Semiconductor moiré materials

Anomalous Phonon Behavior and Tunable Exciton Emissions: Insights into Pressure-Driven Dynamics in Silicon Phosphide

IV-V two-dimensional materials have emerged as key contenders for polarization-sensitive and angle-resolved devices, given their inherent anisotropic physical properties. While these materials exhibit intriguing high-pressure quasi-particle behavior and phase transition, the evolution of quasi-particles and their interactions under external pressure remain elusive. Here, employing a diamond anvil cell and spectroscopic measurements coupled with first-principles calculations, we unveil rarely observed pressure-induced phonon-phonon coupling in layered SiP flakes. This coupling manifests as an anomalous phonon hardening behavior for the A1 mode within a broad wavenumber phonon softening region. Furthermore, we demonstrate the effective tuning of exciton emissions in SiP flakes under pressure, revealing a remarkable 63% enhancement in the degree of polarization (DOP) within the pressure range of 0-3.5 GPa. These findings contribute to our understanding of high-pressure phonon evolution in SiP materials and offer a strategic approach to manipulate the anisotropic performance of in-plane anisotropic 2D materials.

Nematic Metal in a Multivalley Electron Gas: Variational Monte Carlo Analysis and Application to AlAs

The two-dimensional electron gas is of fundamental importance in quantum many-body physics. We study a minimal extension of this model with C_{4} (as opposed to full rotational) symmetry and an electronic dispersion with two valleys with anisotropic effective masses. Electrons in our model interact via Coulomb repulsion, screened by distant metallic gates. Using variational Monte Carlo simulations, we find a broad intermediate range of densities with a metallic valley-polarized, spin-unpolarized ground state. Our results are of direct relevance to the recently discovered "nematic" state in AlAs quantum wells. For the effective mass anisotropy relevant to this system, m_{x}/m_{y}≈5.2, we obtain a transition from an anisotropic metal to a valley-polarized metal at r_{s}≈12 (where r_{s} is the dimensionless Wigner-Seitz radius). At still lower densities, we find a (possibly metastable) valley and spin-polarized state with a reduced electronic anisotropy.

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.

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.

Uncovering the spin ordering in magic-angle graphene via edge state equilibration

The flat bands in magic-angle twisted bilayer graphene (MATBG) provide an especially rich arena to investigate interaction-driven ground states. While progress has been made in identifying the correlated insulators and their excitations at commensurate moiré filling factors, the spin-valley polarizations of the topological states that emerge at high magnetic field remain unknown. Here we introduce a technique based on twist-decoupled van der Waals layers that enables measurement of their electronic band structure and-by studying the backscattering between counter-propagating edge states-the determination of the relative spin polarization of their edge modes. We find that the symmetry-broken quantum Hall states that extend from the charge neutrality point in MATBG are spin unpolarized at even integer filling factors. The measurements also indicate that the correlated Chern insulator emerging from half filling of the flat valence band is spin unpolarized and suggest that its conduction band counterpart may be spin polarized.

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.

Directly imaging spin polarons in a kinetically frustrated Hubbard system

The emergence of quasiparticles in quantum many-body systems underlies the rich phenomenology in many strongly interacting materials. In the context of doped Mott insulators, magnetic polarons are quasiparticles that usually arise from an interplay between the kinetic energy of doped charge carriers and superexchange spin interactions1-8. However, in kinetically frustrated lattices, itinerant spin polarons-bound states of a dopant and a spin flip-have been theoretically predicted even in the absence of superexchange coupling9-14. Despite their important role in the theory of kinetic magnetism, a microscopic observation of these polarons is lacking. Here we directly image itinerant spin polarons in a triangular-lattice Hubbard system realized with ultracold atoms, revealing enhanced antiferromagnetic correlations in the local environment of a hole dopant. In contrast, around a charge dopant, we find ferromagnetic correlations, a manifestation of the elusive Nagaoka effect15,16. We study the evolution of these correlations with interactions and doping, and use higher-order correlation functions to further elucidate the relative contributions of superexchange and kinetic mechanisms. The robustness of itinerant spin polarons at high temperature paves the way for exploring potential mechanisms for hole pairing and superconductivity in frustrated systems10,11. Furthermore, our work provides microscopic insights into related phenomena in triangular-lattice moiré materials17-20.

Mapping twist-tuned multiband topology in bilayer WSe2

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

Excitonic Thermalization Bottleneck in Twisted TMD Heterostructures

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

Non-Hermitian Moiré Valley Filter

A valley filter capable of generating a valley-polarized current is a crucial element in valleytronics, yet its implementation remains challenging. Here, we propose a valley filter made of a graphene bilayer which exhibits a 1D moiré pattern in the overlapping region of the two layers controlled by heterostrain. In the presence of a lattice modulation between layers, electrons propagating in one layer can have valley-dependent dissipation due to valley asymmetric interlayer coupling, thus giving rise to a valley-polarized current. Such a process can be described by an effective non-Hermitian theory, in which the valley filter is driven by a valley-resolved non-Hermitian skin effect. Nearly 100% valley polarization can be achieved within a wide parameter range and the functionality of the valley filter is electrically tunable. The non-Hermitian topological scenario of the valley filter ensures high tolerance against imperfections such as disorder and edge defects. Our work opens a new route for efficient and robust valley filters while significantly relaxing the stringent implementation requirements.

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.

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.

Topological minibands and interaction driven quantum anomalous Hall state in topological insulator based moiré heterostructures

The presence of topological flat minibands in moiré materials provides an opportunity to explore the interplay between topology and correlation. In this work, we study moiré minibands in topological insulator films with two hybridized surface states under a moiré superlattice potential created by two-dimensional insulating materials. We show the lowest conduction (highest valence) Kramers' pair of minibands can beZ 2 non-trivial when the minima (maxima) of moiré potential approximately form a hexagonal lattice with six-fold rotation symmetry. Coulomb interaction can drive the non-trivial Kramers' minibands into the quantum anomalous Hall state when they are half-filled, which is further stabilized by applying external gate voltages to break inversion. We propose the monolayer Sb2 on top of Sb2Te3 films as a candidate based on first principles calculations. Our work demonstrates the topological insulator based moiré heterostructure as a potential platform for studying interacting topological phases.

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.

Atomic-Limit Mott Insulator in [4]Triangulene Frameworks

Triangulene, one unique class of zigzag-edged triangular graphene molecules, has attracted tremendous research interest. In this work, as an ultimate phase of the Mott insulator, we present the realization of the atomic-limit Mott insulator in experimentally synthesized [4]triangulene frameworks ([4]-TGFs) from first-principles calculations. The frontier molecular orbitals of the nonmagnetic [4]triangulene consist of three coupled corner modes. After the isolated [4]triangulene is assembled into [4]-TGF, one special enantiomorphic flat band is created through the coupling of these corner modes, which is identified to be a second-order topological insulator with half-filled topological corner states at the Fermi level. Moreover, [4]-TGF prefers an antiferromagnetic ground state under Hubbard interactions, which further splits these metallic zero-energy states into an atomic-limit Mott insulator with spin-polarized corners. Since the fractional filling of topological corner states is a smoking-gun signature of higher-order topology, our results demonstrate a universal approach to explore the atomic-limit Mott insulators in higher-order topological materials.

Polar alcohol guest molecules regulate the stacking modes of 2-D MOF nanosheets

The modulation of two-dimensional metal-organic framework (2-D MOF) nanosheet stacking is an effective means to improve the properties and promote the application of nanosheets in various fields. Here, we employed a series of alcohol guest molecules (MeOH, EtOH and PrOH) to modulate Zr-BTB (BTB = benzene-1,3,5-tribenzoate) nanosheets and to generate untwisted stacking. The distribution of stacking angles was statistically analyzed from high-angle annular dark-field (HAADF) and fast Fourier transform (FFT) images. The ratios of untwisted stacking were calculated, such as 77.01% untwisted stacking for MeOH, 83.45% for EtOH, and 85.61% for PrOH. The obtained untwisted Zr-BTB showed good separation abilities for different substituted benzene isomers, superior para selectivity and excellent column stability and reusability. Control experiments of 2-D Zr-TCA (TCA = 4,4',4''-tricarboxytriphenylamine) and Zr-TATB (TATB = 4,4',4''-(1,3,5-triazine-2,4,6-triyl)tribenzoic acid) nanosheets with similar pore sizes and stronger polarity regulated by the alcohol guests exhibited moderate separation performance. The electron microscopy images revealed that polar alcohol regulation dominantly generated the twisted stacking of Zr-TCA and Zr-TATB with various Moiré patterns. Polar guest molecules, such as alcohols, provide strong host-guest interactions during the regulation of MOF nanosheet stacking, providing an opportunity to design new porous Moiré materials with application prospects.

Stacking engineering in layered homostructures: transitioning from 2D to 3D architectures

Artificial materials, characterized by their distinctive properties and customized functionalities, occupy a central role in a wide range of applications including electronics, spintronics, optoelectronics, catalysis, and energy storage. The emergence of atomically thin two-dimensional (2D) materials has driven the creation of artificial heterostructures, harnessing the potential of combining various 2D building blocks with complementary properties through the art of stacking engineering. The promising outcomes achieved for heterostructures have spurred an inquisitive exploration of homostructures, where identical 2D layers are precisely stacked. This perspective primarily focuses on the field of stacking engineering within layered homostructures, where precise control over translational or rotational degrees of freedom between vertically stacked planes or layers is paramount. In particular, we provide an overview of recent advancements in the stacking engineering applied to 2D homostructures. Additionally, we will shed light on research endeavors venturing into three-dimensional (3D) structures, which allow us to proactively address the limitations associated with artificial 2D homostructures. We anticipate that the breakthroughs in stacking engineering in 3D materials will provide valuable insights into the mechanisms governing stacking effects. Such advancements have the potential to unlock the full capability of artificial layered homostructures, propelling the future development of materials, physics, and device applications.

Van der Waals epitaxy of tunable moirés enabled by alloying

The unique physics in moiré superlattices of twisted or lattice-mismatched atomic layers holds great promise for future quantum technologies. However, twisted configurations are thermodynamically unfavourable, making accurate twist angle control during growth implausible. While rotationally aligned, lattice-mismatched moirés such as WSe2/WS2 can be synthesized, they lack the critical moiré period tunability, and their formation mechanisms are not well understood. Here, we report the thermodynamically driven van der Waals epitaxy of moirés with a tunable period from 10 to 45 nanometres, using lattice mismatch engineering in two WSSe layers with adjustable chalcogen ratios. Contrary to conventional epitaxy, where lattice-mismatch-induced stress hinders high-quality growth, we reveal the key role of bulk stress in moiré formation and its unique interplay with edge stress in shaping the moiré growth modes. Moreover, the superlattices display tunable interlayer excitons and moiré intralayer excitons. Our studies unveil the epitaxial science of moiré synthesis and lay the foundations for moiré-based technologies.

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.

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

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

Metal-Insulator Transition in a Semiconductor Heterobilayer Model

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

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

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

Simultaneously Regulated Highly Polarized and Long-Lived Valley Excitons in WSe2/GaN Heterostructures

Interlayer excitons, with prolonged lifetimes and tunability, hold potential for advanced optoelectronics. Previous research on the interlayer excitons has been dominated by two-dimensional heterostructures. Here, we construct WSe2/GaN composite heterostructures, in which the doping concentration of GaN and the twist angle of bilayer WSe2 are employed as two ingredients for the manipulation of exciton behaviors and polarizations. The exciton energies in monolayer WSe2/GaN can be regulated continuously by the doping levels of the GaN substrate, and a remarkable increase in the valley polarizations is achieved. Especially in a heterostructure with 4°-twisted bilayer WSe2, a maximum polarization of 38.9% with a long lifetime is achieved for the interlayer exciton. Theoretical calculations reveal that the large polarization and long lifetime are attributed to the high exciton binding energy and large spin flipping energy during depolarization in bilayer WSe2/GaN. This work introduces a distinctive member of the interlayer exciton with a high degree of polarization and a long lifetime.

Dynamically tunable moiré exciton Rydberg states in a monolayer semiconductor on twisted bilayer graphene

Moiré excitons are emergent optical excitations in two-dimensional semiconductors with moiré superlattice potentials. Although these excitations have been observed on several platforms, a system with dynamically tunable moiré potential to tailor their properties is yet to be realized. Here we present a continuously tunable moiré potential in monolayer WSe2, enabled by its proximity to twisted bilayer graphene (TBG) near the magic angle. By tuning local charge density via gating, TBG provides a spatially varying and dynamically tunable dielectric superlattice for modulation of monolayer WSe2 exciton wave functions. We observed emergent moiré exciton Rydberg branches with increased energy splitting following doping of TBG due to exciton wave function hybridization between bright and dark Rydberg states. In addition, emergent Rydberg states can probe strongly correlated states in TBG at the magic angle. Our study provides a new platform for engineering moiré excitons and optical accessibility to electronic states with small correlation gaps in TBG.

Engineering correlated insulators in bilayer graphene with a remote Coulomb superlattice

Electron superlattices allow the engineering of correlated and topological quantum phenomena. The recent emergence of moiré superlattices in two-dimensional heterostructures has led to exciting discoveries related to quantum phenomena. However, the requirement for the moiré pattern poses stringent limitations, and its potential cannot be switched on and off. Here, we demonstrate remote engineering and on/off switching of correlated states in bilayer graphene. Employing a remote Coulomb superlattice realized by localized electrons in twisted bilayer WS2, we impose a Coulomb superlattice in the bilayer graphene with period and strength determined by the twisted bilayer WS2. When the remote superlattice is turned off, the two-dimensional electron gas in the bilayer graphene is described by a Fermi liquid. When it is turned on, correlated insulating states at both integer and fractional filling factors emerge. This approach enables in situ control of correlated quantum phenomena in two-dimensional materials hosting a two-dimensional electron gas.

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.

Recent Strategies for the Synthesis of Phase-Pure Ultrathin 1T/1T' Transition Metal Dichalcogenide Nanosheets

The past few decades have witnessed a notable increase in transition metal dichalcogenide (TMD) related research not only because of the large family of TMD candidates but also because of the various polytypes that arise from the monolayer configuration and layer stacking order. The peculiar physicochemical properties of TMD nanosheets enable an enormous range of applications from fundamental science to industrial technologies based on the preparation of high-quality TMDs. For polymorphic TMDs, the 1T/1T' phase is particularly intriguing because of the enriched density of states, and thus facilitates fruitful chemistry. Herein, we comprehensively discuss the most recent strategies for direct synthesis of phase-pure 1T/1T' TMD nanosheets such as mechanical exfoliation, chemical vapor deposition, wet chemical synthesis, atomic layer deposition, and more. We also review frequently adopted methods for phase engineering in TMD nanosheets ranging from chemical doping and alloying, to charge injection, and irradiation with optical or charged particle beams. Prior to the synthesis methods, we discuss the configuration of TMDs as well as the characterization tools mostly used in experiments. Finally, we discuss the current challenges and opportunities as well as emphasize the promising fields for the future development.

Electrostatic moiré potential from twisted hexagonal boron nitride layers

Moiré superlattices host a rich variety of correlated electronic phases. However, the moiré potential is fixed by interlayer coupling, and it is dependent on the nature of carriers and valleys. In contrast, it has been predicted that twisted hexagonal boron nitride (hBN) layers can impose a periodic electrostatic potential capable of engineering the properties of adjacent functional layers. Here, we show that this potential is described by a theory of electric polarization originating from the interfacial charge redistribution, validated by its dependence on supercell sizes and distance from the twisted interfaces. This enables controllability of the potential depth and profile by controlling the twist angles between the two interfaces. Employing this approach, we further demonstrate how the electrostatic potential from a twisted hBN substrate impedes exciton diffusion in semiconductor monolayers, suggesting opportunities for engineering the properties of adjacent functional layers using the surface potential of a twisted hBN substrate.

Exciton Polaritons in Emergent Two-Dimensional Semiconductors

The "marriage" of light (i.e., photon) and matter (i.e., exciton) in semiconductors leads to the formation of hybrid quasiparticles called exciton polaritons with fascinating quantum phenomena such as Bose-Einstein condensation (BEC) and photon blockade. The research of exciton polaritons has been evolving into an era with emergent two-dimensional (2D) semiconductors and photonic structures for their tremendous potential to break the current limitations of quantum fundamental study and photonic applications. In this Perspective, the basic concepts of 2D excitons, optical resonators, and the strong coupling regime are introduced. The research progress of exciton polaritons is reviewed, and important discoveries (especially the recent ones of 2D exciton polaritons) are highlighted. Subsequently, the emergent 2D exciton polaritons are discussed in detail, ranging from the realization of the strong coupling regime in various photonic systems to the discoveries of attractive phenomena with interesting physics and extensive applications. Moreover, emerging 2D semiconductors, such as 2D perovskites (2DPK) and 2D antiferromagnetic (AFM) semiconductors, are surveyed for the manipulation of exciton polaritons with distinct control degrees of freedom (DOFs). Finally, the outlook on the 2D exciton polaritons and their nonlinear interactions is presented with our initial numerical simulations. This Perspective not only aims to provide an in-depth overview of the latest fundamental findings in 2D exciton polaritons but also attempts to serve as a valuable resource to prospect explorations of quantum optics and topological photonic applications.

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.

Artificial Atoms, Wigner Molecules, and an Emergent Kagome Lattice in Semiconductor Moiré Superlattices

Semiconductor moiré superlattices comprise an array of artificial atoms and provide a highly tunable platform for exploring novel electronic phases. We introduce a theoretical framework for studying moiré quantum matter that treats intra-moiré-atom interactions exactly and is controlled in the limit of large moiré period. We reveal an abundance of new physics arising from strong electron interactions when there are multiple electrons within a moiré unit cell. In particular, at filling factor n=3, the Coulomb interaction within each three-electron moiré atom leads to a three-lobed "Wigner molecule." When their size is comparable to the moiré period, the Wigner molecules form an emergent Kagome lattice. Our Letter identifies two universal length scales characterizing the kinetic and interaction energies in moiré materials and demonstrates a rich phase diagram due to their interplay.

Twist Phase Matching in Two-Dimensional Materials

Optical phase matching involves establishing a proper phase relationship between the fundamental excitation and generated waves to enable efficient optical parametric processes. It is typically achieved through birefringence or periodic polarization. Here, we report that the interlayer twist angle in two-dimensional (2D) materials creates a nonlinear geometric phase that can compensate for the phase mismatch, and the vertical assembly of the 2D layers with a proper twist sequence generates a nontrivial "twist-phase-matching" (twist-PM) regime. The twist-PM model provides superior flexibility in the design of optical crystals, which can be applied for twisted layers with either periodic or random thickness distributions. The designed crystal from the twisted rhombohedral boron nitride films within a thickness of only 3.2  μm is capable of producing a second-harmonic generation with conversion efficiency of ∼8% and facile polarization controllability that is absent in conventional crystals. Our methodology establishes a platform for the rational design and atomic manufacturing of nonlinear optical crystals based on abundant 2D materials.

Vitality of Intralayer Vibration in hBN for Effective Long-Range Interlayer Hole Transfer across High Barriers in MoSe2/hBN/WSe2 Heterostructures

Introducing the two-dimensional (2D) hexagonal boron nitride (hBN) between 2D transition metal dichalcogenide (TMD) layers promises convenient manipulation of the interlayer exciton (IX) and interlayer charge transfer in TMD/hBN/TMD heterostructures, while the role of inserted hBN layers during IX formation is controversial. Employing ab initio nonadiabatic molecular dynamics (NAMD) simulations and the electron-phonon coupling model, we systematically investigate interlayer hole transfer in MoSe2/WSe2 bilayers intercalated by hBN layers with various thicknesses. The conventional direct hole transfer from MoSe2 to WSe2 is decelerated by 2-3 orders of magnitude after the hBN insertion. Meanwhile, a novel channel intermediated by a deeper hole of WSe2 becomes dominant, where the intralayer shear mode of hBN plays a crucial role by reducing the energy barriers for this new channel. The unique role of hBN layers is revealed for the first time, enriching the knowledge of the underlying microscopic mechanisms and providing instructive guidance to practical van der Waals optoelectronic devices.

Moiré synaptic transistor with room-temperature neuromorphic functionality

Moiré quantum materials host exotic electronic phenomena through enhanced internal Coulomb interactions in twisted two-dimensional heterostructures1-4. When combined with the exceptionally high electrostatic control in atomically thin materials5-8, moiré heterostructures have the potential to enable next-generation electronic devices with unprecedented functionality. However, despite extensive exploration, moiré electronic phenomena have thus far been limited to impractically low cryogenic temperatures9-14, thus precluding real-world applications of moiré quantum materials. Here we report the experimental realization and room-temperature operation of a low-power (20 pW) moiré synaptic transistor based on an asymmetric bilayer graphene/hexagonal boron nitride moiré heterostructure. The asymmetric moiré potential gives rise to robust electronic ratchet states, which enable hysteretic, non-volatile injection of charge carriers that control the conductance of the device. The asymmetric gating in dual-gated moiré heterostructures realizes diverse biorealistic neuromorphic functionalities, such as reconfigurable synaptic responses, spatiotemporal-based tempotrons and Bienenstock-Cooper-Munro input-specific adaptation. In this manner, the moiré synaptic transistor enables efficient compute-in-memory designs and edge hardware accelerators for artificial intelligence and machine learning.

Engineering Magnetic Phases of Layered Antiferromagnets by Interfacial Charge Transfer

Van der Waals heterostructures composed of distinct layered materials can display behaviors entirely different from those of each individual layer due to interfacial coupling. Here we investigate the manipulation of magnetic phases in two-dimensional magnets through interfacial charge transfer in heterostructures of magnetic and nonmagnetic layers. This is demonstrated by first-principles calculations, which unveil a transition toward the ferromagnetic phase by stacking antiferromagnetic bilayer CrSBr on graphene. Using an effective model consisting of two electronically coupled single layers, we show that the antiferromagnetic to ferromagnetic magnetic phase transition occurs due to interfacial charge transfer, which enhances ferromagnetism. We further reveal that the magnetic phase transition can also be induced by electron and hole carriers and demonstrate that the phase transition is a spin-canting process. This allows for precise gate-control of noncollinear magnetism on demand. Our work predicts interfacial charge transfer as a potent mechanism to tune magnetic phases in van der Waals heterostructures and creates opportunities for spintronic applications.

Berry Curvature Spectroscopy from Bloch Oscillations

Artificial crystals such as moiré superlattices can have a real-space periodicity much larger than the underlying atomic scale. This facilitates the presence of Bloch oscillations in the presence of a static electric field. We demonstrate that the optical response of such a system, when dressed with a static field, becomes resonant at the frequencies of Bloch oscillations, which are in the terahertz regime when the lattice constant is of the order of 10 nm. In particular, we show within a semiclassical band-projected theory that resonances in the dressed Hall conductivity are proportional to the lattice Fourier components of the Berry curvature. We illustrate our results with a low-energy model on an effective honeycomb lattice.

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.

Roses in the nonperturbative current response of artificial crystals

In two-dimensional artificial crystals with large real-space periodicity, the nonlinear current response to a large applied electric field can feature a strong angular dependence, which encodes information about the band dispersion and Berry curvature of isolated electronic Bloch minibands. Within the relaxation-time approximation, we obtain analytic expressions up to infinite order in the driving field for the current in a band-projected theory with time-reversal and trigonal symmetry. For a fixed field strength, the dependence of the current on the direction of the applied field is given by rose curves whose petal structure is symmetry constrained and is obtained from an expansion in real-space translation vectors. We illustrate our theory with calculations on periodically buckled graphene and twisted double bilayer graphene, wherein the discussed physics can be accessed at experimentally relevant field strengths.

Pressure-Induced Dynamic Tuning of Interlayer Coupling in Twisted WSe2/WSe2 Homobilayers

Moiré superlattices induced by twisted van der Waals (vdW) heterostructures or homostructures have recently gained significant attention due to their potential to generate exotic strong-correlation electronic and phonon phenomena. However, the lack of dynamic tuning for interlayer coupling of moiré superlattices hinders a thorough understanding and development of the moiré correlation state. Here, we present a dynamic tuning method for twisted WSe2/WSe2 homobilayers using a diamond anvil cell (DAC). We demonstrate the powerful tuning of interlayer coupling and observe an enhanced response to pressure for interlayer breathing modes and the rapid descent of indirect excitons in twisted WSe2/WSe2 homobilayers. Our findings indicate that the introduction of a moiré superlattice for WSe2 bilayers gives rise to hybridized excitons, which lead to the different pressure-evolution exciton behaviors compared to natural WSe2 bilayers. Our results provide a novel understanding of moiré physics and offer an effective method to tune interlayer coupling of moiré superlattices.

Visualizing moiré ferroelectricity via plasmons and nano-photocurrent in graphene/twisted-WSe2 structures

Ferroelectricity, a spontaneous and reversible electric polarization, is found in certain classes of van der Waals (vdW) materials. The discovery of ferroelectricity in twisted vdW layers provides new opportunities to engineer spatially dependent electric and optical properties associated with the configuration of moiré superlattice domains and the network of domain walls. Here, we employ near-field infrared nano-imaging and nano-photocurrent measurements to study ferroelectricity in minimally twisted WSe2. The ferroelectric domains are visualized through the imaging of the plasmonic response in a graphene monolayer adjacent to the moiré WSe2 bilayers. Specifically, we find that the ferroelectric polarization in moiré domains is imprinted on the plasmonic response of the graphene. Complementary nano-photocurrent measurements demonstrate that the optoelectronic properties of graphene are also modulated by the proximal ferroelectric domains. Our approach represents an alternative strategy for studying moiré ferroelectricity at native length scales and opens promising prospects for (opto)electronic devices.

Dipolar quantum solids emerging in a Hubbard quantum simulator

In quantum mechanical many-body systems, long-range and anisotropic interactions promote rich spatial structure and can lead to quantum frustration, giving rise to a wealth of complex, strongly correlated quantum phases1. Long-range interactions play an important role in nature; however, quantum simulations of lattice systems have largely not been able to realize such interactions. A wide range of efforts are underway to explore long-range interacting lattice systems using polar molecules2-5, Rydberg atoms2,6-8, optical cavities9-11 or magnetic atoms12-15. Here we realize novel quantum phases in a strongly correlated lattice system with long-range dipolar interactions using ultracold magnetic erbium atoms. As we tune the dipolar interaction to be the dominant energy scale in our system, we observe quantum phase transitions from a superfluid into dipolar quantum solids, which we directly detect using quantum gas microscopy with accordion lattices. Controlling the interaction anisotropy by orienting the dipoles enables us to realize a variety of stripe-ordered states. Furthermore, by transitioning non-adiabatically through the strongly correlated regime, we observe the emergence of a range of metastable stripe-ordered states. This work demonstrates that novel strongly correlated quantum phases can be realized using long-range dipolar interactions in optical lattices, opening the door to quantum simulations of a wide range of lattice models with long-range and anisotropic interactions.

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.

Magnetism-Induced Band-Edge Shift as the Mechanism for Magnetoconductance in CrPS4 Transistors

Transistors realized on the 2D antiferromagnetic semiconductor CrPS4 exhibit large magnetoconductance due to magnetic-field-induced changes in the magnetic state. The microscopic mechanism coupling the conductance and magnetic state is not understood. We identify it by analyzing the evolution of the parameters determining the transistor behavior─carrier mobility and threshold voltage─with temperature and magnetic field. For temperatures T near the Néel temperature TN, the magnetoconductance originates from a mobility increase due to the applied magnetic field that reduces spin fluctuation induced disorder. For T ≪ TN, instead, what changes is the threshold voltage, so that increasing the field at fixed gate voltage increases the density of accumulated electrons. The phenomenon is explained by a conduction band-edge shift correctly predicted by the ab initio calculations. Our results demonstrate that the band structure of CrPS4 depends on its magnetic state and reveal a mechanism for magnetoconductance that had not been identified earlier.

Toward Edge Engineering of Two-Dimensional Layered Transition-Metal Dichalcogenides by Chemical Vapor Deposition

The manipulation of edge configurations and structures in atomically-thin transition metal dichalcogenides (TMDs) for versatile functionalization has attracted intensive interest in recent years. The chemical vapor deposition (CVD) approach has shown promise for TMD edge engineering of atomic edge configurations (1H, 1T or 1T'-zigzag or armchair edges) as well as diverse edge morphologies (1D nanoribbons, 2D dendrites, 3D spirals, etc.). These edge-rich TMD layers offer versatile candidates for probing the physical and chemical properties and exploring potential applications in electronics, optoelectronics, catalysis, sensing, and quantum technologies. In this Review, we present an overview of the current state-of-the-art in the manipulation of TMD atomic edges and edge-rich structures using CVD. We highlight the vast range of distinct properties associated with these edge configurations and structures and provide insights into the opportunities afforded by such edge-functionalized crystals. The objective of this Review is to motivate further research and development efforts to use CVD as a scalable approach to harness the benefits of such crystal-edge engineering.

Magic-angle helical trilayer graphene

We propose magic-angle helical trilayer graphene (HTG), a helical structure featuring identical rotation angles between three consecutive layers of graphene, as a unique and experimentally accessible platform for realizing exotic correlated topological states of matter. While nominally forming a supermoiré (or moiré-of-moiré) structure, we show that HTG locally relaxes into large regions of a periodic single-moiré structure realizing flat topological bands carrying nontrivial valley Chern number. These bands feature near-ideal quantum geometry and are isolated from remote bands by a very large energy gap, making HTG a promising platform for experimental realization of correlated topological states such as integer and fractional quantum anomalous Hall states.

Radiative suppression of exciton-exciton annihilation in a two-dimensional semiconductor

Two-dimensional (2D) semiconductors possess strongly bound excitons, opening novel opportunities for engineering light-matter interaction at the nanoscale. However, their in-plane confinement leads to large non-radiative exciton-exciton annihilation (EEA) processes, setting a fundamental limit for their photonic applications. In this work, we demonstrate suppression of EEA via enhancement of light-matter interaction in hybrid 2D semiconductor-dielectric nanophotonic platforms, by coupling excitons in WS2 monolayers with optical Mie resonances in dielectric nanoantennas. The hybrid system reaches an intermediate light-matter coupling regime, with photoluminescence enhancement factors up to 102. Probing the exciton ultrafast dynamics reveal suppressed EEA for coupled excitons, even under high exciton densities >1012 cm-2. We extract EEA coefficients in the order of 10-3, compared to 10-2 for uncoupled monolayers, as well as a Purcell factor of 4.5. Our results highlight engineering the photonic environment as a route to achieve higher quantum efficiencies, for low-power hybrid devices, and larger exciton densities, towards strongly correlated excitonic phases in 2D semiconductors.

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

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

Quantum Noise Spectroscopy of Dynamical Critical Phenomena

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

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

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

Programming twist angle and strain profiles in 2D materials

Moiré superlattices in twisted two-dimensional materials have generated tremendous excitement as a platform for achieving quantum properties on demand. However, the moiré pattern is highly sensitive to the interlayer atomic registry, and current assembly techniques suffer from imprecise control of the average twist angle, spatial inhomogeneity in the local twist angle, and distortions caused by random strain. We manipulated the moiré patterns in hetero- and homobilayers through in-plane bending of monolayer ribbons, using the tip of an atomic force microscope. This technique achieves continuous variation of twist angles with improved twist-angle homogeneity and reduced random strain, resulting in moiré patterns with tunable wavelength and ultralow disorder. Our results may enable detailed studies of ultralow-disorder moiré systems and the realization of precise strain-engineered devices.