Flat Bands and Mechanical Deformation Effects in the Moiré Superlattice of MoS2-WSe2 Heterobilayers

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

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

Twist Proximity-Endowed Large Figure of Merit in a Band-Modulated CrI3/1T-MoS2 Moiré Superlattice

Moiré superlattices with a robust twist proximity effect in the low-dimensional regime can facilitate nanoscale thermoelectric devices. In pristine systems, the low efficiency and lack of proficient control of thermoelectric properties impede desirable advancements in the field of energy conversion. In the present study, we demonstrate remarkable macroscopic thermoelectric response as a consequence of microscopic band structure modulation via the twist proximity in an engineered CrI3/1T-MoS2 moiré superlattice. The local twist effect, which leads to the microscopic phenomena of electron localization, results in a comprehensive electronic structure modulation. Consequently, these local effects convolute the macroscopic thermoelectric effect. Additionally, flat bands and angle-dependent metallic to semiconducting transitions are observed at 10.89, 23.41, and 30° twist angles. We correlate the observed phenomenon with the augmented spin-charge transport and interconversion via the twist proximity effect in its semiconducting phase. The estimated ultralow electronic and lattice thermal conductivities further corroborate with the observed large figure of merit and Seebeck coefficient. The maximum values of the Seebeck coefficient and figure of merit are estimated to be ∼413 μV/K and ∼4.3 at 200 K for 30° under the constant time relaxation approach. The twist-endowed outstanding thermoelectric effect in moiré superlattices with band modulation unveils a distinctive approach to establish efficient thermoelectric devices.

Influence of Atomic Relaxations on the Moiré Flat Band Wave Functions in Antiparallel Twisted Bilayer WS2

Twisting bilayers of transition metal dichalcogenides gives rise to a moiré potential resulting in flat bands with localized wave functions and enhanced correlation effects. In this work, scanning tunneling microscopy is used to image a WS2 bilayer twisted approximately 3° off the antiparallel alignment. Scanning tunneling spectroscopy reveals localized states in the vicinity of the valence band onset, which is observed to occur first in regions with S-on-S Bernal stacking. In contrast, density functional theory calculations on twisted bilayers that have been relaxed in vacuum predict the highest-lying flat valence band to be localized in regions of AA' stacking. However, agreement with experiment is recovered when the calculations are performed on bilayers in which the atomic displacements from the unrelaxed positions have been reduced, reflecting the influence of the substrate and finite temperature. This demonstrates the delicate interplay of atomic relaxations and the electronic structure of twisted bilayer materials.

Room-temperature wavelike exciton transport in a van der Waals superatomic semiconductor

The transport of energy and information in semiconductors is limited by scattering between electronic carriers and lattice phonons, resulting in diffusive and lossy transport that curtails all semiconductor technologies. Using Re6Se8Cl2, a van der Waals (vdW) superatomic semiconductor, we demonstrate the formation of acoustic exciton-polarons, an electronic quasiparticle shielded from phonon scattering. We directly imaged polaron transport in Re6Se8Cl2 at room temperature, revealing quasi-ballistic, wavelike propagation sustained for a nanosecond and several micrometers. Shielded polaron transport leads to electronic energy propagation lengths orders of magnitude greater than in other vdW semiconductors, exceeding even silicon over a nanosecond. We propose that, counterintuitively, quasi-flat electronic bands and strong exciton-acoustic phonon coupling are together responsible for the transport properties of Re6Se8Cl2, establishing a path to ballistic room-temperature semiconductors.

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.

A van der Waals Heterostructure with an Electronically Textured Moiré Pattern: PtSe2/PtTe2

The interlayer interaction in Pt-dichalcogenides strongly affects their electronic structures. The modulations of the interlayer atom-coordination in vertical heterostructures based on these materials are expected to laterally modify these interlayer interactions and thus provide an opportunity to texture the electronic structure. To determine the effects of local variation of the interlayer atom coordination on the electronic structure of PtSe₂, van der Waals heterostructures of PtSe₂ and PtTe₂ have been synthesized by molecular beam epitaxy. The heterostructure forms a coincidence lattice with 13 unit cells of PtSe₂ matching 12 unit cells of PtTe₂, forming a moiré superstructure. The interaction with PtTe₂ reduces the band gap of PtSe₂ monolayers from 1.8 eV to 0.5 eV. While the band gap is uniform across the moiré unit cell, scanning tunneling spectroscopy and dI/dV mapping identify gap states that are localized within certain regions of the moiré unit cell. Deep states associated with chalcogen p_z-orbitals at binding energies of ∼ -2 eV also exhibit lateral variation within the moiré unit cell, indicative of varying interlayer chalcogen interactions. Density functional theory calculations indicate that local variations in atom coordination in the moiré unit cell cause variations in the charge transfer from PtTe₂ to PtSe₂, thus affecting the value of the interface dipole. Experimentally this is confirmed by measuring the local work function by field emission resonance spectroscopy, which reveals a large work function modulation of ∼0.5 eV within the moiré structure. These results show that the local coordination variation of the chalcogen atoms in the PtSe₂/PtTe₂ van der Waals heterostructure induces a nanoscale electronic structure texture in PtSe₂.

Remarkably Deep Moiré Potential for Intralayer Excitons in MoSe2/MoS2 Twisted Heterobilayers

A moiré superlattice formed in twisted van der Waals bilayers has emerged as a new tuning knob for creating new electronic states in two-dimensional materials. Excitonic properties can also be altered drastically due to the presence of moiré potential. However, quantifying the moiré potential for excitons is nontrivial. By creating a large ensemble of MoSe₂/MoS₂ heterobilayers with a systematic variation of twist angles, we map out the minibands of interlayer and intralayer excitons as a function of twist angles, from which we determine the moiré potential for excitons. Surprisingly, the moiré potential depth for intralayer excitons is up to ∼130 meV, comparable to that for interlayer excitons. This result is markedly different from theoretical calculations based on density functional theory, which show an order of magnitude smaller moiré potential for intralayer excitons. The remarkably deep intralayer moiré potential is understood within the framework of structural reconstruction within the moiré unit cell.

Moiré Potential, Lattice Relaxation, and Layer Polarization in Marginally Twisted MoS2 Bilayers

Artificially twisted heterostructures of semiconducting transition-metal dichalcogenides (TMDs) offer unprecedented control over their electronic and optical properties via the spatial modulation of interlayer interactions and structural reconstruction. Here we study twisted MoS₂ bilayers in a wide range of twist angles near 0° using scanning tunneling microscopy/spectroscopy. We investigate the twist angle dependence of the moiré pattern, which is dominated by lattice reconstruction for small angles (<2°), leading to large triangular domains with rhombohedral stacking. Local spectroscopy measurements reveal a large moiré-potential strength of 100-200 meV for angles <3°. In reconstructed regions, we see a bias-dependent asymmetry between neighboring triangular domains, which we relate to the vertical polarization that is intrinsic to rhombohedral stacked TMDs. This viewpoint is further supported by spectroscopy maps and ambient piezoresponse measurements. Our results provide a microscopic perspective of this new class of interfacial ferroelectrics and can offer clues for designing novel heterostructures that harness this effect.

Anomalous optical excitations from arrays of whirlpooled lattice distortions in moiré superlattices

Moiré superlattices formed by stacking two-dimensional crystals have reinvigorated the pursuit for emergent functionalities of engineered superlattices. Unique optical characteristics can be realized from the interplay between the electronic excitations and the atomic rearrangements owing to their intrinsic softness. Although large-scale reconstructions have been identified at small twist angles, they have been treated as being rigid at large twist angles. Here, we report that moiré superlattices made from single layers of MoS₂ and WSe₂ exhibit a pair of torsional strains with opposite chirality irrespective of the twist angle. The whirlpool-shaped periodic lattice distortions introduce fuzziness in the Raman spectra and universal redshifts to the intralayer excitons for all twist angles. We show that both of these modulations become weaker as the twist angle increases but do not disappear, whereas they are turned off when the constituent layers are not tightly coupled, thus establishing an essential structure-property relationship for moiré superlattices.

Morphology Deformation and Giant Electronic Band Modulation in Long-Wavelength WS2 Moiré Superlattices

As a lattice interference effect, moiré superlattices feature a magnification effect that they respond sensitively to both the extrinsic mechanical perturbations and intrinsic atomic reconstructions. Here, using scanning tunneling microscopy and spectroscopy, we observe that long-wavelength WS₂ superlattices are reconstructed into various moiré morphologies, ranging from regular hexagons to heavily deformed ones. We show that a dedicated interplay between the extrinsic nonuniform heterostrain and the intrinsic atomic reconstruction is responsible for this interesting moiré structure evolution. Importantly, the interplay between these two factors also introduces a local inhomogeneous intralayer strain within a moiré. Contrary to the commonly reported electronic modulation that occurred at the valence band edge due to interlayer hybridization, we find that this local intralayer strain induces a strong modulation at K point of the conduction band, reaching up to 300 meV in the heavily deformed moiré. Our microscopic explorations provide valuable information in understanding the intriguing physics in TMD moirés.

Quantum Spin Hall Edge States and Interlayer Coupling in Twisted Bilayer WTe2

The quantum spin Hall (QSH) effect, characterized by topologically protected spin-polarized edge states, was recently demonstrated in monolayers of the transition metal dichalcogenide (TMD) WTe₂. However, the robustness of this topological protection remains largely unexplored in van der Waals heterostructures containing one or more layers of a QSH insulator. In this work, we use scanning tunneling microscopy and spectroscopy (STM/STS) to explore the topological nature of twisted bilayer (tBL) WTe₂. At the tBL edges, we observe the characteristic spectroscopic signatures of the QSH edge states. For small twist angles, a rectangular moiré pattern develops, which results in local modifications of the band structure. Using first-principles calculations, we quantify the interactions in tBL WTe₂ and its topological edge states as a function of interlayer distance and conclude that it is possible to engineer the topology of WTe₂ bilayers via the twist angle as well as interlayer interactions.

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.

Excitons in semiconductor moiré superlattices

Semiconductor moiré superlattices represent a rapidly developing area of engineered photonic materials and a new platform to explore correlated electron states and quantum simulation. In this Review, we briefly introduce early experiments that identified new exciton resonances in transition metal dichalcogenide heterobilayers and discuss several topics including two types of transition metal dichalcogenide moiré superlattice, new optical selection rules, early evidence of moiré excitons, and how the resonant energy, dynamics and diffusion properties of moiré excitons can be controlled via the twist angle. To interpret optical spectra, it is important to measure the energy modulation within a moiré supercell. In this context, we describe a few scanning tunnelling microscopy experiments that measure the moiré potential landscape directly. Finally, we review a few recent experiments that applied excitonic optical spectroscopy to probe correlated electron phenomena in transition metal dichalcogenide moiré superlattices.

Visualizing Band Profiles of Gate-Tunable Junctions in MoS2/WSe2 Heterostructure Transistors

Heterostructure devices based on two-dimensional materials have been under intensive study due to their intriguing electrical and optical properties. One key factor in understanding these devices is their nanometer-scale band profiles, which is challenging to obtain in devices. Here, we use a technique named contact-mode scanning tunneling spectroscopy to directly visualize the band profiles of MoS₂/WSe₂ heterostructure devices at different gate voltages with nanometer resolution. The long-held view of a conventional p-n junction in the MoS₂/WSe₂ heterostructure is reexamined. Due to strong inter- and intralayer charge transfer, the MoS₂ layer in contact with WSe₂ is found to convert from n-type to p-type, and a series of gate-tunable p-n and p-p⁺ junctions are developed in the devices. Highly conductive edges are also discovered which could strongly affect the device properties.

Effect of the strain on spin-valley transport properties in MoS2 superlattice

The effect of the strain on the spin and valley dependent transport properties, including the conductance and polarization, through a monolayer MoS2 superlattice under Rashba spin-orbit coupling is theoretically investigated. It is found that the conductance strongly depends on the spin and valley degrees of freedom, and spin-inversion can be achieved by MoS2 superlattice. Also, the spin and valley dependent conductance in a monolayer MoS2 superlattice can be efficiently adjusted via strain and the number of the superlattice barriers. Moreover, it is demonstrated that both the magnitude and sign of the spin and valley polarization depend on the strain strength, the number of barriers, and electrostatic barrier height. Both full spin and valley polarized current (with 100% or - 100% efficiency) can be realized in a MoS2 superlattice under strain.

Recent Advances on Transition Metal Dichalcogenides for Electrochemical Energy Conversion

Transition metal dichalcogenides (TMDCs) hold great promise for electrochemical energy conversion technologies in view of their unique structural features associated with the layered structure and ultrathin thickness. Because the inert basal plane accounts for the majority of a TMDC's bulk, activation of the basal plane sites is necessary to fully exploit the intrinsic potential of TMDCs. Here, recent advances on TMDCs-based hybrids/composites with greatly enhanced electrochemical activity are reviewed. After a summary of the synthesis of TMDCs with different sizes and morphologies, comprehensive in-plane activation strategies are described in detail, mainly including in-plane-modification-induced phase transformation, surface-layer modulation, and interlayer modification/coupling. Simultaneously, the underlying mechanisms for improved electrochemical activities are highlighted. Finally, the strategic evaluation on further research directions of TMDCs in-plane activation is featured. This work would shed some light on future design trends of TMDCs-based functional materials for electrochemical energy-related applications.

Imaging moiré flat bands in three-dimensional reconstructed WSe2/WS2 superlattices

Moiré superlattices in transition metal dichalcogenide (TMD) heterostructures can host novel correlated quantum phenomena due to the interplay of narrow moiré flat bands and strong, long-range Coulomb interactions^1-9. However, microscopic knowledge of the atomically reconstructed moiré superlattice and resulting flat bands is still lacking, which is critical for fundamental understanding and control of the correlated moiré phenomena. Here we quantitatively study the moiré flat bands in three-dimensional (3D) reconstructed WSe₂/WS₂ moiré superlattices by comparing scanning tunnelling spectroscopy (STS) of high-quality exfoliated TMD heterostructure devices with ab initio simulations of TMD moiré superlattices. A strong 3D buckling reconstruction accompanied by large in-plane strain redistribution is identified in our WSe₂/WS₂ moiré heterostructures. STS imaging demonstrates that this results in a remarkably narrow and highly localized K-point moiré flat band at the valence band edge of the heterostructure. A series of moiré flat bands are observed at different energies that exhibit varying degrees of localization. Our observations contradict previous simplified theoretical models but agree quantitatively with ab initio simulations that fully capture the 3D structural reconstruction. Our results reveal that the strain redistribution and 3D buckling in TMD heterostructures dominate the effective moiré potential and the corresponding moiré flat bands at the Brillouin zone K points.

Highly Strain-Tunable Interlayer Excitons in MoS2/WSe2 Heterobilayers

Interlayer excitons in heterobilayers of transition-metal dichalcogenides (TMDCs) have generated enormous interest due to their permanent vertical dipole moments and long lifetimes. However, the effects of mechanical strain on the optoelectronic properties of interlayer excitons in heterobilayers remain relatively uncharacterized. Here, we experimentally demonstrate strain tuning of Γ-K interlayer excitons in molybdenum disulfide and tungsten diselenide (MoS₂/WSe₂) wrinkled heterobilayers and obtain a deformation potential constant of ∼107 meV/% uniaxial strain, which is approximately twice that of the intralayer excitons in the constituent monolayers. We further observe a nonmonotonic dependence of the interlayer exciton photoluminescence intensity with strain, which we interpret as being due to the sensitivity of the Γ point to band hybridization arising from the competition between in-plane strain and out-of-plane interlayer coupling. Strain engineering with interlayer excitons in TMDC heterobilayers offers higher strain tunability and new degrees of freedom compared to their monolayer counterparts.

van der Waals Epitaxy of Soft Twisted Bilayers: Lattice Relaxation and Mass Density Waves

Interfaces comprising incommensurate or twisted hexagonal lattices are ubiquitous and of great interest, from adsorbed organic/inorganic interfaces in electronic devices, to superlubricants, and more recently to van der Waals bilayer heterostructures (vdWHs) of graphene and other 2D materials that demonstrate a range of properties such as superconductivity and ferromagnetism. Here we show how growth of 2D crystalline domains of soft block copolymers (BCPs) on patterned hard hexagonal lattices provide fundamental insights into van der Waals heteroepitaxy. At moderate registration forces, it is experimentally found that these BCP-hard lattice vdWHs do not adopt a simple moiré superstructure, but instead adopt local structural relaxations known as mass density waves (MDWs). Simulations reveal that MDWs are a primary mechanism of energy minimization and are the origin of the observed preferential twist angle between the lattices.