Quantum anomalous Hall effect from intertwined moiré bands

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.

Evidence of striped electronic phases in a structurally modulated superlattice

The electronic properties of crystals can be manipulated by superimposing spatially periodic electric, magnetic or structural modulations. Long-wavelength modulations incommensurate with the atomic lattice are particularly interesting1, exemplified by recent advances in two-dimensional (2D) moiré materials2,3. Bulk van der Waals (vdW) superlattices4-8 hosting 2D interfaces between minimally disordered layers represent scalable bulk analogues of artificial vdW heterostructures and present a complementary venue to explore incommensurately modulated 2D states. Here we report the bulk vdW superlattice SrTa2S5 realizing an incommensurate one-dimensional (1D) structural modulation of 2D transition metal dichalcogenide (TMD) H-TaS2 layers. High-quality electronic transport in the H-TaS2 layers, evidenced by quantum oscillations, is made anisotropic by the modulation and exhibits commensurability oscillations paralleling lithographically modulated 2D systems9-11. We also find unconventional, clean-limit superconductivity in SrTa2S5 with a pronounced suppression of interlayer relative to intralayer coherence. The in-plane magnetic field dependence of interlayer critical current, together with electron diffraction from the structural modulation, suggests superconductivity12-14 in SrTa2S5 is spatially modulated and mismatched between adjacent TMD layers. With phenomenology suggestive of pair-density wave superconductivity15-17, SrTa2S5 may present a pathway for microscopic evaluation of this unconventional order18-21. More broadly, SrTa2S5 establishes bulk vdW superlattices as versatile platforms to address long-standing predictions surrounding modulated electronic phases in the form of nanoscale vdW devices12,13 to macroscopic crystals22,23.

Preservation of Topological Surface States in Millimeter-Scale Transferred Membranes

Ultrathin topological insulator membranes are building blocks of exotic quantum matter. However, traditional epitaxy of these materials does not facilitate stacking in arbitrary orders, while mechanical exfoliation from bulk crystals is also challenging due to the non-negligible interlayer coupling therein. Here we liberate millimeter-scale films of the topological insulator Bi2Se3, grown by molecular beam epitaxy, down to 3 quintuple layers. We characterize the preservation of the topological surface states and quantum well states in transferred Bi2Se3 films using angle-resolved photoemission spectroscopy. Leveraging the photon-energy-dependent surface sensitivity, the photoemission spectra taken with 6 and 21.2 eV photons reveal a transfer-induced migration of the topological surface states from the top to the inner layers. By establishing clear electronic structures of the transferred films and unveiling the wave function relocation of the topological surface states, our work lays the physics foundation crucial for the future fabrication of artificially stacked topological materials with single-layer precision.

Spin Gapless Quantum Materials and Devices

Quantum materials, with nontrivial quantum phenomena and mechanisms, promise efficient quantum technologies with enhanced functionalities. Quantum technology is held back because a gap between fundamental science and its implementation is not fully understood yet. In order to capitalize the quantum advantage, a new perspective is required to figure out and close this gap. In this review, spin gapless quantum materials, featured by fully spin-polarized bands and the electron/hole transport, are discussed from the perspective of fundamental understanding and device applications. Spin gapless quantum materials can be simulated by minimal two-band models and could help to understand band structure engineering in various topological quantum materials discovered so far. It is explicitly highlighted that various types of spin gapless band dispersion are fundamental ingredients to understand quantum anomalous Hall effect. Based on conventional transport in the bulk and topological transport on the boundaries, various spintronic device aspects of spin gapless quantum materials as well as their advantages in different models for topological field effect transistors are reviewed.

Directional Localization from a Magnetic Field in Moiré Systems

Moiré materials provide a highly tunable platform in which novel electronic phenomena can emerge. We study strained moiré materials in a uniform magnetic field and predict highly anisotropic electrical conductivity that switches easy axis as magnetic field or strain is varied. The dramatic anisotropy reflects one-dimensional localization (directional localization) of the electron wave functions along a crystal axis due to quantum interference effects. This can be understood in an effective one-dimensional quasiperiodic Aubry-André-Harper-like model, or in a complementary semiclassical picture. This phenomenon should be observable in strained moiré materials at realistic fields and low strain disorder, as well as unstrained systems with anisotropic Fermi surfaces.

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.

Rules for dissipationless topotronics

Topological systems hosting gapless boundary states have attracted huge attention as promising components for next-generation information processing, attributed to their capacity for dissipationless electronics. Nevertheless, recent theoretical and experimental inquiries have revealed the emergence of energy dissipation in precisely quantized electrical transport. Here, we present a criterion for the realization of truly no-dissipation design, characterized as Nin = Ntunl + Nbs, where Nin, Ntunl, and Nbs represent the number of modes participating in injecting, tunneling, and backscattering processes, respectively. The key lies in matching the number of injecting, tunneling, and backscattering modes, ensuring the equilibrium among all engaged modes inside the device. Among all the topological materials, we advocate for the indispensability of Chern insulators exhibiting higher Chern numbers to achieve functional devices and uphold the no-dissipation rule simultaneously. Furthermore, we design the topological current divider and collector, evading dissipation upon fulfilling the established criterion. Our work paves the path for developing the prospective topotronics.

Thermodynamic Response and Neutral Excitations in Integer and Fractional Quantum Anomalous Hall States Emerging from Correlated Flat Bands

Integer and fractional Chern insulators have been extensively explored in correlated flat band models. Recently, the prediction and experimental observation of fractional quantum anomalous Hall (FQAH) states with spontaneous time-reversal symmetry breaking have garnered attention. While the thermodynamics of integer quantum anomalous Hall (IQAH) states have been systematically studied, our theoretical knowledge on thermodynamic properties of FQAH states has been severely limited. Here, we delve into the general thermodynamic response and collective excitations of both IQAH and FQAH states within the paradigmatic flat Chern-band model with remote band considered. Our key findings include (i) in both ν=1 IQAH and ν=1/3 FQAH states, even without spin fluctuations, the charge-neutral collective excitations would lower the onset temperature of these topological states, to a value significantly smaller than the charge gap, due to band mixing and multiparticle scattering; (ii) by employing large-scale thermodynamic simulations in FQAH states in the presence of strong interband mixing between C=±1 bands, we find that the lowest collective excitations manifest as the zero-momentum excitons in the IQAH state, whereas in the FQAH state, they take the form of magnetorotons with finite momentum; (iii) the unique charge oscillations in FQAH states are exhibited with distinct experimental signatures, which we propose to detect in future experiments.

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.

Engineering the Band Topology in a Rhombohedral Trilayer Graphene Moiré Superlattice

Moiré superlattices have become a fertile playground for topological Chern insulators, where the displacement field can tune the quantum geometry and Chern number of the topological band. However, in experiments, displacement field engineering of spontaneous symmetry-breaking Chern bands has not been demonstrated. Here in a rhombohedral trilayer graphene moiré superlattice, we use a thermodynamic probe and transport measurement to monitor the Chern number evolution as a function of the displacement field. At a quarter filling of the moiré band, a novel Chern number of three is unveiled to compete with the well-established number of two upon turning on the electric field and survives when the displacement field is sufficiently strong. The transition can be reconciled by a nematic instability on the Fermi surface due to the pseudomagnetic vector field potentials associated with moiré strain patterns. Our work opens more opportunities to active control of Chern numbers in van der Waals moiré systems.

Polarization-driven band topology evolution in twisted MoTe2 and WSe2

Motivated by recent experimental observations of opposite Chern numbers in R-type twisted MoTe2 and WSe2 homobilayers, we perform large-scale density-functional-theory calculations with machine learning force fields to investigate moiré band topology across a range of twist angles in both materials. We find that the Chern numbers of the moiré frontier bands change sign as a function of twist angle, and this change is driven by the competition between moiré ferroelectricity and piezoelectricity. Our large-scale calculations, enabled by machine learning methods, reveal crucial insights into interactions across different scales in twisted bilayer systems. The interplay between atomic-level relaxation effects and moiré-scale electrostatic potential variation opens new avenues for the design of intertwined topological and correlated states, including the possibility of mimicking higher Landau level physics in the absence of magnetic field.

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.

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.

Low-Temperature Vapor-Phase Growth of 2D Metal Chalcogenides

2D metal chalcogenides (MCs) have garnered significant attention from both scientific and industrial communities due to their potential in developing next-generation functional devices. Vapor-phase deposition methods have proven highly effective in fabricating high-quality 2D MCs. Nevertheless, the conventionally high thermal budgets required for synthesizing 2D MCs pose limitations, particularly in the integration of multiple components and in specialized applications (such as flexible electronics). To overcome these challenges, it is desirable to reduce the thermal energy requirements, thus facilitating the growth of various 2D MCs at lower temperatures. Numerous endeavors have been undertaken to develop low-temperature vapor-phase growth techniques for 2D MCs, and this review aims to provide an overview of the latest advances in low-temperature vapor-phase growth of 2D MCs. Initially, the review highlights the latest progress in achieving high-quality 2D MCs through various low-temperature vapor-phase techniques, including chemical vapor deposition (CVD), metal-organic CVD, plasma-enhanced CVD, atomic layer deposition (ALD), etc. The strengths and current limitations of these methods are also evaluated. Subsequently, the review consolidates the diverse applications of 2D MCs grown at low temperatures, covering fields such as electronics, optoelectronics, flexible devices, and catalysis. Finally, current challenges and future research directions are briefly discussed, considering the most recent progress in the field.

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.

Gold-Template-Assisted Mechanical Exfoliation of Large-Area 2D Layers Enables Efficient and Precise Construction of Moiré Superlattices

Moiré superlattices, consisting of rotationally aligned 2D atomically thin layers, provide a highly novel platform for the study of correlated quantum phenomena. However, reliable and efficient construction of moiré superlattices is challenging because of difficulties to accurately angle-align small exfoliated 2D layers and the need to shun wet-transfer processes. Here, efficient and precise construction of various moiré superlattices is demonstrated by picking up and stacking large-area 2D mono- or few-layer crystals with predetermined crystal axes, made possible by a gold-template-assisted mechanical exfoliation method. The exfoliated 2D layers are semiconductors, superconductors, or magnets and their high quality is confirmed by photoluminescence and Raman spectra and by electrical transport measurements of fabricated field-effect transistors and Hall devices. Twisted homobilayers with angle-twisting accuracy of ≈0.3°, twisted heterobilayers with sub-degree angle-alignment accuracy, and multilayer superlattices are precisely constructed and characterized by their moiré patterns, interlayer excitons, and second harmonic generation. The present study paves the way for exploring emergent phenomena in moiré superlattices.

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.

Evidence of the fractional quantum spin Hall effect in moiré MoTe2

Quantum spin Hall (QSH) insulators are two-dimensional electronic materials that have a bulk band gap similar to an ordinary insulator but have topologically protected pairs of edge modes of opposite chiralities1-6. So far, experimental studies have found only integer QSH insulators with counter-propagating up-spins and down-spins at each edge leading to a quantized conductance G0 = e2/h (with e and h denoting the electron charge and Planck's constant, respectively)7-14. Here we report transport evidence of a fractional QSH insulator in 2.1° twisted bilayer MoTe2, which supports spin-Sz conservation and flat spin-contrasting Chern bands15,16. At filling factor ν = 3 of the moiré valence bands, each edge contributes a conductance3 2 G 0 with zero anomalous Hall conductivity. The state is probably a time-reversal pair of the even-denominator 3/2-fractional Chern insulators. Furthermore, at ν = 2, 4 and 6, we observe a single, double and triple QSH insulator with each edge contributing a conductance G0, 2G0 and 3G0, respectively. Our results open up the possibility of realizing time-reversal symmetric non-abelian anyons and other unexpected topological phases in highly tunable moiré materials17-19.

Spotlight: Visualization of Moiré Quantum Phenomena in Transition Metal Dichalcogenide with Scanning Tunneling Microscopy

Transition metal dichalcogenide (TMD) moiré superlattices have emerged as a significant area of study in condensed matter physics. Thanks to their superior optical properties, tunable electronic band structure, strong Coulomb interactions, and quenched electron kinetic energy, they offer exciting avenues to explore correlated quantum phenomena, topological properties, and light-matter interactions. In recent years, scanning tunneling microscopy (STM) has made significant impacts on the study of these fields by enabling intrinsic surface visualization and spectroscopic measurements with unprecedented atomic scale detail. Here, we spotlight the key findings and innovative developments in imaging and characterization of TMD heterostructures via STM, from its initial implementation on the in situ grown sample to the latest photocurrent tunneling microscopy. The evolution in sample design, progressing from a conductive to an insulating substrate, has not only expanded our control over TMD moiré superlattices but also promoted an understanding of their structures and strongly correlated properties, such as the structural reconstruction and formation of generalized two-dimensional Wigner crystal states. In addition to highlighting recent advancements, we outline upcoming challenges, suggest the direction of future research, and advocate for the versatile use of STM to further comprehend and manipulate the quantum dynamics in TMD moiré superlattices.

Monolayer V_{2}MX_{4}: A New Family of Quantum Anomalous Hall Insulators

We theoretically propose that the van der Waals layered ternary transition metal chalcogenide V_{2}MX_{4} (M=W, Mo; X=S, Se) is a new family of quantum anomalous Hall insulators with sizable bulk gap and Chern number C=-1. The large topological gap originates from the deep band inversion between spin-up bands contributed by d_{xz}, d_{yz} orbitals of V and spin-down band from d_{z^{2}} orbital of M at the Fermi level. Remarkably, the Curie temperature of monolayer V_{2}MX_{4} is predicted to be much higher than that of monolayer MnBi_{2}Te_{4}. Furthermore, the thickness dependence of the Chern number for few multilayers shows interesting oscillating behavior. The general physics from the d orbitals here applies to a large class of ternary transition metal chalcogenide such as Ti_{2}WX_{4} with the space group P-42m. These interesting predictions, if realized experimentally, could greatly promote the research and application of topological quantum physics.

Stacking Order Engineering of Two-Dimensional Materials and Device Applications

Stacking orders in 2D van der Waals (vdW) materials dictate the relative sliding (lateral displacement) and twisting (rotation) between atomically thin layers. By altering the stacking order, many new ferroic, strongly correlated and topological orderings emerge with exotic electrical, optical and magnetic properties. Thanks to the weak vdW interlayer bonding, such highly flexible and energy-efficient stacking order engineering has transformed the design of quantum properties in 2D vdW materials, unleashing the potential for miniaturized high-performance device applications in electronics, spintronics, photonics, and surface chemistry. This Review provides a comprehensive overview of stacking order engineering in 2D vdW materials and their device applications, ranging from the typical fabrication and characterization methods to the novel physical properties and the emergent slidetronics and twistronics device prototyping. The main emphasis is on the critical role of stacking orders affecting the interlayer charge transfer, orbital coupling and flat band formation for the design of innovative materials with on-demand quantum properties and surface potentials. By demonstrating a correlation between the stacking configurations and device functionality, we highlight their implications for next-generation electronic, photonic and chemical energy conversion devices. We conclude with our perspective of this exciting field including challenges and opportunities for future stacking order engineering research.

Phase and Composition Engineering of Self-Intercalated 2D Metallic Tantalum Sulfide for Second-Harmonic Generation

Self-intercalation in two-dimensional (2D) materials is significant, as it offers a versatile approach to modify material properties, enabling the creation of interesting functional materials, which is essential in advancing applications across various fields. Here, we define ic-2D materials as covalently bonded compounds that result from the self-intercalation of a metal into layered 2D compounds. However, precisely growing ic-2D materials with controllable phases and self-intercalation concentrations to fully exploit the applications in the ic-2D family remains a great challenge. Herein, we demonstrated the controlled synthesis of self-intercalated H-phase and T-phase Ta1+xS2 via a temperature-driven chemical vapor deposition (CVD) approach with a viable intercalation concentration spanning from 10% to 58%. Atomic-resolution scanning transmission electron microscopy-annular dark field imaging demonstrated that the self-intercalated Ta atoms occupy the octahedral vacancies located at the van der Waals gap. The nonperiodic Ta atoms break the centrosymmetry structure and Fermi surface properties of intrinsic TaS2. Therefore, ic-2D T-phase Ta1+xS2 consistently exhibit a spontaneous nonlinear optical (NLO) effect regardless of the sample thickness and self-intercalation concentrations. Our results propose an approach to activate the NLO response of centrosymmetric 2D materials, achieving the modulation of a wide range of optoelectronic properties via nonperiodic self-intercalation in the ic-2D family.

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.

Orbital-Selectivity-Induced Robust Quantum Anomalous Hall Effect in Hund's Metals MgFeP

Ferromagnetic (FM) states with high Curie temperatures (Tc) and strong spin-orbit coupling (SOC) are indispensable for the long-sought room-temperature quantum anomalous Hall (QAH) effects. Here, we propose a two-dimensional (2D) iron-based monolayer MgFeP that exhibits a notably high FM Tc (about 1525 K) along with exceptional structural stabilities. The unique multiorbital nature in MgFeP, where localized d x 2 - y 2 and dxz/yz orbitals coexist with itinerant dxy and dz2 orbitals, renders the monolayer a Hund's metal and in an orbital-selective Mott phase (OSMP). This OSMP triggers an FM double exchange mechanism, rationalizing the high Tc in the Hund's metal. This material transitions to a QAH insulator upon consideration of the SOC effect. By leveraging orbital selectivity, the QAH band gap can be enlarged by more than two times (to 137 meV). Our findings showcase Hund's metals as a promising material platform for realizing high-performance quantum topological electronic devices.

Fractional quantum anomalous Hall effect in multilayer graphene

The fractional quantum anomalous Hall effect (FQAHE), the analogue of the fractional quantum Hall effect1 at zero magnetic field, is predicted to exist in topological flat bands under spontaneous time-reversal-symmetry breaking2-6. The demonstration of FQAHE could lead to non-Abelian anyons that form the basis of topological quantum computation7-9. So far, FQAHE has been observed only in twisted MoTe2 at a moiré filling factor v > 1/2 (refs. 10-13). Graphene-based moiré superlattices are believed to host FQAHE with the potential advantage of superior material quality and higher electron mobility. Here we report the observation of integer and fractional QAH effects in a rhombohedral pentalayer graphene-hBN moiré superlattice. At zero magnetic field, we observed plateaus of quantized Hall resistance [Formula: see text] at v = 1, 2/3, 3/5, 4/7, 4/9, 3/7 and 2/5 of the moiré superlattice, respectively, accompanied by clear dips in the longitudinal resistance Rxx. Rxy equals [Formula: see text] at v = 1/2 and varies linearly with v, similar to the composite Fermi liquid in the half-filled lowest Landau level at high magnetic fields14-16. By tuning the gate-displacement field D and v, we observed phase transitions from composite Fermi liquid and FQAH states to other correlated electron states. Our system provides an ideal platform for exploring charge fractionalization and (non-Abelian) anyonic braiding at zero magnetic field7-9,17-19, especially considering a lateral junction between FQAHE and superconducting regions in the same device20-22.

Remote imprinting of moiré lattices

Two-dimensional moiré materials are formed by overlaying two layered crystals with small differences in orientation or/and lattice constant, where their direct coupling generates moiré potentials. Moiré materials have emerged as a platform for the discovery of new physics and device concepts, but while moiré materials are highly tunable, once formed, moiré lattices cannot be easily altered. Here we demonstrate the electrostatic imprinting of moiré lattices onto a target monolayer semiconductor. The moiré potential-created by a lattice of electrons that is supported by a Mott insulator state in a remote MoSe2/WS2 moiré bilayer-imprints a moiré potential that generates flat bands and correlated insulating states in the target monolayer and can be turned on/off by gate tuning the doping density of the moiré bilayer. Additionally, we studied the interplay between the electrostatic and structural relaxation contributions to moiré imprinting. Our results demonstrate a pathway towards gate control of moiré lattices.

Quantized anomalous Hall resistivity achieved in molecular beam epitaxy-grown MnBi2Te4 thin films

The intrinsic magnetic topological insulator MnBi2Te4 provides a feasible pathway to the high-temperature quantum anomalous Hall (QAH) effect as well as various novel topological quantum phases. Although quantized transport properties have been observed in exfoliated MnBi2Te4 thin flakes, it remains a big challenge to achieve molecular beam epitaxy (MBE)-grown MnBi2Te4 thin films even close to the quantized regime. In this work, we report the realization of quantized anomalous Hall resistivity in MBE-grown MnBi2Te4 thin films with the chemical potential tuned by both controlled in situ oxygen exposure and top gating. We find that elongated post-annealing obviously elevates the temperature to achieve quantization of the Hall resistivity, but also increases the residual longitudinal resistivity, indicating a picture of high-quality QAH puddles weakly coupled by tunnel barriers. These results help to clarify the puzzles in previous experimental studies on MnBi2Te4 and to find a way out of the big difficulty in obtaining MnBi2Te4 samples showing quantized transport properties.

ARPES investigation of the electronic structure and its evolution in magnetic topological insulator MnBi2+2nTe4+3n family

In the past 5 years, there has been significant research interest in the intrinsic magnetic topological insulator family compounds MnBi2+2nTe4+3n (where n = 0, 1, 2 …). In particular, exfoliated thin films of MnBi2Te4 have led to numerous experimental breakthroughs, such as the quantum anomalous Hall effect, axion insulator phase and high-Chern number quantum Hall effect without Landau levels. However, despite extensive efforts, the energy gap of the topological surface states due to exchange magnetic coupling, which is a key feature of the characteristic band structure of the system, remains experimentally elusive. The electronic structure measured by using angle-resolved photoemission (ARPES) shows significant deviation from ab initio prediction and scanning tunneling spectroscopy measurements, making it challenging to understand the transport results based on the electronic structure. This paper reviews the measurements of the band structure of MnBi2+2nTe4+3n magnetic topological insulators using ARPES, focusing on the evolution of their electronic structures with temperature, surface and bulk doping and film thickness. The aim of the review is to construct a unified picture of the electronic structure of MnBi2+2nTe4+3n compounds and explore possible control of their topological properties.

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.

Terahertz linear/non-linear anomalous Hall conductivity of moiré TMD hetero-nanoribbons as topological valleytronics materials

Twisted moiré van der Waals heterostructures hold promise to provide a robust quantum simulation platform for strongly correlated materials and realize elusive states of matter such as topological states in the laboratory. We demonstrated that the moiré bands of twisted transition metal dichalcogenide (TMD) hetero-nanoribbons exhibit non-trivial topological order due to the tendency of valence and conduction band states in K valleys to form giant band gaps when spin-orbit coupling (SOC) is taken into account. Among the features of twisted WS[Formula: see text]/MoS[Formula: see text] and WSe[Formula: see text]/MoSe[Formula: see text], we found that the heavy fermions associated with the topological flat bands and the presence of strongly correlated states, enhance anomalous Hall conductivity (AHC) away from the magic angle. By band analysis, we showed that the topmost conduction bands from the ± K-valleys are perfectly flat and carry a spin/valley Chern number. Moreover, we showed that the non-linear anomalous Hall effect in moiré TMD hetero-nanoribbons can be used to manipulate terahertz (THz) radiation. Our findings establish twisted heterostructures of group-VI TMD nanoribbons as a tunable platform for engineering topological valley quantum phases and THz non-linear Hall conductivity.

Tuning commensurability in twisted van der Waals bilayers

Moiré superlattices based on van der Waals bilayers1-4 created at small twist angles lead to a long wavelength pattern with approximate translational symmetry. At large twist angles (θt), moiré patterns are, in general, incommensurate except for a few discrete angles. Here we show that large-angle twisted bilayers offer distinctly different platforms. More specifically, by using twisted tungsten diselenide bilayers, we create the incommensurate dodecagon quasicrystals at θt = 30° and the commensurate moiré crystals at θt = 21.8° and 38.2°. Valley-resolved scanning tunnelling spectroscopy shows disparate behaviours between moiré crystals (with translational symmetry) and quasicrystals (with broken translational symmetry). In particular, the K valley shows rich electronic structures exemplified by the formation of mini-gaps near the valence band maximum. These discoveries demonstrate that bilayers with large twist angles offer a design platform to explore moiré physics beyond those formed with small twist angles.

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.

Imaging quantum oscillations and millitesla pseudomagnetic fields in graphene

The exceptional control of the electronic energy bands in atomically thin quantum materials has led to the discovery of several emergent phenomena1. However, at present there is no versatile method for mapping the local band structure in advanced two-dimensional materials devices in which the active layer is commonly embedded in the insulating layers and metallic gates. Using a scanning superconducting quantum interference device, here we image the de Haas-van Alphen quantum oscillations in a model system, the Bernal-stacked trilayer graphene with dual gates, which shows several highly tunable bands2-4. By resolving thermodynamic quantum oscillations spanning more than 100 Landau levels in low magnetic fields, we reconstruct the band structure and its evolution with the displacement field with excellent precision and nanoscale spatial resolution. Moreover, by developing Landau-level interferometry, we show shear-strain-induced pseudomagnetic fields and map their spatial dependence. In contrast to artificially induced large strain, which leads to pseudomagnetic fields of hundreds of tesla5-7, we detect naturally occurring pseudomagnetic fields as low as 1 mT corresponding to graphene twisting by 1 millidegree, two orders of magnitude lower than the typical angle disorder in twisted bilayer graphene8-11. This ability to resolve the local band structure and strain at the nanoscale level enables the characterization and use of tunable band engineering in practical van der Waals devices.

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.

Moiré-Assisted Strain Transfer in Vertical van der Waals Heterostructures

Strain provides a powerful method to study 2D monolayers and to tune their properties. The same approach also has great potential for van-der-Waals (vdW) heterostructures. However, we need to understand how strain can be applied to vertically stacked vdW structures, for which strain transfer from one layer to the next remains little explored. In our experiment, we fabricated vertical heterostructures consisting of transition metal dichalcogenides (TMDCs) monolayers that were deposited on a flexible substrate. These TMDC heterostructures allowed us to read out separately the strain in each monolayer by photoluminescence measurements. We find that, in TMDC heterostructures with large twist angles (>5°), strain transfer is limited. However, for aligned heterostructures with small twist angles (≤5°), near unity strain transfer efficiency is observed. We correlate this finding with the moiré domains formed in the aligned heterostructures by reconstruction.

Orbital multiferroicity in pentalayer rhombohedral graphene

Ferroic orders describe spontaneous polarization of spin, charge and lattice degrees of freedom in materials. Materials exhibiting multiple ferroic orders, known as multiferroics, have important parts in multifunctional electrical and magnetic device applications1-4. Two-dimensional materials with honeycomb lattices offer opportunities to engineer unconventional multiferroicity, in which the ferroic orders are driven purely by the orbital degrees of freedom and not by electron spin. These include ferro-valleytricity corresponding to the electron valley5 and ferro-orbital-magnetism6 supported by quantum geometric effects. These orbital multiferroics could offer strong valley-magnetic couplings and large responses to external fields-enabling device applications such as multiple-state memory elements and electric control of the valley and magnetic states. Here we report orbital multiferroicity in pentalayer rhombohedral graphene using low-temperature magneto-transport measurements. We observed anomalous Hall signals Rxy with an exceptionally large Hall angle (tanΘH > 0.6) and orbital magnetic hysteresis at hole doping. There are four such states with different valley polarizations and orbital magnetizations, forming a valley-magnetic quartet. By sweeping the gate electric field E, we observed a butterfly-shaped hysteresis of Rxy connecting the quartet. This hysteresis indicates a ferro-valleytronic order that couples to the composite field E · B (where B is the magnetic field), but not to the individual fields. Tuning E would switch each ferroic order independently and achieve non-volatile switching of them together. Our observations demonstrate a previously unknown type of multiferroics and point to electrically tunable ultralow-power valleytronic and magnetic devices.

Kinetic magnetism in triangular moiré materials

Magnetic properties of materials ranging from conventional ferromagnetic metals to strongly correlated materials such as cuprates originate from Coulomb exchange interactions. The existence of alternate mechanisms for magnetism that could naturally facilitate electrical control has been discussed theoretically1-7, but an experimental demonstration8 in an extended system has been missing. Here we investigate MoSe2/WS2 van der Waals heterostructures in the vicinity of Mott insulator states of electrons forming a frustrated triangular lattice and observe direct evidence of magnetic correlations originating from a kinetic mechanism. By directly measuring electronic magnetization through the strength of the polarization-selective attractive polaron resonance9,10, we find that when the Mott state is electron-doped, the system exhibits ferromagnetic correlations in agreement with the Nagaoka mechanism.

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.

Thermodynamic evidence of fractional Chern insulator in moiré MoTe2

Chern insulators, which are the lattice analogues of the quantum Hall states, can potentially manifest high-temperature topological orders at zero magnetic field to enable next-generation topological quantum devices1-3. Until now, integer Chern insulators have been experimentally demonstrated in several systems at zero magnetic field3-8, whereas fractional Chern insulators have been reported in only graphene-based systems under a finite magnetic field9,10. The emergence of semiconductor moiré materials11, which support tunable topological flat bands12,13, provides an opportunity to realize fractional Chern insulators13-16. Here we report thermodynamic evidence of both integer and fractional Chern insulators at zero magnetic field in small-angle twisted bilayer MoTe2 by combining the local electronic compressibility and magneto-optical measurements. At hole filling factor ν = 1 and 2/3, the system is incompressible and spontaneously breaks time-reversal symmetry. We show that they are integer and fractional Chern insulators, respectively, from the dispersion of the state in the filling factor with an applied magnetic field. We further demonstrate electric-field-tuned topological phase transitions involving the Chern insulators. Our findings pave the way for the demonstration of quantized fractional Hall conductance and anyonic excitation and braiding17 in semiconductor moiré materials.

Signatures of fractional quantum anomalous Hall states in twisted MoTe2

The interplay between spontaneous symmetry breaking and topology can result in exotic quantum states of matter. A celebrated example is the quantum anomalous Hall (QAH) state, which exhibits an integer quantum Hall effect at zero magnetic field owing to intrinsic ferromagnetism1-3. In the presence of strong electron-electron interactions, fractional QAH (FQAH) states at zero magnetic field can emerge4-8. These states could host fractional excitations, including non-Abelian anyons-crucial building blocks for topological quantum computation9. Here we report experimental signatures of FQAH states in a twisted molybdenum ditelluride (MoTe2) bilayer. Magnetic circular dichroism measurements reveal robust ferromagnetic states at fractionally hole-filled moiré minibands. Using trion photoluminescence as a sensor10, we obtain a Landau fan diagram showing linear shifts in carrier densities corresponding to filling factor v = -2/3 and v = -3/5 ferromagnetic states with applied magnetic field. These shifts match the Streda formula dispersion of FQAH states with fractionally quantized Hall conductance of [Formula: see text] and [Formula: see text], respectively. Moreover, the v = -1 state exhibits a dispersion corresponding to Chern number -1, consistent with the predicted QAH state11-14. In comparison, several non-ferromagnetic states on the electron-doping side do not disperse, that is, they are trivial correlated insulators. The observed topological states can be electrically driven into topologically trivial states. Our findings provide evidence of the long-sought FQAH states, demonstrating MoTe2 moiré superlattices as a platform for exploring fractional excitations.

Observation of fractionally quantized anomalous Hall effect

The integer quantum anomalous Hall (QAH) effect is a lattice analogue of the quantum Hall effect at zero magnetic field1-3. This phenomenon occurs in systems with topologically non-trivial bands and spontaneous time-reversal symmetry breaking. Discovery of its fractional counterpart in the presence of strong electron correlations, that is, the fractional QAH effect4-7, would open a new chapter in condensed matter physics. Here we report the direct observation of both integer and fractional QAH effects in electrical measurements on twisted bilayer MoTe2. At zero magnetic field, near filling factor ν = -1 (one hole per moiré unit cell), we see an integer QAH plateau in the Hall resistance Rxy quantized to h/e2 ± 0.1%, whereas the longitudinal resistance Rxx vanishes. Remarkably, at ν  =  -2/3 and -3/5, we see plateau features in Rxy at [Formula: see text] and [Formula: see text], respectively, whereas Rxx remains small. All features shift linearly versus applied magnetic field with slopes matching the corresponding Chern numbers -1, -2/3 and -3/5, precisely as expected for integer and fractional QAH states. Additionally, at zero magnetic field, Rxy is approximately 2h/e2 near half-filling (ν  = -1/2) and varies linearly as ν  is tuned. This behaviour resembles that of the composite Fermi liquid in the half-filled lowest Landau level of a two-dimensional electron gas at high magnetic field8-14. Direct observation of the fractional QAH and associated effects enables research in charge fractionalization and anyonic statistics at zero magnetic field.

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.

Manipulating Topological Phases in Magnetic Topological Insulators

Magnetic topological insulators (MTIs) are a group of materials that feature topological band structures with concurrent magnetism, which can offer new opportunities for technological advancements in various applications, such as spintronics and quantum computing. The combination of topology and magnetism introduces a rich spectrum of topological phases in MTIs, which can be controllably manipulated by tuning material parameters such as doping profiles, interfacial proximity effect, or external conditions such as pressure and electric field. In this paper, we first review the mainstream MTI material platforms where the quantum anomalous Hall effect can be achieved, along with other exotic topological phases in MTIs. We then focus on highlighting recent developments in modulating topological properties in MTI with finite-size limit, pressure, electric field, and magnetic proximity effect. The manipulation of topological phases in MTIs provides an exciting avenue for advancing both fundamental research and practical applications. As this field continues to develop, further investigations into the interplay between topology and magnetism in MTIs will undoubtedly pave the way for innovative breakthroughs in the fundamental understanding of topological physics as well as practical applications.

Ferroic Phases in Two-Dimensional Materials

Two-dimensional (2D) ferroics, namely ferroelectric, ferromagnetic, and ferroelastic materials, are attracting rising interest due to their fascinating physical properties and promising functional applications. A variety of 2D ferroic phases, as well as 2D multiferroics and the novel 2D ferrovalleytronics/ferrotoroidics, have been recently predicted by theory, even down to the single atomic layers. Meanwhile, some of them have already been experimentally verified. In addition to the intrinsic 2D ferroics, appropriate stacking, doping, and defects can also artificially regulate the ferroic phases of 2D materials. Correspondingly, ferroic ordering in 2D materials exhibits enormous potential for future high density memory devices, energy conversion devices, and sensing devices, among other applications. In this paper, the recent research progresses on 2D ferroic phases are comprehensively reviewed, with emphasis on chemistry and structural origin of the ferroic properties. In addition, the promising applications of the 2D ferroics for information storage, optoelectronics, and sensing are also briefly discussed. Finally, we envisioned a few possible pathways for the future 2D ferroics research and development. This comprehensive overview on the 2D ferroic phases can provide an atlas for this field and facilitate further exploration of the intriguing new materials and physical phenomena, which will generate tremendous impact on future functional materials and devices.

1/4 is the new 1/2 when topology is intertwined with Mottness

In non-interacting systems, bands from non-trivial topology emerge strictly at half-filling and exhibit either the quantum anomalous Hall or spin Hall effects. Here we show using determinantal quantum Monte Carlo and an exactly solvable strongly interacting model that these topological states now shift to quarter filling. A topological Mott insulator is the underlying cause. The peak in the spin susceptibility is consistent with a possible ferromagnetic state at T = 0. The onset of such magnetism would convert the quantum spin Hall to a quantum anomalous Hall effect. While such a symmetry-broken phase typically is accompanied by a gap, we find that the interaction strength must exceed a critical value for this to occur. Hence, we predict that topology can obtain in a gapless phase but only in the presence of interactions in dispersive bands. These results explain the recent quarter-filled quantum anomalous Hall effects seen in moiré systems.

Interlayer donor-acceptor pair excitons in MoSe2/WSe2 moiré heterobilayer

Localized interlayer excitons (LIXs) in two-dimensional moiré superlattices exhibit sharp and dense emission peaks, making them promising as highly tunable single-photon sources. However, the fundamental nature of these LIXs is still elusive. Here, we show the donor-acceptor pair (DAP) mechanism as one of the origins of these excitonic peaks. Numerical simulation results of the DAP model agree with the experimental photoluminescence spectra of LIX in the moiré MoSe2/WSe2 heterobilayer. In particular, we find that the emission energy-lifetime correlation and the nonmonotonic power dependence of the lifetime agree well with the DAP IX model. Our results provide insight into the physical mechanism of LIX formation in moiré heterostructures and pave new directions for engineering interlayer exciton properties in moiré superlattices.

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.

Revealing intrinsic domains and fluctuations of moiré magnetism by a wide-field quantum microscope

Moiré magnetism featured by stacking engineered atomic registry and lattice interactions has recently emerged as an appealing quantum state of matter at the forefront of condensed matter physics research. Nanoscale imaging of moiré magnets is highly desirable and serves as a prerequisite to investigate a broad range of intriguing physics underlying the interplay between topology, electronic correlations, and unconventional nanomagnetism. Here we report spin defect-based wide-field imaging of magnetic domains and spin fluctuations in twisted double trilayer (tDT) chromium triiodide CrI3. We explicitly show that intrinsic moiré domains of opposite magnetizations appear over arrays of moiré supercells in low-twist-angle tDT CrI3. In contrast, spin fluctuations measured in tDT CrI3 manifest little spatial variations on the same mesoscopic length scale due to the dominant driving force of intralayer exchange interaction. Our results enrich the current understanding of exotic magnetic phases sustained by moiré magnetism and highlight the opportunities provided by quantum spin sensors in probing microscopic spin related phenomena on two-dimensional flatland.

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.