer-selective, excitonic-insulator and layer-hybridized regions. We demonstrate that these correlated phases affect the interlayer exciton non-radiative decay pathways. These results reveal the role of strong correlation on interlayer exciton dynamics and pave the way for studying the layer-resolved strong correlation behaviour in moiré heterostructures.

Probing correlated states with plasmons

Understanding the nature of strongly correlated states in flat-band materials (such as moiré heterostructures) is at the forefront of both experimental and theoretical pursuits. While magnetotransport, scanning probe, and optical techniques are often very successful in investigating the properties of the underlying order, the exact nature of the ground state often remains unknown. Here, we propose to leverage strong light-matter coupling present in the flat-band systems to gain insight through dynamical dielectric response into the structure of the many-body ground state. We argue that because of the enlargement of the effective lattice of the system arising from correlations, conventional long-range plasmon becomes "folded" to yield a multiband plasmon spectrum. We detail several mechanisms through which the structure of the plasmon spectrum and that of the dynamical dielectric response is susceptible to the underlying order, revealing valued insights such as the interaction-driven band gaps, spin-structure, and the order periodicity.

Rapid and Direct Liquid-Phase Synthesis of Luminescent Metal Halide Superlattices

The crystallization of nanocrystal building blocks into artificial superlattices has emerged as an efficient approach for tailoring the nanoscale properties and functionalities of novel devices. To date, ordered arrays of colloidal metal halide nanocrystals have mainly been achieved by using post-synthetic strategies. Here, a rapid and direct liquid-phase synthesis is presented to achieve a highly robust crystallization of luminescent metal halide nanocrystals into perfect face-centered-cubic (FCC) superlattices on the micrometer scale. The continuous growth of individual nanocrystals is observed within the superlattice, followed by the disassembly of the superlattices into individually dispersed nanocrystals owing to the highly repulsive interparticle interactions induced by large nanocrystals. Transmission electron microscopy characterization reveals that owing to an increase in solvent entropy, the structure of the superlattices transforms from FCC to hexagonal close-packed (HCP) and the nanocrystals disassemble. The FCC superlattice exhibits a single and slightly redshifted emission, due to the reabsorption-free property of the building block units. Compared to individual nanocrystals, the superlattices have three times higher quantum yield with improved environmental stability, making them ideal for use as ultrabright blue-light emitters. This study is expected to facilitate the creation of metamaterials with ordered nanocrystal structures and their practical applications.

Gate-tunable heavy fermions in a moiré Kondo lattice

The Kondo lattice-a matrix of local magnetic moments coupled through spin-exchange interactions to itinerant conduction electrons-is a prototype of strongly correlated quantum matter1-4. Usually, Kondo lattices are realized in intermetallic compounds containing lanthanide or actinide1,2. The complex electronic structure and limited tunability of both the electron density and exchange interactions in these bulk materials pose considerable challenges to studying Kondo lattice physics. Here we report the realization of a synthetic Kondo lattice in AB-stacked MoTe2/WSe2 moiré bilayers, in which the MoTe2 layer is tuned to a Mott insulating state, supporting a triangular moiré lattice of local moments, and the WSe2 layer is doped with itinerant conduction carriers. We observe heavy fermions with a large Fermi surface below the Kondo temperature. We also observe the destruction of the heavy fermions by an external magnetic field with an abrupt decrease in the Fermi surface size and quasi-particle mass. We further demonstrate widely and continuously gate-tunable Kondo temperatures through either the itinerant carrier density or the Kondo interaction. Our study opens the possibility of in situ access to the phase diagram of the Kondo lattice with exotic quantum criticalities in a single device based on semiconductor moiré materials2-9.