One-dimensional flat bands in twisted bilayer germanium selenide

Emergent phases in graphene flat bands

Electronic correlations in two-dimensional materials play a crucial role in stabilising emergent phases of matter. The realisation of correlation-driven phenomena in graphene has remained a longstanding goal, primarily due to the absence of strong electron-electron interactions within its low-energy bands. In this context, magic-angle twisted bilayer graphene has recently emerged as a novel platform featuring correlated phases favoured by the low-energy flat bands of the underlying moiré superlattice. Notably, the observation of correlated insulators and superconductivity, and the interplay between these phases have garnered significant attention. A wealth of correlated phases with unprecedented tunability was discovered subsequently, including orbital ferromagnetism, Chern insulators, strange metallicity, density waves, and nematicity. However, a comprehensive understanding of these closely competing phases remains elusive. The ability to controllably twist and stack multiple graphene layers has enabled the creation of a whole new family of moiré superlattices with myriad properties. Here, we review the progress and development achieved so far, encompassing the rich phase diagrams offered by these graphene-based moiré systems. Additionally, we discuss multiple phases recently observed in non-moiré multilayer graphene systems. Finally, we outline future opportunities and challenges for the exploration of hidden phases in this new generation of moiré materials.

In-plane anisotropic two-dimensional materials for twistronics

In-plane anisotropic two-dimensional (2D) materials exhibit in-plane orientation-dependent properties. The anisotropic unit cell causes these materials to show lower symmetry but more diverse physical properties than in-plane isotropic 2D materials. In addition, the artificial stacking of in-plane anisotropic 2D materials can generate new phenomena that cannot be achieved in in-plane isotropic 2D materials. In this perspective we provide an overview of representative in-plane anisotropic 2D materials and their properties, such as black phosphorus, group IV monochalcogenides, group VI transition metal dichalcogenides with 1T' and Tdphases, and rhenium dichalcogenides. In addition, we discuss recent theoretical and experimental investigations of twistronics using in-plane anisotropic 2D materials. Both in-plane anisotropic 2D materials and their twistronics hold considerable potential for advancing the field of 2D materials, particularly in the context of orientation-dependent optoelectronic devices.

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.

Carbon Kagome nanotubes-quasi-one-dimensional nanostructures with flat bands

In recent years, a number of bulk materials and heterostructures have been explored due their connections with exotic materials phenomena emanating from flat band physics and strong electronic correlation. The possibility of realizing such fascinating material properties in simple realistic nanostructures is particularly exciting, especially as the investigation of exotic states of electronic matter in wire-like geometries is relatively unexplored in the literature. Motivated by these considerations, we introduce in this work carbon Kagome nanotubes (CKNTs)-a new allotrope of carbon formed by rolling up Kagome graphene, and investigate this material using specialized first principles calculations. We identify two principal varieties of CKNTs-armchair and zigzag, and find both varieties to be stable at room temperature, based on ab initio molecular dynamics simulations. CKNTs are metallic and feature dispersionless states (i.e., flat bands) near the Fermi level throughout their Brillouin zone, along with an associated singular peak in the electronic density of states. We calculate the mechanical and electronic response of CKNTs to torsional and axial strains, and show that CKNTs appear to be more mechanically compliant than conventional carbon nanotubes (CNTs). Additionally, we find that the electronic properties of CKNTs undergo significant electronic transitions-with emergent partial flat bands and tilted Dirac points-when twisted. We develop a relatively simple tight-binding model that can explain many of these electronic features. We also discuss possible routes for the synthesis of CKNTs. Overall, CKNTs appear to be unique and striking examples of realistic elemental quasi-one-dimensional materials that may display fascinating material properties due to strong electronic correlation. Distorted CKNTs may provide an interesting nanomaterial platform where flat band physics and chirality induced anomalous transport effects may be studied together.

Tunable 1D van der Waals Nanostructures by Vapor-Liquid-Solid Growth

ConspectusVapor-liquid-solid (VLS) growth using molten metal catalysts has traditionally been used to synthesize nanowires from different 3D-crystalline semiconductors. With their anisotropic structure and properties, 2D/layered semiconductors create additional opportunities for materials design when shaped into 1D nanostructures. In contrast to hexagonal 2D crystals such as graphene, h-BN, and transition metal dichalcogenides, which tend to roll up into nanotubes, VLS growth of layered group III and group IV monochalcogenides produces diverse nanowire and nanoribbon morphologies that crystallize in a bulk-like layered structure with nanometer-scale footprint and lengths exceeding tens of micrometers. In this Account, we discuss the achievable morphologies, the mechanisms governing key structural features, and the emerging functional properties of these 1D van der Waals (vdW) architectures. Recent results highlight rich sets of phenomena that qualify these materials as a distinct class of nanostructures, far beyond a mere extension of 3D-crystalline VLS nanowires to vdW crystals.The main difference between 3D- and vdW crystals, the pronounced in-plane/cross-plane anisotropy of layered materials, motivates investigating the factors governing the layer orientation. Recent research suggests that the VLS catalyst plays a key role, and that its modification via the choice of chalcogens or through modifiers added to the growth precursor can switch both the nanostructure morphology and vdW layering. In many instances, ordinary layered structures are not formed but VLS growth is dominated by morphologies─often containing a crystal defect─that present reduced or vanishing layer nucleation barriers, thus achieving fast growth and emerging as the principal synthesis product. Prominent defect morphologies include vdW bicrystals growing by a twin-plane reentrant process and chiral nanowires formed by spiral growth around an axial screw dislocation. The latter carry particular promise, e.g., for twistronics. In vdW nanowires, Eshelby twist─a progressive crystal rotation caused by the dislocation stress field─translates into interlayer twist that is precisely tunable via the wire diameter. Projected onto a helicoid vdW interface, the resulting twist moirés not only modify the electronic structure but also realize configurations without equivalent in planar systems, such as continuously variable twist and twist homojunctions.1D vdW nanostructures derive distinct functionality from both their layered structure and embedded defects. Correlated electron microscopy methods including imaging, nanobeam diffraction, as well as electron-stimulated local absorption and luminescence spectroscopies combine to an exceptionally powerful probe of this emerging functionality, identifying twist-moiré induced electronic modulations and chiral photonic modes, demonstrating the benign nature of defects in optoelectronics, and uncovering ferroelectricity via symmetry-breaking by single-layer stacking faults in vdW nanowires. Far-reaching possibilities for tuning crystal structure, morphology, and defects create a rich playground for the discovery of new functional nanomaterials based on vdW crystals. Given the prominence of defects and extensive prospects for controlling their character and placement during synthesis, 1D vdW nanostructures have the potential to cause a paradigm shift in the science of electronic materials, replacing the traditional strategy of suppressing crystal imperfections with an alternative philosophy that embraces the use of individual defects with designed properties as drivers of technology.

One-Dimensional Moiré Physics and Chemistry in Heterostrained Bilayer Graphene

Twisted bilayer graphene (tBLG) has emerged as a promising platform for exploring exotic electronic phases. However, the formation of moiré patterns in tBLG has thus far been confined to the introduction of twist angles between the layers. Here, we propose heterostrained bilayer graphene (hBLG), as an alternative avenue for accessing twist angle-free moiré physics via lattice mismatch. Using atomistic and first-principles calculations, we demonstrate that the uniaxial heterostrain can promote isolated flat electronic bands around the Fermi level. Furthermore, the heterostrain-induced out-of-plane lattice relaxation may lead to a spatially modulated reactivity of the surface layer, paving the way for moiré-driven chemistry and magnetism. We anticipate that our findings can be readily generalized to other layered materials.

1D Electronic Flat Bands in Untwisted Moiré Superlattices

After the preparation of 2D electronic flat band (EFB) in van der Waals (vdW) superlattices, recent measurements suggest the existence of 1D electronic flat bands (1D-EFBs) in twisted vdW bilayers. However, the realization of 1D-EFBs is experimentally elusive in untwisted 2D layers, which is desired considering their fabrication and scalability. Herein, the discovery of 1D-EFBs is reported in an untwisted in situ-grown two atomic-layer Bi(110) superlattice self-aligned on an SnSe(001) substrate using scanning probe microscopy measurements and density functional theory calculations. While the Bi-Bi dimers of Bi zigzag (ZZ) chains are buckled, the epitaxial lattice mismatch between the Bi and SnSe layers induces two 1D buckling reversal regions (BRRs) extending along the ZZ direction in each Bi(110)-11 × 11 supercell. A series of 1D-EFBs arises spatially following BRRs that isolate electronic states along the armchair (AC) direction and localize electrons in 1D extended states along ZZ due to quantum interference at a topological node. This work provides a generalized strategy for engineering 1D-EFBs in utilizing lattice mismatch between untwisted rectangular vdW layers.

Atomic Bose-Einstein condensate in twisted-bilayer optical lattices

Observation of strong correlations and superconductivity in twisted-bilayer graphene^1-4 has stimulated tremendous interest in fundamental and applied physics^5-8. In this system, the superposition of two twisted honeycomb lattices, generating a moiré pattern, is the key to the observed flat electronic bands, slow electron velocity and large density of states^9-12. Extension of the twisted-bilayer system to new configurations is highly desired, which can provide exciting prospects to investigate twistronics beyond bilayer graphene. Here we demonstrate a quantum simulation of superfluid to Mott insulator transition in twisted-bilayer square lattices based on atomic Bose-Einstein condensates loaded into spin-dependent optical lattices. The lattices are made of two sets of laser beams that independently address atoms in different spin states, which form the synthetic dimension accommodating the two layers. The interlayer coupling is highly controllable by a microwave field, which enables the occurrence of a lowest flat band and new correlated phases in the strong coupling limit. We directly observe the spatial moiré pattern and the momentum diffraction, which confirm the presence of two forms of superfluid and a modified superfluid to insulator transition in twisted-bilayer lattices. Our scheme is generic and can be applied to different lattice geometries and for both boson and fermion systems. This opens up a new direction for exploring moiré physics in ultracold atoms with highly controllable optical lattices.

Engineering Grain Boundaries in Two-Dimensional Electronic Materials

Engineering the boundary structures in 2D materials provides an unprecedented opportunity to program the physical properties of the materials with extensive tunability and realize innovative devices with advanced functionalities. However, structural engineering technology is still in its infancy, and creating artificial boundary structures with high reproducibility remains difficult. In this review, various emergent properties of 2D materials with different grain boundaries, and the current techniques to control the structures, are introduced. The remaining challenges for scalable and reproducible structure control and the outlook on the future directions of the related techniques are also discussed.

Observation of moiré excitons in the twisted WS2/WS2 homostructure

Moiré superlattices offer a fascinating platform for designing the properties of optical excitons. The moiré pattern can generate an ordered exciton array in space, making it possible for topological excitons and quantum emitters. Recently, evidence of moiré excitons in the twisted heterostructures of TMDs has been widely reported. However, to date, the capture and investigation of moiré excitons in the twisted homostructure (T-HS) remain elusive. Here, we report the observation of moiré excitons in the WS₂/WS₂ T-HS with a twist angle of about 1.5°. The PL spectrum of the T-HS region shows many small peaks with nearly constant peak spacing, which is attributed to the reconstructed moiré potential generated by the reconstructed moiré pattern to confine the intralayer excitons, thereby forming an ordered moiré exciton array. Furthermore, we have studied the influence of temperature and laser power on the moiré excitons as well as the valley polarization of the moiré excitons. Our results provide a promising prospect for further exploration of artificial excitonic crystals and quantum emitters of TMD moiré patterns.

Controllable Edge Epitaxy of Helical GeSe/GeS Heterostructures

Emerging twistronics based on van der Waals (vdWs) materials has attracted great interest in condensed matter physics. Recently, more neoteric three-dimensional (3D) architectures with interlayer twist are realized in germanium sulfide (GeS) crystals. Here, we further demonstrate a convenient way for tailoring the twist rate of helical GeS crystals via tuning of the growth temperature. Under higher growth temperatures, the twist angles between successive nanoplates of the GeS mesowires (MWs) are statistically smaller, which can be understood by the dynamics of the catalyst during the growth. Moreover, we fabricate self-assembled helical heterostructures by introducing germanium selenide (GeSe) onto helical GeS crystals via edge epitaxy. Besides the helical architecture, the moiré superlattices at the twisted interfaces are also inherited. Compared with GeS MWs, helical GeSe/GeS heterostructures exhibit improved electrical conductivity and photoresponse. These results manifest new opportunities in future electronics and optoelectronics by harnessing 3D twistronics based on vdWs materials.

Designing 1D correlated-electron states by non-Euclidean topography of 2D monolayers

Two-dimensional (2D) bilayers, twisted to particular angles to display electronic flat bands, are being extensively explored for physics of strongly correlated 2D systems. However, the similar rich physics of one-dimensional (1D) strongly correlated systems remains elusive as it is largely inaccessible by twists. Here, a distinctive way to create 1D flat bands is proposed, by either stamping or growing a 2D monolayer on a non-Euclidean topography-patterned surface. Using boron nitride (hBN) as an example, our analysis employing elastic plate theory, density-functional and coarse-grained tight-binding method reveals that hBN’s bi-periodic sinusoidal deformation creates pseudo- electric and magnetic fields with unexpected spatial dependence. A combination of these fields leads to anisotropic confinement and 1D flat bands. Moreover, changing the periodic undulations can tune the bandwidth, to drive the system to different strongly correlated regimes such as density waves, Luttinger liquid, and Mott insulator. The 1D nature of these states differs from those obtained in twisted materials and can be exploited to study the exciting physics of 1D quantum systems.

Flat electronic bands and the ensuing correlated phases have been explored in twisted 2D bilayers and in periodically buckled graphene. Here the authors propose a strategy to realize 1D flat bands with a tunable bandwidth in a 2D semiconductor deposited on a patterned substrate with a non-zero Gaussian curvature.

One-dimensional Luttinger liquids in a two-dimensional moiré lattice

The Luttinger liquid (LL) model of one-dimensional (1D) electronic systems provides a powerful tool for understanding strongly correlated physics, including phenomena such as spin-charge separation¹. Substantial theoretical efforts have attempted to extend the LL phenomenology to two dimensions, especially in models of closely packed arrays of 1D quantum wires^2-13, each being described as a LL. Such coupled-wire models have been successfully used to construct two-dimensional (2D) anisotropic non-Fermi liquids^2-6, quantum Hall states^7-9, topological phases^10,11 and quantum spin liquids^12,13. However, an experimental demonstration of high-quality arrays of 1D LLs suitable for realizing these models remains absent. Here we report the experimental realization of 2D arrays of 1D LLs with crystalline quality in a moiré superlattice made of twisted bilayer tungsten ditelluride (tWTe₂). Originating from the anisotropic lattice of the monolayer, the moiré pattern of tWTe₂ hosts identical, parallel 1D electronic channels, separated by a fixed nanoscale distance, which is tuneable by the interlayer twist angle. At a twist angle of approximately 5 degrees, we find that hole-doped tWTe₂ exhibits exceptionally large transport anisotropy with a resistance ratio of around 1,000 between two orthogonal in-plane directions. The across-wire conductance exhibits power-law scaling behaviours, consistent with the formation of a 2D anisotropic phase that resembles an array of LLs. Our results open the door for realizing a variety of correlated and topological quantum phases based on coupled-wire models and LL physics.

Free-standing large, ultrathin germanium selenide van der Waals ribbons by combined vapor-liquid-solid growth and edge attachment

Among group IV monochalcogenides, layered GeSe is of interest for its anisotropic properties, 1.3 eV direct band gap, ferroelectricity, high mobility, and excellent environmental stability. Electronic, optoelectronic and photovoltaic applications depend on the development of synthesis approaches that yield large quantities of crystalline flakes with controllable size and thickness. Here, we demonstrate the growth of single-crystalline GeSe nanoribbons by a vapor-liquid-solid process over Au catalyst on different substrates at low thermal budget. The nanoribbons crystallize in a layered structure, with ribbon axis along the armchair direction of the van der Waals layers. The ribbon morphology is determined by catalyst driven fast longitudinal growth accompanied by lateral expansion via edge-specific incorporation into the basal planes. This combined growth mechanism enables temperature controlled realization of ribbons with typical widths of up to 30 μm and lengths exceeding 100 μm, while maintaining sub-50 nm thickness. Nanoscale cathodoluminescence spectroscopy on individual GeSe nanoribbons demonstrates intense temperature-dependent band-edge emission up to room temperature, with fundamental bandgap and temperature coefficient of E_g(0) = 1.29 eV and α = 3.0 × 10^-4 eV K^-1, respectively, confirming high quality GeSe with low concentration of non-radiative recombination centers promising for optoelectronic applications including light emitters, photodetectors, and solar cells.

Moiré bands in twisted trilayer black phosphorene: effects of pressure and electric field

Twist-induced moiré bands and accompanied correlated phenomena have been extensively investigated in twisted hexagonal lattices with weak interlayer coupling. However, the formation of moiré bands in strongly coupled layered materials and their controlled tuning remain largely unexplored. Here, we systematically study the moiré bands in twisted trilayer black phosphorene (TTbP) and the influences of pressure and electric field on them. Moiré states can form in various TTbPs even when the twist angle is larger than 16° similar to that of twisted bilayer bP. However, different TTbPs show different localization patterns depending on the twisting layer, leading to distinct dipolar behaviors. While these moiré states become quasi-one-dimensional (1D) as the twist angle decreases, external pressure causes the crossover of moiré states from quasi-1D to 0D with a dramatic change in localization areas and greatly reduced bandwidth. Interestingly, compared to twisted bilayer and pristine bP, TTbPs show a much larger electric-field induced Stark effect, controllable by either the twist angle or twist layer. Our work thus demonstrates TTbP as an attractive platform to explore moiré-controlled electronic and optical properties, as well as tunable optoelectronic applications.

Interlayer Interactions in 1D Van der Waals Moiré Superlattices

Studying two-dimensional (2D) van der Waals (vdW) moiré superlattices and their interlayer interactions have received surging attention after recent discoveries of many new phases of matter that are highly tunable. Different atomistic registry between layers forming the inner and outer nanotubes can also form one-dimensional (1D) vdW moiré superlattices. In this review, experimental observations and theoretical perspectives related to interlayer interactions in 1D vdW moiré superlattices are summarized. The discussion focuses on double-walled carbon nanotubes (DWNTs), a model 1D vdW moiré system, and the authors highlight the new optical features emerging from the non-trivial strong interlayer coupling effect and the unique physics in 1D DWNTs. Future directions and questions in probing the intriguing physical phenomena in 1D vdW moiré superlattices such as, correlated physics in different 1D moiré systems beyond DWNTs are proposed and discussed.

Realization of nearly dispersionless bands with strong orbital anisotropy from destructive interference in twisted bilayer MoS2

Recently, the twist angle between adjacent sheets of stacked van der Waals materials emerged as a new knob to engineer correlated states of matter in two-dimensional heterostructures in a controlled manner, giving rise to emergent phenomena such as superconductivity or correlated insulating states. Here, we use an ab initio based approach to characterize the electronic properties of twisted bilayer MoS₂. We report that, in marked contrast to twisted bilayer graphene, slightly hole-doped MoS₂ realizes a strongly asymmetric p_x-p_y Hubbard model on the honeycomb lattice, with two almost entirely dispersionless bands emerging due to destructive interference. The origin of these dispersionless bands, is similar to that of the flat bands in the prototypical Lieb or Kagome lattices and co-exists with the general band flattening at small twist angle due to the moiré interference. We study the collective behavior of twisted bilayer MoS₂ in the presence of interactions, and characterize an array of different magnetic and orbitally-ordered correlated phases, which may be susceptible to quantum fluctuations giving rise to exotic, purely quantum, states of matter.

Twisted van der Waals systems are known to host flat electronic bands, originating from moire potential. Here, the authors predict from purely geometric considerations a new type of nearly dispersionless bands in twisted bilayer MoS₂, resulting from destructive interference between effective lattice hopping matrix elements.

Lattice reconstruction induced multiple ultra-flat bands in twisted bilayer WSe2

Moiré superlattices in van der Waals heterostructures provide a tunable platform to study emergent properties that are absent in the natural crystal form. Twisted bilayer transition metal dichalcogenides (TB-TMDs) can host moiré flat bands over a wide range of twist angles. For twist angle close to 60°, it was predicted that TB-TMDs undergo a lattice reconstruction which causes the formation of ultra-flat bands. Here, by using scanning tunneling microscopy and spectroscopy, we show the emergence of multiple ultra-flat bands in twisted bilayer WSe₂ when the twist angle is within 3° of 60°. The ultra-flat bands are manifested as narrow tunneling conductance peaks with estimated bandwidth less than 10 meV, which is only a fraction of the estimated on-site Coulomb repulsion energy. The number of these ultra-flat bands and spatial distribution of the wavefunctions match well with the theoretical predictions, strongly evidencing that the observed ultra-flat bands are induced by lattice reconstruction. Our work provides a foundation for further study of the exotic correlated phases in TB-TMDs.

It was predicted that lattice reconstruction can lead to the emergence of multiple ultra-flat electronic bands in twisted bilayer transition metal dichalcogenides. Here, by using scanning tunneling microscopy and spectroscopy, the authors demonstrate such bands in twisted bilayer WSe₂.

Engineering Three-Dimensional Moiré Flat Bands

Twisting two adjacent layers of van der Waals materials with respect to each other can lead to flat two-dimensional electronic bands which enables a wealth of physical phenomena. Here, we generalize this concept of so-called moiré flat bands to engineer flat bands in all three spatial dimensions controlled by the twist angle. The basic concept is to stack the material such that the large spatial moiré interference patterns are spatially shifted from one twisted layer to the next. We exemplify the general concept by considering graphitic systems, boron nitride, and WSe2, but the approach is applicable to any two-dimensional van der Waals material. For hexagonal boron nitride, we develop an ab initio fitted tight binding model that captures the corresponding three-dimensional low-energy electronic structure. We outline that interesting three-dimensional correlated phases of matter can be induced and controlled following this route, including quantum magnets and unconventional superconducting states.

Moiré patterns of twisted bilayer antimonene and their structural and electronic transition

Interlayer twisting in two-dimensional (2D) van der Waals (vdW) heterostructures often leads to a periodic moiré pattern which is a superlattice structure on top of the original atomic lattice of the 2D layers. The formation of a moiré superlattice can be accompanied by a significant structural reconstruction and ultra-flat electronic bands. The moiré superlattice is typically built with a tunable scale by controlling the rotation angle θ between the individual 2D layers. In this paper, we report the structural reconstruction and electronic transition in moiré patterns of twisted bilayer antimonene, based on Kohn-Sham density functional theory calculations. Starting from rigid moiré structures, the atomic relaxation leads to an array of high-symmetry stacking domains with soliton boundaries through a vortex-like reconstruction. For twist angle θ≤ 6.01°, the impact of the structural reconstruction on the electronic bands becomes very significant, in the appearance of flat bands at the valence band edge, and no magic angle is required for the flat bands to appear in the 2D Sb moiré patterns. Both inhomogeneous interlayer hybridization and local strain are found to be responsible for the formation of these flat electronic bands.

Electronic structures and anisotropic carrier mobilities of monolayer ternary metal iodides MLaI5(M=Mg, Ca, Sr, Ba)

Exploiting two-dimensional (2D) materials with natural band gaps and anisotropic quasi-one-dimensional (quasi-1D) carrier transport character is essential in high-performance nanoscale transistors and photodetectors. Herein, the stabilities, electronic structures and carrier mobilities of 2D monolayer ternary metal iodides MLaI₅(M = Mg, Ca, Sr, Ba) have been explored by utilizing first-principles calculations combined with numerical calculations. It is found that exfoliating MLaI₅monolayers are feasible owing to low cleavage energy of 0.19-0.21 J m^-2and MLaI₅monolayers are thermodynamically stable based on phonon spectra. MLaI₅monolayers are semiconductors with band gaps ranging from 2.08 eV for MgLaI₅to 2.51 eV for BaLaI₅. The carrier mobility is reasonably examined considering both acoustic deformation potential scattering and polar optical phonon scattering mechanisms. All MLaI₅monolayers demonstrate superior anisotropic and quasi-1D carrier transport character due to the striped structures. In particular, the anisotropic ratios of electron and hole mobilities along different directions reach hundreds and tens for MLaI₅monolayers, respectively. Thus, the effective electron-hole spatial separation could be actually achieved. Moreover, the absolute locations of band edges of MLaI₅monolayers have been aligned. These results would provide fundamental insights for MLaI₅monolayers applying in nano-electronic and optoelectronic devices.

Predictions of moiré excitons in twisted two-dimensional organic-inorganic halide perovskites

Recent breakthrough in synthesizing arbitrary vertical heterostructures of Ruddlesden–Popper (RP) perovskites opens doors to myriad quantum optoelectronic applications. However, it is not clear whether moiré excitons and flat bands can be formed in such heterostructures. Here, we predict from first principles that twisted homobilayers of RP perovskite, MA₂PbI₄, can host moiré excitons and yield flat energy bands. The moiré excitons exhibit unique and hybridized characteristics with electrons confined in a single layer of a striped distribution while holes localized in both layers. Nearly flat valence bands can be formed in the bilayers with relatively large twist angles, thanks to the presence of hydrogen bonds that strengthen the interlayer coupling. External pressures can further increase the interlayer coupling, yielding more localized moiré excitons and flatter valence bands. Finally, electrostatic gating is predicted to tune the degree of hybridization, energy, position and localization of moiré excitons in twisted MA₂PbI₄ bilayers.

Excitonic states in twisted MA₂PbI₄ bilayers were calculated by first-principles calculations.

Moiréless correlations in ABCA graphene

Atomically thin van der Waals materials stacked with an interlayer twist have proven to be an excellent platform toward achieving gate-tunable correlated phenomena linked to the formation of flat electronic bands. In this work we demonstrate the formation of emergent correlated phases in multilayer rhombohedral graphene--a simple material that also exhibits a flat electronic band edge but without the need of having a moiré superlattice induced by twisted van der Waals layers. We show that two layers of bilayer graphene that are twisted by an arbitrary tiny angle host large (micrometer-scale) regions of uniform rhombohedral four-layer (ABCA) graphene that can be independently studied. Scanning tunneling spectroscopy reveals that ABCA graphene hosts an unprecedentedly sharp van Hove singularity of 3-5-meV half-width. We demonstrate that when this van Hove singularity straddles the Fermi level, a correlated many-body gap emerges with peak-to-peak value of 9.5 meV at charge neutrality. Mean-field theoretical calculations for model with short-ranged interactions indicate that two primary candidates for the appearance of this broken symmetry state are a charge-transfer excitonic insulator and a ferrimagnet. Finally, we show that ABCA graphene hosts surface topological helical edge states at natural interfaces with ABAB graphene which can be turned on and off with gate voltage, implying that small-angle twisted double-bilayer graphene is an ideal programmable topological quantum material.

Moiré metrology of energy landscapes in van der Waals heterostructures

The emerging field of twistronics, which harnesses the twist angle between two-dimensional materials, represents a promising route for the design of quantum materials, as the twist-angle-induced superlattices offer means to control topology and strong correlations. At the small twist limit, and particularly under strain, as atomic relaxation prevails, the emergent moiré superlattice encodes elusive insights into the local interlayer interaction. Here we introduce moiré metrology as a combined experiment-theory framework to probe the stacking energy landscape of bilayer structures at the 0.1 meV/atom scale, outperforming the gold-standard of quantum chemistry. Through studying the shapes of moiré domains with numerous nano-imaging techniques, and correlating with multi-scale modelling, we assess and refine first-principle models for the interlayer interaction. We document the prowess of moiré metrology for three representative twisted systems: bilayer graphene, double bilayer graphene and H-stacked MoSe2/WSe2. Moiré metrology establishes sought after experimental benchmarks for interlayer interaction, thus enabling accurate modelling of twisted multilayers.

Switchable Asymmetric Moiré Patterns with Strongly Localized States

Most moiré pattern structures are constructed by twisting the angle of two similar 2D materials. The corresponding electronic structures are fixed in device applications. Here we study moiré patterns constructed with monolayers of InSe and ferroelectric In₂Se₃. The ferroelectricity of In₂Se₃ induces deep electron trap states and allows the switch of moiré pattern by an applied electric field. Using a unique linear scaling computational method, we systematically studied the electronic structures, localized state sizes, and strong correlation effects of switchable moiré patterns of systems containing close to 10 000 atoms.