Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices

Layer-dependent evolution of electronic structures and correlations in rhombohedral multilayer graphene

The recent discovery of superconductivity and magnetism in trilayer rhombohedral graphene (RG) establishes an ideal, untwisted platform to study strong correlation electronic phenomena. However, the correlated effects in multilayer RG have received limited attention, and, particularly, the evolution of the correlations with increasing layer number remains an unresolved question. Here we show the observation of layer-dependent electronic structures and correlations-under surprising liquid nitrogen temperature-in RG multilayers from 3 to 9 layers by using scanning tunnelling microscopy and spectroscopy. We explicitly determine layer-enhanced low-energy flat bands and interlayer coupling strengths. The former directly demonstrates the further flattening of low-energy bands in thicker RG, and the latter indicates the presence of varying interlayer interactions in RG multilayers. Moreover, we find significant splittings of the flat bands, ranging from ~50 meV to 80 meV, at 77 K when they are partially filled, indicating the emergence of interaction-induced strongly correlated states. Particularly, the strength of the correlated states is notably enhanced in thicker RG and reaches its maximum in the six-layer, validating directly theoretical predictions and establishing abundant new candidates for strongly correlated systems. Our results provide valuable insights into the layer dependence of the electronic properties in RG and demonstrate it as a suitable system for investigating robust and highly accessible correlated phases.

Valley-Hybridized Gate-Tunable 1D Exciton Confinement in MoSe2

Controlling excitons at the nanoscale in semiconductor materials represents a formidable challenge in the quantum photonics and optoelectronics fields. Monolayers of transition metal dichalcogenides (TMDs) offer inherent 2D confinement and possess significant exciton binding energies, making them promising candidates for achieving electric-field-based confinement of excitons without dissociation. Exploiting the valley degree of freedom associated with these confined states further broadens the prospects for exciton engineering. Here, we show electric control of light polarization emitted from one-dimensional (1D) quantum-confined states in MoSe2. Building on previous reports of tunable trapping potentials and linearly polarized emission, we extend this understanding by demonstrating how nonuniform in-plane electric fields enable in situ control of these effects and highlight the role of gate-tunable valley hybridization in these localized states. Their polarization is entirely engineered through either the 1D confinement potential's geometry or an out-of-plane magnetic field. Controlling nonuniform in-plane electric fields in TMDs enables control of the energy (up to five times its line width), polarization state (from circular to linear), and position of 1D confined excitonic states (5 nm V-1).

Realizing one-dimensional moiré chains with strong electron localization in two-dimensional twisted bilayer WSe2

Two-dimensional (2D) moiré systems based on twisted bilayer graphene and transition metal dichalcogenides provide a promising platform to investigate emergent phenomena driven by strong electron-electron interactions in partially filled flat bands. A natural question arises: Is it possible to expand the 2D correlated moiré physics to one-dimensional (1D) that electron-electron correlation is expected to be further enhanced? This requires selectively doping of 1D moiré chain, which seems to be not within the grasp of today's technology. Therefore, an experimental demonstration of the 1D moiré chain with partially filled electronic states remains absent. Here, we show that we can introduce 1D boundaries, separating two regions with different twist angles, in twisted bilayer WSe2 (tWSe2) by using scanning tunneling microscopy (STM) and demonstrate that the electronic states of 1D moiré sites along the boundaries can be selectively filled. The strong localized charge states of correlated moiré electrons in the 1D moiré chain can be directly imaged and manipulated by combining a back-gate voltage with the STM bias voltage. Our results open the door for realizing new correlated electronic states of the 1D moiré chain in 2D systems.

Signature of Correlated Insulator in Electric Field Controlled Superlattice

On a two-dimensional crystal, a "superlattice" with nanometer-scale periodicity can be imposed to tune the Bloch electron spectrum, enabling novel physical properties inaccessible in the original crystal. While creating 2D superlattices by means of nanopatterned electric gates has been studied for band structure engineering in recent years, evidence of electron correlations─which drive many problems at the forefront of physics research─remains to be uncovered. In this work, we demonstrate signatures of a correlated insulator phase in Bernal-stacked bilayer graphene modulated by a gate-defined superlattice potential, manifested as resistance peaks centered at integer multiples of single electron per superlattice unit cell carrier densities. The observation is consistent with the formation of a stack of flat low-energy bands due to the superlattice potential combined with inversion symmetry breaking. Our work paves the way to custom-designed superlattices for studying band structure engineering and strongly correlated electrons in 2D materials.

Three-Dimensional Moiré Crystal in Ultracold Atomic Gases

The work intends to extend the moiré physics to three dimensions. Three-dimensional moiré patterns can be realized in ultracold atomic gases by coupling two spin states in spin-dependent optical lattices with a relative twist, a structure currently unachievable in solid-state materials. We give the commensurate conditions under which the three-dimensional moiré pattern features a periodic structure termed a three-dimensional moiré crystal. We emphasize a key distinction of three-dimensional moiré physics: In three dimensions, the twist operation generically does not commute with the rotational symmetry of the original lattice, unlike in two dimensions, where these two always commute. Consequently, the moiré crystal can exhibit a crystalline structure that differs from the original underlying lattice. We demonstrate that twisting a simple cubic lattice can generate various crystal structures. This capability of altering crystal structures by twisting offers a broad range of tunability for three-dimensional band structures.

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.

Coherent Modulation of Two-Dimensional Moiré States with On-Chip THz Waves

van der Waals (vdW) structures host a broad range of physical phenomena. New opportunities arise if different functional layers are remotely modulated or coupled in a device structure. Here we demonstrate the in situ coherent modulation of moiré excitons and correlated Mott insulators in transition metal dichalcogenide (TMD) moirés with on-chip terahertz (THz) waves. Using common dual-gated device structures of a TMD moiré bilayer sandwiched between two few-layer graphene (fl-Gr) gates with hexagonal boron nitride (h-BN) spacers, we launch coherent phonon wavepackets at ∼0.4-1 THz from the fl-Gr gates by femtosecond laser excitation. The waves travel through the h-BN spacer, arrive at the TMD bilayer with precise timing, and coherently modulate the moiré excitons or Mott states. These results demonstrate that the fl-Gr gates, often used for electrical control, can serve as on-chip opto-elastic transducers to generate THz waves for coherent control and vibrational entanglement of functional layers in moiré devices.

Robust flat bands in twisted trilayer graphene moiré quasicrystals

Moiré structures formed by twisting three layers of graphene with two independent twist angles present an ideal platform for studying correlated quantum phenomena, as an infinite set of angle pairs is predicted to exhibit flat bands. Moreover, the two mutually incommensurate moiré patterns among the twisted trilayer graphene (TTG) can form highly tunable moiré quasicrystals. This enables us to extend correlated physics in periodic moiré crystals to quasiperiodic systems. However, direct local characterization of the structure of the moiré quasicrystals and of the resulting flat bands are still lacking, which is crucial to fundamental understanding and control of the correlated moiré physics. Here, we demonstrate the existence of flat bands in a series of TTGs with various twist angle pairs and show that the TTGs with different magic angle pairs are strikingly dissimilar in their atomic and electronic structures. The lattice relaxation and the interference between moiré patterns are highly dependent on the twist angles. Our direct spatial mappings, supported by theoretical calculations, reveal that the localization of the flat bands exhibits distinct symmetries in different regions of the moiré quasicrystals.

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.

Vacancy-Induced Tunable Kondo Effect in Twisted Bilayer Graphene

In single sheets of graphene, vacancy-induced states have been shown to host an effective spin-1/2 hole that can be Kondo screened at low temperatures. Here, we show how these vacancy-induced impurity states survive in twisted bilayer graphene (TBG), which thus provides a tunable system to probe the critical destruction of the Kondo effect in pseudogap hosts. Ab initio calculations and atomic-scale modeling are used to determine the nature of the vacancy states in the vicinity of the magic angle in TBG, demonstrating that the vacancy can be treated as a quantum impurity. Utilizing this insight, we construct an Anderson impurity model with a TBG host that we solve using the numerical renormalization group combined with the kernel polynomial method. We determine the phase diagram of the model and show how there is a strict dichotomy between vacancies in the AA/BB versus AB/BA tunneling regions. In AB/BA vacancies, the Kondo temperature at the magic angle develops a broad distribution with a tail to vanishing temperatures due to multifractal wave functions at the magic angle. We argue that scanning tunneling microscopy in the vicinity of the vacancy can act as a probe of both the critical single-particle states and the underlying many-body ground state in magic-angle TBG.

Mott Transition for a Lieb-Liniger Gas in a Shallow Quasiperiodic Potential: Delocalization Induced by Disorder

Disorder or quasidisorder is known to favor localization in many-body Bose systems. Here, in contrast, we demonstrate an anomalous delocalization effect induced by incommensurability in quasiperiodic lattices. Loading ultracold atoms in two shallow periodic lattices with equal amplitude and either equal or incommensurate spatial periods, we show the onset of a Mott transition not only in the periodic case but also in the quasiperiodic case. Switching from periodic to quasiperiodic potential with the same amplitude, we find that the Mott insulator turns into a delocalized superfluid. Our experimental results agree with quantum Monte Carlo calculations, showing this anomalous delocalization induced by the interplay between the disorder and interaction.

Understanding disorder in monolayer graphene devices with gate-defined superlattices

Engineering superlattices (SLs)-which are spatially periodic potential landscapes for electrons-is an emerging approach for the realization of exotic properties, including superconductivity and correlated insulators, in two-dimensional materials. While moiré SL engineering has been a popular approach, nanopatterning is an attractive alternative offering control over the pattern and wavelength of the SL. However, the disorder arising in the system due to imperfect nanopatterning is seldom studied. Here, by creating a square lattice of nanoholes in the SiO2dielectric layer using nanolithography, we study the SL potential and the disorder formed in hBN-graphene-hBN heterostructures. Specifically, we observe that while electrical transport shows distinct SL satellite peaks, the disorder of the device is significantly higher than graphene devices without any SL. We use finite-element simulations combined with a resistor network model to calculate the effects of this disorder on the transport properties of graphene. We consider three types of disorder: nanohole size variations, adjacent nanohole mergers, and nanohole vacancies. Comparing our experimental results with the model, we find that the disorder primarily originates from nanohole size variations rather than nanohole mergers in square SLs. We further confirm the validity of our model by comparing the results with quantum transport simulations. Our findings highlight the applicability of our simple framework to predict and engineer disorder in patterned SLs, specifically correlating variations in the resultant SL patterns to the observed disorder. Our combined experimental and theoretical results could serve as a valuable guide for optimizing nanofabrication processes to engineer disorder in nanopatterned SLs.

Synthesis, Modulation, and Application of Two-Dimensional TMD Heterostructures

Two-dimensional (2D) transition metal dichalcogenide (TMD) heterostructures have attracted a lot of attention due to their rich material diversity and stack geometry, precise controllability of structure and properties, and potential practical applications. These heterostructures not only overcome the inherent limitations of individual materials but also enable the realization of new properties through appropriate combinations, establishing a platform to explore new physical and chemical properties at micro-nano-pico scales. In this review, we systematically summarize the latest research progress in the synthesis, modulation, and application of 2D TMD heterostructures. We first introduce the latest techniques for fabricating 2D TMD heterostructures, examining the rationale, mechanisms, advantages, and disadvantages of each strategy. Furthermore, we emphasize the importance of characteristic modulation in 2D TMD heterostructures and discuss some approaches to achieve novel functionalities. Then, we summarize the representative applications of 2D TMD heterostructures. Finally, we highlight the challenges and future perspectives in the synthesis and device fabrication of 2D TMD heterostructures and provide some feasible solutions.

Nonlinear physics of moiré superlattices

Nonlinear physics is one of the most important research fields in modern physics and materials science. It offers an unprecedented paradigm for exploring many fascinating physical phenomena and realizing diverse cutting-edge applications inconceivable in the framework of linear processes. Here we review the recent theoretical and experimental progress concerning the nonlinear physics of synthetic quantum moiré superlattices. We focus on the emerging nonlinear electronic, optical and optoelectronic properties of moiré superlattices, including but not limited to the nonlinear anomalous Hall effect, dynamically twistable harmonic generation, nonlinear optical chirality, ultralow-power-threshold optical solitons and spontaneous photogalvanic effect. We also present our perspectives on the future opportunities and challenges in this rapidly progressing field, and highlight the implications for advances in both fundamental physics and technological innovations.

Homo-Site Nucleation Growth of Twisted Bilayer MoS2 with Commensurate Angles

Moiré superlattices, composed of two layers of transition metal dichalcogenides with a relative twist angle, provide a novel platform for exploring the correlated electronic phases and excitonic physics. Here, a gas-flow perturbation chemical vapor deposition (CVD) approach is demonstrated to directly grow MoS2 bilayer with versatile twist angles. It is found that the formation of twisted bilayer MoS2 homostructures sensitively depends on the gas-flow perturbation modes, correspondingly featuring the nucleation sites of the second layer at the same (homo-site) as or at the different (hetero-site) from that of the first layer. The commensurate twist angle of ≈22° in homo-site nucleation strategy accounts for ≈16% among the broad range of twist angles due to its low formation energy, which is in consistence with the theoretical calculation. More importantly, moiré interlayer excitons with the enhanced photoluminescence (PL) intensity and the prolonged lifetime are evidenced in the twisted bilayer MoS2 with a commensurate angle of 22°, which is owing to the reason that the strong moiré potential facilitates the interlayer excitons to be trapped in the moiré superlattices. The work provides a feasible route to controllably built twisted MoS2 homostructures with strong moiré potential to investigate the correlated physics in twistronics systems.

Interlayer and Moiré excitons in atomically thin double layers: From individual quantum emitters to degenerate ensembles

Abstract

Interlayer excitons (IXs), composed of electron and hole states localized in different layers, excel in bilayers composed of atomically thin van der Waals materials such as semiconducting transition-metal dichalcogenides (TMDs) due to drastically enlarged exciton binding energies, exciting spin-valley properties, elongated lifetimes, and large permanent dipoles. The latter allows modification by electric fields and the study of thermalized bosonic quasiparticles, from the single particle level to interacting degenerate dense ensembles. Additionally, the freedom to combine bilayers of different van der Waals materials without lattice or relative twist-angle constraints leads to layer-hybridized and Moiré excitons, which can be widely engineered. This article covers fundamental aspects of IXs, including correlation phenomena as well as the consequence of Moiré superlattices with a strong focus on TMD homo- and heterobilayers.

Graphical abstract

Modulation of Kondo Behavior in a Two-Dimensional Epitaxial Bilayer Bi(111)/Fe3GeTe2 Moiré Heterostructure

Artificial two-dimensional (2D) moiré superlattices provide a platform for generating exotic quantum matter or phenomena. Here, an epitaxial heterostructure composed of bilayer Bi(111) and an Fe3GeTe2 substrate with a zero-twist angle is acquired by molecular beam epitaxy. Scanning tunneling microscopy and spectroscopy studies reveal the spatially tailored Kondo resonance and interfacial magnetism within this moiré superlattice. Combined with first-principles calculations, it is found that the modulation effect of the moiré superlattice originates from the interfacial orbital hybridization between Bi and Fe atoms. Our work provides a tunable platform for strong electron correlation studies to explore 2D artificial heavy Fermion systems and interface magnetism.

Moiré Exchange Effect in Twisted WSe_{2}/WS_{2} Heterobilayer

Moiré superlattices of layered transition metal dichalcogenides are proven to host periodic electron crystals due to strong correlation effects. These electron crystals can also be intertwined with intricate magnetic phenomena. In this Letter, we present our findings on the moiré exchange effect, resulting from the modulation of local magnetic moments by electron crystals within well-aligned WSe_{2}/WS_{2} heterobilayers. Employing polarization-resolved magneto-optical spectroscopy, we unveil a high-energy excitonic resonance near one hole per moiré unit cell (v=-1), which possesses a giant g factor several times greater than the already very large g factor of the WSe_{2} A exciton in this heterostructure. Supported by continuum model calculations, these high-energy states are found to be dark excitons brightened through Umklapp scattering from the moiré mini-Brillouin zone. When the carriers form a Mott insulating state near v=-1, the Coulomb exchange between doped carriers and excitons forms an effective magnetic field with moiré periodicity. This moiré exchange effect gives rise to the observed giant g factor for the excitonic Umklapp state.

Strong light-matter coupling in van der Waals materials

In recent years, two-dimensional (2D) van der Waals materials have emerged as a focal point in materials research, drawing increasing attention due to their potential for isolating and synergistically combining diverse atomic layers. Atomically thin transition metal dichalcogenides (TMDs) are one of the most alluring van der Waals materials owing to their exceptional electronic and optical properties. The tightly bound excitons with giant oscillator strength render TMDs an ideal platform to investigate strong light-matter coupling when they are integrated with optical cavities, providing a wide range of possibilities for exploring novel polaritonic physics and devices. In this review, we focused on recent advances in TMD-based strong light-matter coupling. In the foremost position, we discuss the various optical structures strongly coupled to TMD materials, such as Fabry-Perot cavities, photonic crystals, and plasmonic nanocavities. We then present several intriguing properties and relevant device applications of TMD polaritons. In the end, we delineate promising future directions for the study of strong light-matter coupling in van der Waals materials.

Modulation of Electrostatic Potential in 2D Crystal Engineered by an Array of Alternating Polar Molecules

The moiré potential in rotationally misfit two-dimensional (2D) heterostructures has been used to build artificial exciton and electron lattices, which have become platforms for realizing exotic electronic phases. Here, we demonstrate a different approach to create a superlattice potential in 2D crystals by using the near field of an array of polar molecules. A bilayer of titanyl phthalocyanine (TiOPc), consisting of alternating out-of-plane dipoles, is deposited on monolayer MoS2. Time-resolved two-photon photoemission spectroscopy reveals a pair of interlayer exciton states with an energy difference of ∼0.1 eV, which is consistent with the electrostatic potential modulation induced by the TiOPc bilayer as determined by density functional theory calculations. Because the symmetry and the period of this potential superlattice can be changed readily by using molecules of different shapes and sizes, molecule/2D heterostructures can be promising platforms for designing artificial exciton and electron lattices.

Two-dimensional electrons at mirror and twistronic twin boundaries in van der Waals ferroelectrics

Semiconducting transition metal dichalcogenides (MX2) occur in 2H and rhombohedral (3R) polytypes, respectively distinguished by anti-parallel and parallel orientation of consecutive monolayer lattices. In its bulk form, 3R-MX2 is ferroelectric, hosting an out-of-plane electric polarisation, the direction of which is dictated by stacking. Here, we predict that twin boundaries, separating adjacent polarisation domains with reversed built-in electric fields, are able to host two-dimensional electrons and holes with an areal density reaching  ~ 1013cm-2. Our modelling suggests that n-doped twin boundaries have a more promising binding energy than p-doped ones, whereas hole accumulation is stable at external surfaces of a twinned film. We also propose that assembling pairs of mono-twin films with a 'magic' twist angle θ* that provides commensurability between the moiré pattern at the interface and the accumulated carrier density, should promote a regime of strongly correlated states of electrons, such as Wigner crystals, and we specify the values of θ* for homo- and heterostructures of various TMDs.

Realizing Topological Superconductivity in Tunable Bose-Fermi Mixtures with Transition Metal Dichalcogenide Heterostructures

Heterostructures of two-dimensional transition metal dichalcogenides are emerging as a promising platform for investigating exotic correlated states of matter. Here, we propose to engineer Bose-Fermi mixtures in these systems by coupling interlayer excitons to doped charges in a trilayer structure. Their interactions are determined by the interlayer trion, whose spin-selective nature allows excitons to mediate an attractive interaction between charge carriers of only one spin species. Remarkably, we find that this causes the system to become unstable to topological p+ip superconductivity at low temperatures. We then demonstrate a general mechanism to develop and control this unconventional state by tuning the trion binding energy using a solid-state Feshbach resonance.

Evidence for electron-hole crystals in a Mott insulator

The coexistence of correlated electron and hole crystals enables the realization of quantum excitonic states, capable of hosting counterflow superfluidity and topological orders with long-range quantum entanglement. Here we report evidence for imbalanced electron-hole crystals in a doped Mott insulator, namely, α-RuCl3, through gate-tunable non-invasive van der Waals doping from graphene. Real-space imaging via scanning tunnelling microscopy reveals two distinct charge orderings at the lower and upper Hubbard band energies, whose origin is attributed to the correlation-driven honeycomb hole crystal composed of hole-rich Ru sites and rotational-symmetry-breaking paired electron crystal composed of electron-rich Ru-Ru bonds, respectively. Moreover, a gate-induced transition of electron-hole crystals is directly visualized, further corroborating their nature as correlation-driven charge crystals. The realization and atom-resolved visualization of imbalanced electron-hole crystals in a doped Mott insulator opens new doors in the search for correlated bosonic states within strongly correlated materials.

Spontaneous Supercrystal Formation During a Strain-Engineered Metal-Insulator Transition

Mott metal-insulator transitions possess electronic, magnetic, and structural degrees of freedom promising next-generation energy-efficient electronics. A previously unknown, hierarchically ordered, and anisotropic supercrystal state is reported and its intrinsic formation characterized in-situ during a Mott transition in a Ca2RuO4 thin film. Machine learning-assisted X-ray nanodiffraction together with cryogenic electron microscopy reveal multi-scale periodic domain formation at and below the film transition temperature (TFilm ≈ 200-250 K) and a separate anisotropic spatial structure at and above TFilm. Local resistivity measurements imply an intrinsic coupling of the supercrystal orientation to the material's anisotropic conductivity. These findings add a new degree of complexity to the physical understanding of Mott transitions, opening opportunities for designing materials with tunable electronic properties.

Enhancement of Interlayer Exciton Emission in a TMDC Heterostructure via a Multi-Resonant Chirped Microresonator Upto Room Temperature

We report on multi-resonance chirped distributed Bragg reflector (DBR) microcavities. These systems are employed to investigate the light-mater interaction with both intra- and inter-layer excitons of transition metal dichalcogenide (TMDC) bilayer heterostructures. The chirped DBRs consisting of SiO2 and Si3N4 layers of gradually varying thickness exhibit a broad stopband with a width exceeding 600 nm. Importantly, the structures provide multiple resonances across a broad spectral range, which can be matched to resonances of the embedded TMDC heterostructures. Studying cavity-coupled emission of both intra- and inter-layer excitons from an integrated WSe2/MoSe2 heterostructure in a chirped microcavity system, an enhanced interlayer exciton emission with a Purcell factor of 6.67 ± 1.02 at 4 K is observed. The cavity-enhanced emission of the interlayer exciton is used to investigate its temperature-dependent luminescence lifetime of 60 ps at room temperature. The cavity system modestly suppresses intralayer exciton emission by intentional detuning, thereby promoting a higher IX population and enhancing cavity-coupled interlayer exciton emission. This approach provides an intriguing platform for future studies of energetically distant and confined excitons in different semiconducting materials, which paves the way for various applications such as microlasers and single-photon sources by enabling precise emission control and utilizing multimode resonance light-matter interaction.

Spatial Filtering of Interlayer Exciton Ground State in WSe2/MoS2 Heterobilayer

Long-life interlayer excitons (IXs) in transition metal dichalcogenide (TMD) heterostructure are promising for realizing excitonic condensates at high temperatures. Critical to this objective is to separate the IX ground state (the lowest energy of IX state) emission from other states' emissions. Filtering the IX ground state is also essential in uncovering the dynamics of correlated excitonic states, such as the excitonic Mott insulator. Here, we show that the IX ground state in the WSe2/MoS2 heterobilayer can be separated from other states by its spatial profile. The emissions from different moiré IX modes are identified by their different energies and spatial distributions, which fits well with the rate-diffusion model for cascading emission. Our results show spatial filtering of the ground state mode and enrich the toolbox to realize correlated states at elevated temperatures.

Electrically tunable non-radiative lifetime in WS2/WSe2 heterostructures

Van der Waals heterostructures based on transition metal dichalcogenides (TMDs) have emerged as excellent candidates for next-generation optoelectronics and valleytronics, due to their fascinating physical properties. The understanding and active control of the relaxation dynamics of heterostructures play a crucial role in device design and optimization. Here, we investigate the back-gate modulation of exciton dynamics in a WS2/WSe2 heterostructure by combining time-resolved photoluminescence (TRPL) and transient absorption spectroscopy (TAS) at cryogenic temperatures. We find that the non-radiative relaxation lifetimes of photocarriers in heterostructures can be electrically controlled for samples with different twist-angles, whereas such lifetime tuning is not present in standalone monolayers. We attribute such an observation to doping-controlled competition between interlayer and intralayer recombination pathways in high-quality WS2/WSe2 samples. The simultaneous measurement of TRPL and TAS lifetimes within the same sample provides additional insight into the influence of coexisting excitons and background carriers on the photo-response, and points to the potential of tailoring light-matter interactions in TMD heterostructures.

Strain-free MoS2/ZrGe2N4 van der Waals Heterostructure: Tunable Electronic Properties with Type-II Band Alignment

Vertically stacked van der Waals heterostructures (vdW-HS) amplify the scope of 2D materials for emerging technological applications, such as nanodevices and solar cells. Here, we present a first-principles study on the formation energy and electronic properties of the heterobilayer (HBL) MoS2/ZrGe2N4, which forms a strain-free vdW-HS thanks to the identical lattice parameters of its constituents. This system has an indirect band gap with type-II band alignment, with the highest occupied and lowest unoccupied states localized on MoS2 and ZrGe2N4, respectively. Biaxial strain, which generally reduces the band gap regardless of compression or expansion, is applied to tune the electronic properties of the HBL. A small amount of tensile strain (>1%) leads to an indirect-to-direct transition, thereby shifting the band edges at the center of the Brillouin zone and leading to optical absorption in the visible region. These results suggest the potential application of HBL MoS2/ZrGe2N4 in optoelectronic devices.

Anomalous Interlayer Exciton Diffusion in WS2/WSe2 Moiré Heterostructure

Stacking van der Waals crystals allows for the on-demand creation of a periodic potential landscape to tailor the transport of quasiparticle excitations. We investigate the diffusion of photoexcited electron-hole pairs, or excitons, at the interface of WS2/WSe2 van der Waals heterostructure over a wide range of temperatures. We observe the appearance of distinct interlayer excitons for parallel and antiparallel stacking and track their diffusion through spatially and temporally resolved photoluminescence spectroscopy from 30 to 250 K. While the measured exciton diffusivity decreases with temperature, it surprisingly plateaus below 90 K. Our observations cannot be explained by classical models like hopping in the moiré potential. A combination of ab initio theory and molecular dynamics simulations suggests that low-energy phonons arising from the mismatched lattices of moiré heterostructures, also known as phasons, play a key role in describing and understanding this anomalous behavior of exciton diffusion. Our observations indicate that the moiré potential landscape is dynamic down to very low temperatures and that the phason modes can enable efficient transport of energy in the form of excitons.

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.

Boosting Monolayer Transition Metal Dichalcogenides Growth by Hydrogen-Free Ramping during Chemical Vapor Deposition

The controlled vapor-phase synthesis of two-dimensional (2D) transition metal dichalcogenides (TMDs) is essential for functional applications. While chemical vapor deposition (CVD) techniques have been successful for transition metal sulfides, extending these methods to selenides and tellurides often faces challenges due to uncertain roles of hydrogen (H2) in their synthesis. Using CVD growth of MoSe2 as an example, this study illustrates the role of a H2-free environment during temperature ramping in suppressing the reduction of MoO3, which promotes effective vaporization and selenization of the Mo precursor to form MoSe2 monolayers with excellent crystal quality. As-synthesized MoSe2 monolayer-based field-effect transistors show excellent carrier mobility of up to 20.9 cm2/(V·s) with an on-off ratio of 7 × 107. This approach can be extended to other TMDs, such as WSe2, MoTe2, and MoSe2/WSe2 in-plane heterostructures. Our work provides a rational and facile approach to reproducibly synthesize high-quality TMD monolayers, facilitating their translation from laboratory to manufacturing.

Wigner molecular crystals from multielectron moiré artificial atoms

Semiconductor moiré superlattices provide a versatile platform to engineer quantum solids composed of artificial atoms on moiré sites. Previous studies have mostly focused on the simplest correlated quantum solid-the Fermi-Hubbard model-in which intra-atom interactions are simplified to a single onsite repulsion energy U. Here we report the experimental observation of Wigner molecular crystals emerging from multielectron artificial atoms in twisted bilayer tungsten disulfide moiré superlattices. Using scanning tunneling microscopy, we demonstrate that Wigner molecules appear in multielectron artificial atoms when Coulomb interactions dominate. The array of Wigner molecules observed in a moiré superlattice comprises a crystalline phase of electrons: the Wigner molecular crystal, which is shown to be highly tunable through mechanical strain, moiré period, and carrier charge type.

Effect of doping and defects on the electronic properties of MoS2/WSe2 bilayer heterostructure: a first-principles study

This work studies the effect of Nb, Mo, Re dopant, and Se vacancy in WSe2 on the electronic and optical properties of the MoS2/WSe2 bilayer heterostructure based on first-principles calculations. Our research shows that the MoS2/WSe2 bilayer heterostructure exhibits a type-II band alignment with a valence band offset (VBO) of 1.07 eV and a conduction band offset (CBO) of 1.00 eV. It also shows that different dopants or defects can considerably modulate the energy band alignment and interlayer charge transfer of the heterostructure. Owing to the orbital hybridization of the dopant atoms with other atoms and the consequent enhancement of the coupling between the two structural layers, a transition of the band alignment from type-II to type-I is realized with the Re dopant. The effect of doping and defects on the electronic properties of heterojunctions contributes to applications in high-performance optoelectronic devices.

Correlated Charge Density Wave Insulators in Chirally Twisted Triple Bilayer Graphene

Electrons residing in a flat-band system can play a vital role in triggering spectacular phenomenology due to relatively large interactions and spontaneous breaking of different degeneracies. In this work, we demonstrate chirally twisted triple bilayer graphene, a new moiré structure formed by three pieces of helically stacked Bernal bilayer graphene, as a highly tunable flat-band system. In addition to the correlated insulators showing at integer moiré fillings, commonly attributed to interaction induced symmetry broken isospin flavors in graphene, we observe abundant insulating states at half-integer moiré fillings, suggesting a longer-range interaction and the formation of charge density wave insulators which spontaneously break the moiré translation symmetry. With weak out-of-plane magnetic field applied, as observed half-integer filling states are enhanced and more quarter-integer filling states appear, pointing toward further quadrupling moiré unit cells. The insulating states at fractional fillings combined with Hartree-Fock calculations demonstrate the observation of a new type of correlated charge density wave insulators in graphene and points to a new accessible twist manner engineering correlated moiré electronics.

Chern Insulator States with Tunable Chern Numbers in a Graphene Moiré Superlattice

Moiré superlattices, constituted by two-dimensional materials, demonstrate a variety of strongly correlated and topological phenomena including correlated insulators, superconductivity, and integer/fractional Chern insulators. In the realm of topological nontrivial Chern insulators within specific moiré superlattices, previous studies usually observe a single Chern number at a given filling factor in a device. Here we present the observation of gate-tunable Chern numbers within the Chern insulator state of an ABC-stacked trilayer graphene/hexagonal boron nitride moiré superlattice device. Near quarter filling, the moiré superlattice exhibits spontaneous valley polarization and distinct ferromagnetism associated with the Chern insulator states over a range of the displacement field. Surprisingly we find a transition of the Chern number from C = 3 to 4 as the displacement field is increased. Our observation of gate-tunable correlated Chern insulators suggests new ways to control and manipulate topological states in a moiré superlattice device.

Sublattice Structure and Topology in Spontaneously Crystallized Electronic States

The prediction and realization of the quantum anomalous Hall effect are often intimately connected to honeycomb lattices in which the sublattice degree of freedom plays a central role in the nontrivial topology. Two-dimensional Wigner crystals, on the other hand, form triangular lattices without sublattice degrees of freedom, resulting in a topologically trivial state. Here, we discuss the possibility of spontaneously formed honeycomb-lattice crystals that exhibit the quantum anomalous Hall effect. Starting from a single-band system with nontrivial quantum geometry, we derive the mean-field energy functional of a class of crystal states and express it as a model of sublattice pseudospins in momentum space. We find that nontrivial quantum geometry leads to extra terms in the pseudospin model that break an effective "time-reversal symmetry" and favor a topologically nontrivial pseudospin texture. When the effects of these extra terms dominate over the ferromagnetic exchange coupling between pseudospins, the anomalous Hall crystal state becomes energetically favorable over the trivial Wigner crystal state.

Double Superconducting Dome of Quasi Two-Dimensional TaS2 in Non-Centrosymmetric van der Waals Heterostructure

Two-dimensional van der Waals heterostructures (2D-vdWHs) based on transition metal dichalcogenides (TMDs) provide unparalleled control over electronic properties. However, the interlayer coupling is challenged by the interfacial misalignment and defects, which hinders a comprehensive understanding of the intertwined electronic orders, especially superconductivity and charge density wave (CDW). Here, by using pressure to regulate the interlayer coupling of non-centrosymmetric 6R-TaS2 vdWHs, we observe an unprecedented phase diagram in TMDs. This phase diagram encompasses successive suppression of the original CDW states from alternating H-layer and T-layer configurations, the emergence and disappearance of a new CDW-like state, and a double superconducting dome induced by different interlayer coupling effects. These results not only illuminate the crucial role of interlayer coupling in shaping the complex phase diagram of TMD systems but also pave a new avenue for the creation of a novel family of bulk heterostructures with customized 2D properties.

Tunable exciton valley-pseudospin orders in moiré superlattices

Excitons in two-dimensional (2D) semiconductors have offered an attractive platform for optoelectronic and valleytronic devices. Further realizations of correlated phases of excitons promise device concepts not possible in the single particle picture. Here we report tunable exciton "spin" orders in WSe2/WS2 moiré superlattices. We find evidence of an in-plane (xy) order of exciton "spin"-here, valley pseudospin-around exciton filling vex = 1, which strongly suppresses the out-of-plane "spin" polarization. Upon increasing vex or applying a small magnetic field of ~10 mT, it transitions into an out-of-plane ferromagnetic (FM-z) spin order that spontaneously enhances the "spin" polarization, i.e., the circular helicity of emission light is higher than the excitation. The phase diagram is qualitatively captured by a spin-1/2 Bose-Hubbard model and is distinct from the fermion case. Our study paves the way for engineering exotic phases of matter from correlated spinor bosons, opening the door to a host of unconventional quantum devices.

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.

Observation of interlayer plasmon polaron in graphene/WS2 heterostructures

Harnessing electronic excitations involving coherent coupling to bosonic modes is essential for the design and control of emergent phenomena in quantum materials. In situations where charge carriers induce a lattice distortion due to the electron-phonon interaction, the conducting states get "dressed", which leads to the formation of polaronic quasiparticles. The exploration of polaronic effects on low-energy excitations is in its infancy in two-dimensional materials. Here, we present the discovery of an interlayer plasmon polaron in heterostructures composed of graphene on top of single-layer WS2. By using micro-focused angle-resolved photoemission spectroscopy during in situ doping of the top graphene layer, we observe a strong quasiparticle peak accompanied by several carrier density-dependent shake-off replicas around the single-layer WS2 conduction band minimum. Our results are explained by an effective many-body model in terms of a coupling between single-layer WS2 conduction electrons and an interlayer plasmon mode. It is important to take into account the presence of such interlayer collective modes, as they have profound consequences for the electronic and optical properties of heterostructures that are routinely explored in many device architectures involving 2D transition metal dichalcogenides.

Imaging moiré excited states with photocurrent tunnelling microscopy

Moiré superlattices provide a highly tuneable and versatile platform to explore novel quantum phases and exotic excited states ranging from correlated insulators to moiré excitons. Scanning tunnelling microscopy has played a key role in probing microscopic behaviours of the moiré correlated ground states at the atomic scale. However, imaging of quantum excited states in moiré heterostructures remains an outstanding challenge. Here we develop a photocurrent tunnelling microscopy technique that combines laser excitation and scanning tunnelling spectroscopy to directly visualize the electron and hole distribution within the photoexcited moiré exciton in twisted bilayer WS2. The tunnelling photocurrent alternates between positive and negative polarities at different locations within a single moiré unit cell. This alternating photocurrent originates from the in-plane charge transfer moiré exciton in twisted bilayer WS2, predicted by our GW-Bethe-Salpeter equation calculations, that emerges from the competition between the electron-hole Coulomb interaction and the moiré potential landscape. Our technique enables the exploration of photoexcited non-equilibrium moiré phenomena at the atomic scale.

Mapping charge excitations in generalized Wigner crystals

Transition metal dichalcogenide-based moiré superlattices exhibit strong electron-electron correlations, thus giving rise to strongly correlated quantum phenomena such as generalized Wigner crystal states. Evidence of Wigner crystals in transition metal dichalcogenide moire superlattices has been widely reported from various optical spectroscopy and electrical conductivity measurements, while their microscopic nature has been limited to the basic lattice structure. Theoretical studies predict that unusual quasiparticle excitations across the correlated gap between upper and lower Hubbard bands can arise due to long-range Coulomb interactions in generalized Wigner crystal states. However, the microscopic proof of such quasiparticle excitations is challenging because of the low excitation energy of the Wigner crystal. Here we describe a scanning single-electron charging spectroscopy technique with nanometre spatial resolution and single-electron charge resolution that enables us to directly image electron and hole wavefunctions and to determine the thermodynamic gap of generalized Wigner crystal states in twisted WS2 moiré heterostructures. High-resolution scanning single-electron charging spectroscopy combines scanning tunnelling microscopy with a monolayer graphene sensing layer, thus enabling the generation of individual electron and hole quasiparticles in generalized Wigner crystals. We show that electron and hole quasiparticles have complementary wavefunction distributions and that thermodynamic gaps of ∼50 meV exist for the 1/3 and 2/3 generalized Wigner crystal states in twisted WS2.

Conduction Band Replicas in a 2D Moiré Semiconductor Heterobilayer

Stacking monolayer semiconductors creates moiré patterns, leading to correlated and topological electronic phenomena, but measurements of the electronic structure underpinning these phenomena are scarce. Here, we investigate the properties of the conduction band in moiré heterobilayers of WS2/WSe2 using submicrometer angle-resolved photoemission spectroscopy with electrostatic gating. We find that at all twist angles the conduction band edge is the K-point valley of the WS2, with a band gap of 1.58 ± 0.03 eV. From the resolved conduction band dispersion, we deduce an effective mass of 0.15 ± 0.02 me. Additionally, we observe replicas of the conduction band displaced by reciprocal lattice vectors of the moiré superlattice. We argue that the replicas result from the moiré potential modifying the conduction band states rather than final-state diffraction. Interestingly, the replicas display an intensity pattern with reduced 3-fold symmetry, which we show implicates the pseudo vector potential associated with in-plane strain in moiré band formation.

Superlattice Quantum Solid of Dipolar Excitons

We study dipolar excitons confined at 330 mK in a square electrostatic lattice of a GaAs double quantum well. In the dipolar occupation blockade regime, at 3/2 filling, we evidence that excitons form a face-centered superlattice quantum solid. This phase is realized with high purity across 36 lattice sites, in a regime where the mean interaction energy exceeds the depth of the electrostatic lattice confinement. The superlattice solid then closely relates to Wigner crystals.

Atomic-scale visualization of the interlayer Rydberg exciton complex in moiré heterostructures

Excitonic systems, facilitated by optical pumping, electrostatic gating or magnetic field, sustain composite particles with fascinating physics. Although various intriguing excitonic phases have been revealed via global measurements, the atomic-scale accessibility towards excitons has yet to be established. Here, we realize the ground-state interlayer exciton complexes through the intrinsic charge transfer in monolayer YbCl3/graphite heterostructure. Combining scanning tunneling microscope and theoretical calculations, the excitonic in-gap states are directly profiled. The out-of-plane excitonic charge clouds exhibit oscillating Rydberg nodal structure, while their in-plane arrangements are determined by moiré periodicity. Exploiting the tunneling probe to reflect the shape of charge clouds, we reveal the principal quantum number hierarchy of Rydberg series, which points to an excitonic energy-level configuration with unusually large binding energy. Our results demonstrate the feasibility of mapping out the charge clouds of excitons microscopically and pave a brand-new way to directly investigate the nanoscale order of exotic correlated phases.

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.

Correlation-driven nonequilibrium exciton site transition in a WSe2/WS2 moiré supercell

Moiré superlattices of transition metal dichalcogenides offer a unique platform to explore correlated exciton physics with optical spectroscopy. Whereas the spatially modulated potentials evoke that the exciton resonances are distinct depending on a site in a moiré supercell, there have been no clear demonstration how the moiré excitons trapped in different sites dynamically interact with the doped carriers; so far the exciton-electron dynamic interactions were presumed to be site-dependent. Thus, the transient emergence of nonequilibrium correlations are open questions, but existing studies are limited to steady-state optical measurements. Here we report experimental fingerprints of site-dependent exciton correlations under continuous-wave as well as ultrashort optical excitations. In near-zero angle-aligned WSe2/WS2 heterobilayers, we observe intriguing polarization switching and strongly enhanced Pauli blocking near the Mott insulating state, dictating the dominant correlation-driven effects. When the twist angle is near 60°, no such correlations are observed, suggesting the strong dependence of atomic registry in moiré supercell configuration. Our studies open the door to largely unexplored nonequilibrium correlations of excitons in moiré superlattices.

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.

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.

The Emergence of the Hexagonal Lattice in Two-Dimensional Wigner Fragments

At very low density, the electrons in a uniform electron gas spontaneously break symmetry and form a crystalline lattice called a Wigner crystal. But which type of crystal will the electrons form? We report a numerical study of the density profiles of fragments of Wigner crystals from first principles. To simulate Wigner fragments, we use Clifford periodic boundary conditions and a renormalized distance in the Coulomb potential. Moreover, we show that high-spin restricted open-shell Hartree-Fock theory becomes exact in the low-density limit. We are thus able to accurately capture the localization in two-dimensional Wigner fragments with many electrons. No assumptions about the positions where the electrons will localize are made. The density profiles we obtain emerge naturally when we minimize the total energy of the system. We clearly observe the emergence of the hexagonal crystal structure, which has been predicted to be the ground-state structure of the two-dimensional Wigner crystal.