Interlayer couplings, Moiré patterns, and 2D electronic superlattices in MoS2/WSe2 hetero-bilayers

Nonlinear photovoltaic effects in monolayer semiconductor and layered magnetic material hetero-interface with P- and T-symmetry broken system

Stacking two non-polar materials with different inversion- and rotational-symmetries shows unique nonlinear photovoltaic properties, with potential applications such as in next generation solar-cells. These nonlinear photocurrent properties could be further extended with broken time reversal symmetry present in magnetic materials, however, the combination of time reversal and rotation symmetry breaking has not been fully explored. Herein, we investigate the nonlinear photovoltaic responses in van der Waals heterostructure compromising of monolayer semiconductor and layered magnetic material, MoS2/CrPS4; a system with broken P- and T-symmetry. We clearly observe the finite spontaneous photocurrent as shift current at the interface of the MoS2/CrPS4 heterostructure. Moreover, we demonstrate that the spontaneous photocurrent drastically changes according to the magnetic phases of CrPS4. The magnetic phase dependent spontaneous nonlinear photocurrent provides a platform for studying nonlinear photoresponses in systems with broken P- and T-symmetry, and the potential development of magnetic controllable photovoltaic devices.

Enhanced coherence from correlated states in WSe2/MoS2 moiré heterobilayer

Moiré superlattices in van der Waals materials have emerged as a promising platform for studying the correlated states in condensed matter physics. These correlated states have substantial effects on the emission coherence, an important parameter for quantum light applications. However, the effect of correlated states on the excitonic emission coherence is largely unexplored. Here, we show that the coherence of moiré interlayer exciton emission in tungsten diselenide (WSe2)/molybdenum disulfide (MoS2) heterobilayers is sensitive to the correlated insulating states in this material. We demonstrate that the emission linewidth of interlayer exciton shows a dip at a particular power range, which we attributed to the excitonic (bosonic) interaction. Moreover, such linewidth minima also appear in the doping dependence of the photoluminescence spectrum at the integer electronic filling factor, fel = 1, demonstrating the effect of the electronic (fermionic) correlated insulating state on the interlayer exciton emission coherence. Our results demonstrate the richness of exciton-exciton and exciton-electron interactions in moiré semiconductors and pave the way for engineering emission coherence by controlling such interactions.

Deep Moiré Potential and Absence of Layer Polarization in Twisted Trilayer WS2

Twisted transition metal dichalcogenides (TMDs) hetero/homobilayers have been extensively reported to exhibit strongly correlated states and interfacial ferroelectricity. It is reasonable to anticipate that the twist angle could also significantly influence the electronic properties of multilayer TMDs. However, the quantitative study of moiré potential and the exploration of interlayer charge transfer in twisted multilayer TMDs have not been carried out. Here, using scanning tunneling microscopy and spectroscopy, we study the structure and in situ electronic properties of a twisted trilayer WS2 (TT-WS2) with twist angles of 3.35° and 0.35°. A "double-moiré" superlattice structure is detected, consisting of a completely reconstructed moiré into triangular domains and an unreconstructed one. Through comparing with the electronic properties of twisted bilayer WS2, we observe a significantly enhanced moiré potential up to 200 meV and the absence of layer polarization in the TT-WS2. Our results pave the way for further research and application of twisted multilayer TMDs.

Time resolution of terahertz scanning tunneling microscopy measurements inside a superconducting magnet using a hollow waveguide

A terahertz scanning tunneling microscope (THz-STM) is an STM that allows us to perform time-resolved measurements of tunneling currents with high temporal resolution, in addition to the high spatial resolution of STMs. In such a device, it is necessary to guide the THz beam to the STM tip, which can be difficult if there are tight space restrictions due to experimental requirements, such as ultra-high vacuum and high magnetic fields. We aim to develop a THz-STM that allows us to measure tunneling currents in high magnetic fields at cryogenic temperatures with a time resolution on the order of picoseconds. In this paper, we placed a specially designed chamber containing a homemade STM head inside a superconducting magnet and performed time-resolved measurements of the tunneling current between the Pt-Ir tip and a highly oriented pyrolytic graphite (HOPG) sample. To introduce the THz pulse into the STM chamber, we used a narrow pipe as a waveguide and evaluated a time resolution of better than 1 ps, which suggests that the realization of a THz-STM for multi-extreme conditions with picosecond time resolution is possible.

Minimizing Sensor-Sample Distances in Scanning Nitrogen-Vacancy Magnetometry

Scanning magnetometry with nitrogen-vacancy (NV) centers in diamond has led to significant advances in the sensitive imaging of magnetic systems. The spatial resolution of the technique, however, remains limited to tens to hundreds of nanometers, even for probes where NV centers are engineered within 10 nm from the tip apex. Here, we present a correlated investigation of the crucial parameters that determine the spatial resolution: the mechanical and magnetic stand-off distances, as well as the subsurface NV center depth in diamond. We study their contributions using mechanical approach curves, photoluminescence measurements, magnetometry scans, and nuclear magnetic resonance (NMR) spectroscopy of surface adsorbates. We first show that the stand-off distance is mainly limited by features on the surface of the diamond tip, hindering mechanical access. Next, we demonstrate that frequency-modulated (FM) atomic force microscopy feedback partially overcomes this issue, leading to closer and more consistent magnetic stand-off distances (26-87 nm) compared with the more common amplitude-modulated feedback (43-128 nm). FM operation thus permits improved magnetic imaging of sub-100-nm spin textures, shown for the spin cycloid in BiFeO3 and domain walls in a CoFeB synthetic antiferromagnet. Finally, by examining 1H and 19F NMR signals in soft contact with a polytetrafluoroethylene surface, we demonstrate a minimum NV-to-sample distance of 7.9 ± 0.4 nm.

Understanding Twist-Angle-Dependent Carrier Lifetimes in MoSSe Bilayer

Two-dimensional (2D) materials with tunable interlayer interactions hold immense potential for optoelectronic and photocatalytic applications. Understanding the dependence of carrier dynamics on twist angle in Janus bilayers is essential, as it directly impacts device efficiency. This study employs time-dependent density functional theory (TD-DFT) and nonadiabatic molecular dynamics (NAMD) to investigate twist-angle-dependent carrier dynamics in Janus MoSSe bilayers with type-II band alignment. Simulations reveal ultrafast charge transfer times of approximately 70 and 500 fs, largely independent of the twist angle due to multiple intermediate states. In contrast, the electron-hole recombination times depend strongly on twist angles, extending up to 133 ns for twisted configurations (21.8° and 38.2°) compared to 57 ns in high-symmetry bilayers (0.0° and 60.0°). Structural randomness in twisted bilayers weakens interlayer interactions, reducing nonadiabatic coupling and coherence time, which collectively prolong carrier lifetimes. These findings offer valuable guidance for designing 2D materials for high-efficiency photovoltaics and long-durable photocatalysts.

Data-Driven Discovery of High-Performance Heterobilayer Transition Metal Dichalcogenide-Based Sliding Ferroelectrics

The development of efficient sliding ferroelectric (FE) materials is crucial for advancing next-generation low-power nanodevices. Currently, most efforts focus on homobilayer two-dimensional materials, except for the experimentally reported heterobilayer sliding FE, MoS2/WS2. Here, we first screened 870 transition metal dichalcogenide (TMD) bilayer heterostructures derived from experimentally characterized monolayer TMDs and systematically investigated their sliding ferroelectric behavior across various stacking configurations using high-throughput calculations. On the basis of the generated data, we developed an efficient descriptor, named the amplitude of Allen electronegativity difference (Δχm), for identifying van der Waals heterobilayers with sliding FE properties. Finally, 16 semiconducting TMD heterobilayers are identified as exhibiting interlayer sliding FE alongside low switching barriers (<21 meV/f.u.), with 10 outperforming the experimental MoS2/WS2 system, showing the largest out-of-plane polarization (OPP) values up to 10 times higher than MoS2/WS2. These materials exhibit favorable band gaps (0.60-1.80 eV) using the HSE06 method, making them suitable for sliding FE applications. Our findings reveal that polarization switching in these heterobilayers is strongly influenced by the interplay of stacking patterns, material electronegativity, charge transfer, and electronic structures. This study provides a robust framework for designing novel sliding ferroelectric materials and offers a theoretical basis for future experimental research.

Circular Dichroism and Interlayer Exciton Hall Effect in Transition Metal Dichalcogenides Homobilayers

In van der Waals (vdW) architectures of transition metal dichalcogenides (TMDCs), the coupling between interlayer exciton and quantum degrees of freedom opens unprecedented opportunities for excitonic physics. Taking the MoSe2 homobilayer as representative, we identify that the interlayer registry defines the nature and dynamics of the lowest-energy interlayer exciton. The large layer polarization (Pn) is proved, which ensures the formation of layer-resolved interlayer excitons. In particular, sliding ferroelectric polarization couples to the dipole orientation of the interlayer exciton, thus achieving the long-sought electric control of excitonic states. In line with the phase winding of the Bloch states under C3 rotational symmetry, we clarify the valley optical circular dichroism, enriching the exciton valleytronics. We also elucidate the Hall effect of the layer- and valley-polarized interlayer excitons, which advances our understanding of the spatial transport properties of the composite particles and provides new insights into the exciton-based applications.

Spontaneous curvature in two-dimensional van der Waals heterostructures

Two-dimensional (2D) van der Waals heterostructures consist of different 2D crystals with diverse properties, constituting the cornerstone of the new generation of 2D electronic devices. Yet interfaces in heterostructures inevitably break bulk symmetry and structural continuity, resulting in delicate atomic rearrangements and novel electronic structures. In this paper, we predict that 2D interfaces undergo "spontaneous curvature", which means when two flat 2D layers approach each other, they inevitably experience out-of-plane curvature. Based on deep-learning-assisted large-scale molecular dynamics simulations, we observe significant out-of-plane displacements up to 3.8 Å in graphene/BN bilayers induced by curvature, producing a stable hexagonal moiré pattern, which agrees well with experimentally observations. Additionally, the out-of-plane flexibility of 2D crystals enables the propagation of curvature throughout the system, thereby influencing the mechanical properties of the heterostructure. These findings offer fundamental insights into the atomic structure in 2D van der Waals heterostructures and pave the way for their applications in devices.

Continuous Strain Modulation of Moiré Superlattice Symmetry From Triangle to Rectangle

Moiré superlattices formed in van der Waals (vdW) bilayers of 2D materials provide an ideal platform for studying previously undescribed physics, including correlated electronic states and moiré excitons, owing to the wide-range tunability of their lattice constants. However, their crystal symmetry is fixed by the monolayer structure, and the lack of a straightforward technique for modulating the symmetry of moiré superlattices has impeded progress in this field. Herein, a simple, room-temperature, ambient method for controlling superlattice symmetry is reported. The method uses vdW heterostructures on a flexible substrate; by bending the substrate, a uniaxial strain is introduced. Based on numerical calculations, a strain condition is designed to deform the moiré superlattice from triangular to rectangular, and visualized the continuous deformation of real-space moiré superlattices using piezoresponse force microscopy. The band calculations show that nearly flat moiré minibands remain in the rectangular lattice; therefore, this method provides an additional tuning knob for the Hamiltonian of moiré quantum matter.

Momentum-Direct Infrared Interlayer Exciton and Photodetection in Multilayer van der Waals Heterostructures

Interlayer excitons (IX), spatially separated electron-hole pair quasiparticles, can form in type-II van der Waals heterostructures (vdWH). To date, the most widely studied IX in hetero- and homobilayer transition metal dichalcogenides feature momentum-indirect and visible interlayer recombinations. However, momentum-direct IX emissions and interlayer absorptions, especially in the infrared, are crucial for excitonic devices but remain underexplored. In this work, we propose and construct a multilayer WSe2/InSe vdWH that hosts momentum-direct IX and manifests near-infrared interlayer absorptions at room temperature, verified by first-principles density functional theory calculations. We conduct power- and temperature-dependent photoluminescence spectroscopies and extract the IX binding energy to be 43 ± 5 meV. Furthermore, we manipulate the IX emission electrically via the Stark effect and tune its energy by 180 meV. Taking advantage of the direct interlayer absorption, we fabricate a near-infrared vdWH photodetector modulated by strong photogating effect, and achieve the optimal photoresponsivity, specific detectivity, and response time of 33 A W-1, 1.8 × 1010 Jones, and 3.7 μs at 1150 nm. In addition, we test the imaging capability of the photodetector by integrating it into a single-pixel imaging system. Our work showcases the possibility for constructing infrared-responsive vdWH that hosts momentum-direct IX for future excitonic devices of optoelectronic applications.

A Deterministic Method to Construct a Common Supercell Between Two Similar Crystalline Surfaces

Here, a deterministic algorithm is proposed, that is capable of constructing a common supercell between two similar crystalline surfaces without scanning all possible cases. Using the complex plane, the 2D lattice is defined as the 2D complex vector. Then, the relationship between two surfaces becomes the eigenvector-eigenvalue relation where an operator corresponds to a transformation matrix. It is shown that this transformation matrix can be directly determined from the lattice parameters and rotation angle of the two given crystalline surfaces with O(log Nmax) time complexity, where Nmax is the maximum index of repetition matrix elements. This process is much faster than the conventional brute force approach (O ( N max 4 ) $O(N_{\mathrm{max}}^4)$ ). By implementing the method in Python code, experimental 2D heterostructures and their moiré patterns and additionally find new moiré patterns that have not yet been reported are successfully generated. According to the density functional theory (DFT) calculations, some of the new moiré patterns are expected to be as stable as experimentally-observed moiré patterns. Taken together, it is believed that the method can be widely applied as a useful tool for designing new heterostructures with interesting properties.

Energy spectrum theory of incommensurate systems

Because of the lack of translational symmetry, calculating the energy spectrum of an incommensurate system has always been a theoretical challenge. Here, we propose a natural approach to generalize energy band theory to incommensurate systems without reliance on the commensurate approximation, thus providing a comprehensive energy spectrum theory of incommensurate systems. Except for a truncation-dependent weighting factor, the formulae of this theory are formally almost identical to that of Bloch electrons, making it particularly suitable for complex incommensurate structures. To illustrate the application of this theory, we give three typical examples: one-dimensional bichromatic and trichromatic incommensurate potential models, as well as a moiré quasicrystal. Our theory establishes a fundamental framework for understanding incommensurate systems.

Polarization and Charge-Separation of Moiré Excitons in van der Waals Heterostructures

Twisted transition metal dichalcogenide (TMD) bilayers exhibit periodic moiré potentials, which can trap excitons at certain high-symmetry sites. At small twist angles, TMD lattices undergo an atomic reconstruction, altering the moiré potential landscape via the formation of large domains, potentially separating the charges in-plane and leading to the formation of intralayer charge-transfer (CT) excitons. Here, we employ a microscopic, material-specific theory to investigate the intralayer charge-separation in atomically reconstructed MoSe2-WSe2 heterostructures. We identify three distinct and twist-angle-dependent exciton regimes including localized Wannier-like excitons, polarized excitons, and intralayer CT excitons. We calculate the moiré site hopping for these excitons and predict a fundamentally different twist-angle-dependence compared to regular Wannier excitons - presenting an experimentally accessible key signature for the emergence of intralayer CT excitons. Furthermore, we show that the charge separation and its impact on the hopping can be efficiently tuned via dielectric engineering.

Long-distance decay-less spin transport in indirect excitons in a van der Waals heterostructure

In addition to its fundamental interest, the long-distance spin transport is essential for spintronic devices. However, the spin relaxation caused by scattering of the particles carrying the spin limits spin transport. We explored spatially indirect excitons (IXs) in van der Waals heterostructures composed of atomically thin layers of transition-metal dichalcogenides as spin carries. We observed the long-distance spin transport: the spin polarized excitons travel over the entire sample,  ~10 micron away from the excitation spot, with no spin density decay. This transport is characterized by the 1/e decay distances reaching  ~100 micron. The 1/e decay distances are extracted from fits over the  ~10 micron sample size. The emergence of long-distance spin transport is observed at the densities and temperatures where the IX transport decay distances and, in turn, scattering times are strongly enhanced. The suppression of IX scattering suppresses the spin relaxation and enables the long-distance spin transport.

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.

Towards the scalable synthesis of two-dimensional heterostructures and superlattices beyond exfoliation and restacking

Two-dimensional transition metal dichalcogenides, which feature atomically thin geometry and dangling-bond-free surfaces, have attracted intense interest for diverse technology applications, including ultra-miniaturized transistors towards the subnanometre scale. A straightforward exfoliation-and-restacking approach has been widely used for nearly arbitrary assembly of diverse two-dimensional (2D) heterostructures, superlattices and moiré superlattices, providing a versatile materials platform for fundamental investigations of exotic physical phenomena and proof-of-concept device demonstrations. While this approach has contributed importantly to the recent flourishing of 2D materials research, it is clearly unsuitable for practical technologies. Capturing the full potential of 2D transition metal dichalcogenides requires robust and scalable synthesis of these atomically thin materials and their heterostructures with designable spatial modulation of chemical compositions and electronic structures. The extreme aspect ratio, lack of intrinsic substrate and highly delicate nature of the atomically thin crystals present fundamental difficulties in material synthesis. Here we summarize the key challenges, highlight current advances and outline opportunities in the scalable synthesis of transition metal dichalcogenide-based heterostructures, superlattices and moiré superlattices.

Advanced Characterization of the Spatial Variation of Moiré Heterostructures and Moiré Excitons

In this short review, an overview of recent progress in deploying advanced characterization techniques is provided to understand the effects of spatial variation and inhomogeneities in moiré heterostructures over multiple length scales. Particular emphasis is placed on correlating the impact of twist angle misalignment, nano-scale disorder, and atomic relaxation on the moiré potential and its collective excitations, particularly moiré excitons. Finally, future technological applications leveraging moiré excitons are discussed.

Twist Angle-Dependent Phonon Hybridization in WSe2/WSe2 Homobilayer

The emerging moiré superstructure of twisted transition metal dichalcogenides (TMDs) leads to various correlated electronic and optical properties compared to those of twisted bilayer graphene. In such a versatile architecture, phonons can also be renormalized and evolve due to atomic reconstruction, which, in turn, depends on the twist angle. However, observing this reconstruction and its relationship to phonon behavior with conventional, cost-effective imaging methods remains challenging. Here, we used noninvasive Raman spectroscopy on twisted WSe2/WSe2 (t-WSe2) homobilayers to examine the evolution of phonon modes due to interlayer coupling and atomic reconstruction. Unlike in the natural bilayer (NB), ∼0° as well as ∼60° t-WSe2 samples, the nearly degenerate A1g/E2g mode in the twisted samples (1-7°) split into a doublet in addition to the nondegenerate B2g mode, and the maximum splitting is observed around 2-3°. Our detailed theoretical calculations qualitatively capture the splitting and its dependence as a function of the twist angle and highlight the role of the moiré potential in phonon hybridization. Additionally, we found that around the 2° twist angle, the anharmonic phonon-phonon interaction is higher than the natural bilayer and decreases for larger twist angles. Interestingly, we observed anomalous Raman frequency softening and line-width increase with the decreasing temperature below 50 K, pointing to the combined effect of enhanced electron-phonon coupling and cubic anharmonic interactions in moiré superlattice.

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

Abstract

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

Graphical abstract

Twisted MoSe2 Homobilayer Behaving as a Heterobilayer

Heterostructures (HSs) formed by the transition-metal dichalcogenide materials have shown great promise in next-generation (opto)electronic applications. An artificially twisted HS allows us to manipulate the optical and electronic properties. In this work, we introduce the understanding of the energy transfer (ET) process governed by the dipolar interaction in a twisted molybdenum diselenide (MoSe2) homobilayer without any charge-blocking interlayer. We fabricated an unconventional homobilayer (i.e., HS) with a large twist angle (∼57°) by combining the chemical vapor deposition (CVD) and mechanical exfoliation (Exf.) techniques to fully exploit the lattice parameter mismatch and indirect/direct (CVD/Exf.) bandgap nature. These effectively weaken the interlayer charge transfer and allow the ET to control the carrier recombination channels. Our experimental and theoretical results explain a massive HS photoluminescence enhancement due to an efficient ET process. This work shows that the electronically decoupled MoSe2 homobilayer is coupled by the ET process, mimicking a "true" heterobilayer nature.

Crossover between rigid and reconstructed moiré lattice in h-BN-encapsulated twisted bilayer WSe2 with different twist angles

A moiré lattice in a twisted-bilayer transition metal dichalcogenide (tBL-TMD) exhibits a complex atomic reconstruction effect when its twist angle is less than a few degrees. The influence of the atomic reconstruction on material properties of the tBL-TMD has been of particular interest. In this study, we performed scanning transmission electron microscopy (STEM) imaging of a moiré lattice in h-BN-encapsulated twisted bilayer WSe2 with various twist angles. Atomic-resolution imaging of the moiré lattice revealed a reconstructed moiré lattice below a crossover twist angle of ∼4° and a rigid moiré lattice above this angle. Our findings indicate that h-BN encapsulation has a considerable influence on lattice reconstruction, as the crossover twist angle was larger in h-BN-encapsulated devices compared to non-encapsulated devices. We believe that this difference is due to the improved flatness and uniformity of the twisted bilayers with h-BN encapsulation. Our results provide a foundation for a deeper understanding of the lattice reconstruction in twisted TMD materials with h-BN encapsulation.

DFT-Assisted Investigation of the Electric Field and Charge Density Distribution of Pristine and Defective 2D WSe2 by Differential Phase Contrast Imaging

Most properties of solid materials are defined by their internal electric field and charge density distributions which so far are difficult to measure with high spatial resolution. Especially for 2D materials, the atomic electric fields influence the optoelectronic properties. In this study, the atomic-scale electric field and charge density distribution of WSe2 bi- and trilayers are revealed using an emerging microscopy technique, differential phase contrast (DPC) imaging in scanning transmission electron microscopy (STEM). For pristine material, a higher positive charge density located at the selenium atomic columns compared to the tungsten atomic columns is obtained and tentatively explained by a coherent scattering effect. Furthermore, the change in the electric field distribution induced by a missing selenium atomic column is investigated. A characteristic electric field distribution in the vicinity of the defect with locally reduced magnitudes compared to the pristine lattice is observed. This effect is accompanied by a considerable inward relaxation of the surrounding lattice, which according to first principles DFT calculation is fully compatible with a missing column of Se atoms. This shows that DPC imaging, as an electric field sensitive technique, provides additional and remarkable information to the otherwise only structural analysis obtained with conventional STEM imaging.

Exploring Anisotropic Carrier Transport in WSe2-WTe2 Superlattices: A Computational Study

Superlattice structures offer distinct benefits in modern semiconductor technology, enabling the development of a deeper understanding of their sublayer arising from the interfaces. However, the advancement of large-scale applications encounters additional concerns, such as the stability and performance of the superlattice. In this study, we employ density functional theory calculations combined with the Boltzmann transport theory to comprehensively analyze the electronic structural and transport properties of the hexagonal phase of WSe2 and the WSe2-WTe2 superlattice for their applications in carrier transport fields. Previous studies showed that longitudinal acoustics phonon limited carrier mobility determined by deformation potential theory (DPT) often compromises the accuracy and overestimates the relaxation time by 2 orders. Herein, we conduct an in-depth analysis of band structural and transport properties, addressing the aforementioned inconsistency by exclusively incorporating scattering from longitudinal optical phonons to accurately compute mobility using the Fröhlich interaction. Our findings reveal a significant enhancement in mobility for both electrons and holes in the WSe2-WTe2 superlattice, reaching 545 and 476 cm2 V-1 s-1, respectively, compared to 104 and 132 cm2 V-1 s-1 for WSe2, which suggests that this superlattice is a promising material for electronics and transport applications.

Topological Network Modes in a Twisted Moiré Phononic Crystal

Twisted moiré materials, a new class of layered structures with different twist angles for neighboring layers, are attracting great attention because of the rich intriguing physical phenomena associated with them. Of particular interest are the topological network modes, first proposed in the small angle twisted bilayer graphene under interlayer bias. Here we report the observations of such topological network modes in twisted moiré phononic crystals without requiring the external bias fields. Acoustic topological network modes that can be constructed in a wide range of twist angles are both observed in the domain walls with and without reconstructions, which serve as the analogy of the lattice relaxations in electronic moiré materials. Topological robustness of the topological network modes is observed by introducing valley-preserved defects to the network channel. Furthermore, the network can be reconfigured into two-dimensional patterns with any desired connectivity, offering a unique prototype platform for acoustic applications.

Conduction Band Replicas in a 2D Moiré Semiconductor Heterobilayer

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

Microscopy aided detection of the self-intercalation mechanism and in situ electronic properties in chromium selenide

Two-dimensional (2D) chromium-based self-intercalated materials Cr1+nX2 (0 ≤ n ≤ 1, X = S, Se, Te) have attracted much attention because of their tunable magnetism with good environmental stability. Intriguingly, the magnetic and electrical properties of the materials can be effectively tuned by altering the coverage and spatial arrangement of the intercalated Cr (ic-Cr) within the van der Waals gap, contributing to different stoichiometries. Several different Cr1+nX2 systems have been widely investigated recently; however, those with the same stoichiometric ratio (such as Cr1.25Te2) were reported to exhibit disparate magnetic properties, which still lacks explanation. Therefore, a systematic in situ study of the mechanisms with microscopy techniques is in high demand to look into the origin of these discrepancies. Herein, 2D self-intercalated Cr1+nSe2 nanoflakes were synthesized as a platform to conduct the characterization. Combining scanning transmission electron microscopy (STEM) and scanning tunneling microscopy (STM), we studied in depth the microscopic structure and local electronic properties of the Cr1+nSe2 nanoflakes. The self-intercalation mechanism of ic-Cr and local stoichiometric-ratio variation in a Cr1+nSe2 ultrathin nanoflake is clearly detected at the nanometer scale. Scanning tunneling spectroscopy (STS) measurements indicate that Cr1.5Se2/Cr2Se2 and Cr1.25Se2 exhibit conductive and semiconductive behaviors, respectively. The STM tip manipulation method is further applied to manipulate the microstructure of Cr1+nSe2, which successfully produces clean zigzag-type boundaries. Our systematic microscopy study paves the way for the in-depth study of the magnetic mechanism of 2D self-intercalated magnets at the nano/micro scale and the development of new magnetic and spintronic devices.

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.

Twisted van der Waals Quantum Materials: Fundamentals, Tunability, and Applications

Twisted van der Waals (vdW) quantum materials have emerged as a rapidly developing field of two-dimensional (2D) semiconductors. These materials establish a new central research area and provide a promising platform for studying quantum phenomena and investigating the engineering of novel optoelectronic properties such as single photon emission, nonlinear optical response, magnon physics, and topological superconductivity. These captivating electronic and optical properties result from, and can be tailored by, the interlayer coupling using moiré patterns formed by vertically stacking atomic layers with controlled angle misorientation or lattice mismatch. Their outstanding properties and the high degree of tunability position them as compelling building blocks for both compact quantum-enabled devices and classical optoelectronics. This paper offers a comprehensive review of recent advancements in the understanding and manipulation of twisted van der Waals structures and presents a survey of the state-of-the-art research on moiré superlattices, encompassing interdisciplinary interests. It delves into fundamental theories, synthesis and fabrication, and visualization techniques, and the wide range of novel physical phenomena exhibited by these structures, with a focus on their potential for practical device integration in applications ranging from quantum information to biosensors, and including classical optoelectronics such as modulators, light emitting diodes, lasers, and photodetectors. It highlights the unique ability of moiré superlattices to connect multiple disciplines, covering chemistry, electronics, optics, photonics, magnetism, topological and quantum physics. This comprehensive review provides a valuable resource for researchers interested in moiré superlattices, shedding light on their fundamental characteristics and their potential for transformative applications in various fields.

Twisting two-dimensional iron sulfide layers into coincident site superlattices via intercalation chemistry

Layered van der Waals (vdW) materials are susceptible not only to various stacking polymorphs through translations but also twisted structures due to rotations between layers. Here, we study the influence of such layer-to-layer twisting through the intercalation of ethylenediamine (EDA) molecules into tetragonal iron sulfide (Mackinawite FeS). Selected area electron diffraction patterns of intercalated FeS display reflections corresponding to multiple square lattices with a fixed angle between them, contrary to a single square lattice seen in the unintercalated phase. The observed twist angles of 49.13° and 22.98° result from a superstructure formation well described by the coincident site lattice (CSL) theory. According to the CSL theory, these measured twist angles lead to the formation of larger coincident site supercells. We build these CSL models for FeS using crystallographic group-subgroup transformations and find simulated electron diffraction patterns from the model to agree with the experimentally measured data.

Second-harmonic generation in 2D moiré superlattices composed of bilayer transition metal dichalcogenides

Moiré superlattices (MSLs) in twisted two-dimensional van der Waals materials feature twist-angle-dependent crystal symmetry and strong optical nonlinearities. By adjusting the twist angle in bilayer van der Waals materials, the second-harmonic generation (SHG) can be controlled. Here, we focus on exploring the electronic and SHG properties of MSLs in 2D bilayer transition metal dichalcogenides (TMDs) with different twist angles through first-principles calculations. We constructed MSL structures of five TMD materials, including three single-phase materials (MoS2, WS2, and MoSe2) and two heterojunctions (MoS2/MoSe2 and MoS2/WS2) with twist angles of 9.4°, 13.2°, 21.8°, 32.2°, and 42.1° without lattice mismatch. Our findings demonstrate a consistent variation in the SHG susceptibility among different TMD MSLs as a response to twist-angle changes. The underlying reason for the twist-angle dependence of SHG is that the twist angle regulates the interlayer coupling strength, affecting the optical band gap of MSLs and subsequently tuning the SHG susceptibility. Through a comparison of the static SHG susceptibility values, we identified the twist angle of 9.4° as the configuration that yields the highest SHG susceptibility (e.g. 358.5 pm V-1 for the 9.4° MoSe2 MSL). This value is even twice that of the monolayer (173.3 pm V-1 for monolayer MoSe2) and AA'-stacked bilayer structures (139.8 pm V-1 for AA' MoSe2). This high SHG susceptibility is attributed to the strong interlayer coupling in the 9.4° MSL, which enhances the valence band energy (contributed by the antibonding orbitals of chalcogen-pz and transition metal-dz2) and consequently leads to a small optical band gap, thus improving the optical transitions. The findings of this study provide a straightforward way to improve the SHG performance of bilayer TMDs and also throw light on the sensitive relationship between the twist angle, band structure and SHG properties of TMD MSLs.

Localisation-to-delocalisation transition of moiré excitons in WSe2/MoSe2 heterostructures

Moiré excitons (MXs) are electron-hole pairs localised by the periodic (moiré) potential forming in two-dimensional heterostructures (HSs). MXs can be exploited, e.g., for creating nanoscale-ordered quantum emitters and achieving or probing strongly correlated electronic phases at relatively high temperatures. Here, we studied the exciton properties of WSe2/MoSe2 HSs from T = 6 K to room temperature using time-resolved and continuous-wave micro-photoluminescence also under a magnetic field. The exciton dynamics and emission lineshape evolution with temperature show clear signatures that MXs de-trap from the moiré potential and turn into free interlayer excitons (IXs) for temperatures above 100 K. The MX-to-IX transition is also apparent from the exciton magnetic moment reversing its sign when the moiré potential is not capable of localising excitons at elevated temperatures. Concomitantly, the exciton formation and decay times reduce drastically. Thus, our findings establish the conditions for a truly confined nature of the exciton states in a moiré superlattice with increasing temperature and photo-generated carrier density.

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

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

Ab Initio Quantum Dynamics Simulation of the Impact of Graphene on the Carrier Lifetime of the ZnV2O6 Photocatalyst

We used a nonadiabatic molecular dynamics simulation to determine the carrier dynamics of a graphene/ZnV2O6 heterostructure in the search for an effective photocatalyst material. The C-2p orbital promotes the wave function overlap, guiding electrons to move between graphene and ZnV2O6, successfully achieving good mixing with the valence and conduction bands in ZnV2O6 materials, which is conducive to supporting carrier migration. The overlap between graphene/ZnV2O6 electrons and hole wave functions is less than that of ZnV2O6, and there is small absolute nonadiabatic coupling. The charge separation caused by graphene increases the carrier lifetime and prevents nonradiative electron-hole recombination. This study reveals the microscopic mechanism of extending the carrier lifetime of ZnV2O6 by introducing graphene, providing useful insights for regulating the electronic structure, promoting electron transfer and ultrafast electron and hole transfer. This strategy provides design considerations for advanced photocatalytic materials.

Direct Visualization of Dark Interlayer Exciton Transport in Moiré Superlattices

Moiré superlattices have emerged as an unprecedented manipulation tool for engineering correlated quantum phenomena in van der Waals heterostructures. With moiré potentials as a naturally configurable solid-state that sustains high exciton density, interlayer excitons in transition metal dichalcogenide heterostructures are expected to achieve high-temperature exciton condensation. However, the exciton degeneracy state is usually optically inactive due to the finite momentum of interlayer excitons. Experimental observation of dark interlayer excitons in moiré potentials remains challenging. Here we directly visualize the dark interlayer exciton transport in WS2/h-BN/WSe2 heterostructures using femtosecond transient absorption microscopy. We observe a transition from classical free exciton gas to quantum degeneracy by imaging temperature-dependent exciton transport. Below a critical degeneracy temperature, exciton diffusion rates exhibit an accelerating downward trend, which can be explained well by a nonlinear quantum diffusion model. These results open the door to quantum information processing and high-precision metrology in moiré superlattices.

Tuning commensurability in twisted van der Waals bilayers

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

Strongly Localized Moiré Exciton in Twisted Homobilayers

Artificially molding exciton flux is the cornerstone for developing promising excitonic devices. In the emerging hetero/homobilayers, the spatial separated charges prolong exciton lifetimes and create out-plane dipoles, facilitating electrically control exciton flux on a large scale, and the nanoscale periodic moiré potentials arising from twist-angle or/and lattice mismatch can substantially alter exciton dynamics, which are mainly proved in the heterostructures. However, the spatially indirect excitons dynamics in homobilayers without lattice mismatch remain elusive. Here the nonequilibrium dynamics of indirect exciton in homobilayers are systematically investigated. The homobilayers with slightly twist-angle can induce a deep moiré potential (>50 meV) in the energy landscape of indirect excitons, resulting in a strongly localized moiré excitons insulating the transport dynamics from phonons and disorder. These findings provide insights into the exciton dynamics and many-body physics in moiré superlattices modulated energy landscape, with implications for designing excitonic devices operating at room temperature.

Polytypic Two-Dimensional FeAs with High Anisotropy

In the realm of two-dimensional (2D) crystal growth, the chemical composition often determines the thermodynamically favored crystallographic structures. This relationship poses a challenge in synthesizing novel 2D crystals without altering their chemical elements, resulting in the rarity of achieving specific crystallographic symmetries or lattice parameters. We present 2D polymorphic FeAs crystals that completely differ from bulk orthorhombic FeAs (Pnma), differing in the stacking sequence, i.e., polytypes. Preparing polytypic FeAs outlines a strategy for independently controlling each symmetry operator, which includes the mirror plane for 2Q-FeAs (I4/mmm) and the glide plane for 1Q-FeAs (P4/nmm). As such, compared to bulk FeAs, polytypic 2D FeAs shows highly anisotropic properties such as electrical conductivity, Young's modulus, and friction coefficient. This work represents a concept of expanding 2D crystal libraries with a given chemical composition but various crystal symmetries.

Anisotropic Interlayer Force Field for Group-VI Transition Metal Dichalcogenides

An anisotropic interlayer force field that describes the interlayer interactions in homogeneous and heterogeneous interfaces of group-VI transition metal dichalcogenides (MX2, where M = Mo, W, and X = S, Se) is presented. The force field is benchmarked against density functional theory calculations for bilayer systems within the Heyd-Scuseria-Ernzerhof hybrid density functional approximation, augmented by a nonlocal many-body dispersion treatment of long-range correlation. The parametrization yields good agreement with the reference calculations of binding energy curves and sliding potential energy surfaces. It is found to be transferable to transition metal dichalcogenide (TMD) junctions outside of the training set that contain the same atom types. Calculated bulk moduli agree with most previous dispersion-corrected density functional theory predictions, which underestimate the available experimental values. Calculated phonon spectra of the various junctions under consideration demonstrate the importance of appropriately treating the anisotropic nature of the layered interfaces. Considering our previous parametrization for MoS2, the anisotropic interlayer potential enables accurate and efficient large-scale simulations of the dynamical, tribological, and thermal transport properties of a large set of homogeneous and heterogeneous TMD interfaces.

Moiré Superlattice Structure of Pleated Trilayer Graphene Imaged by 4D Scanning Transmission Electron Microscopy

Moiré superlattices in graphene arise from rotational twists in stacked 2D layers, leading to specific band structures, charge density and interlayer electron and excitonic interactions. The periodicities in bilayer graphene moiré lattices are given by a simple moiré basis vector that describes periodic oscillations in atomic density. The addition of a third layer to form trilayer graphene generates a moiré lattice comprised of multiple harmonics that do not occur in bilayer systems, leading to nontrivial crystal symmetries. Here, we use atomic resolution 4D-scanning transmission electron microscopy to study atomic structure in bilayer and trilayer graphene moiré superlattices and use 4D-STEM to map the electric fields to show subtle variations in the long-range moiré patterns. We show that monolayer graphene folded into an S-bend graphene pleat produces trilayer moiré superlattices with both small (<2°) and larger twist angles (7-30°). Annular in-plane electric field concentrations are detected in high angle bilayers due to overlapping rotated graphene hexagons in each layer. The presence of a third low angle twisted layer in S-bend trilayer graphene, introduces a long-range modulation of the atomic structure so that no real space unit cell is detected. By directly imaging trilayer moiré harmonics that span from picoscale to nanoscale using 4D-STEM, we gain insights into the complex spatial distributions of atomic density and electric fields in trilayer twisted layered materials.

Nonlinear Optical Responses of Janus MoSSe/MoS2 Heterobilayers Optimized by Stacking Order and Strain

Nonlinear optical responses in second harmonic generation (SHG) of van der Waals heterobilayers, Janus MoSSe/MoS2, are theoretically optimized as a function of strain and stacking order by adopting an exchange-correlation hybrid functional and a real-time approach in first-principles calculation. We find that the calculated nonlinear susceptibility, χ(2), in AA stacking (550 pm/V) becomes three times as large as AB stacking (170 pm/V) due to the broken inversion symmetry in the AA stacking. The present theoretical prediction is compared with the observed SHG spectra of Janus MoSSe/MoS2 heterobilayers, in which the peak SHG intensity of AA stacking becomes four times as large as AB stacking. Furthermore, a relatively large, two-dimensional strain (4%) that breaks the C3v point group symmetry of the MoSSe/MoS2, enhances calculated χ(2) values for both AA (900 pm/V) and AB (300 pm/V) stackings 1.6 times as large as that without strain.

In Situ Twistronics: A New Platform Based on Superlubricity

Twistronics, an emerging field focused on exploring the unique electrical properties induced by twist interface in graphene multilayers, has garnered significant attention in recent years. The general manipulation of twist angle depends on the assembly of van der Waals (vdW) layered materials, which has led to the discovery of unconventional superconductivity, ferroelectricity, and nonlinear optics, thereby expanding the realm of twistronics. Recently, in situ tuning of interlayer conductivity in vdW layered materials has been achieved based on scanning probe microscope. In this Perspective, the advancements in in situ twistronics are focused on by reviewing the state-of-the-art in situ manipulating technology, discussing the underlying mechanism based on the concept of structural superlubricity, and exploiting the real-time twistronic tests under scanning electron microscope (SEM). It is shown that the real-time manipulation under SEM allows for visualizing and monitoring the interface status during in situ twistronic testing. By harnessing the unique tribological properties of vdW layered materials, this novel platform not only enhances the fabrication of twistronic devices but also facilitates the fundamental understanding of interface phenomena in vdW layered materials. Moreover, this platform holds great promise for the application of twistronic-mechanical systems, providing avenues for the integration of twistronics into various mechanical frameworks.

Pressure tuning of minibands in MoS2/WSe2 heterostructures revealed by moiré phonons

Moiré superlattices of two-dimensional heterostructures arose as a new platform to investigate emergent behaviour in quantum solids with unprecedented tunability. To glean insights into the physics of these systems, it is paramount to discover new probes of the moiré potential and moiré minibands, as well as their dependence on external tuning parameters. Hydrostatic pressure is a powerful control parameter, since it allows to continuously and reversibly enhance the moiré potential. Here we use high pressure to tune the minibands in a rotationally aligned MoS2/WSe2 moiré heterostructure, and show that their evolution can be probed via moiré phonons. The latter are Raman-inactive phonons from the individual layers that are activated by the moiré potential. Moiré phonons manifest themselves as satellite Raman peaks arising exclusively from the heterostructure region, increasing in intensity and frequency under applied pressure. Further theoretical analysis reveals that their scattering rate is directly connected to the moiré potential strength. By comparing the experimental and calculated pressure-induced enhancement, we obtain numerical estimates for the moiré potential amplitude and its pressure dependence. The present work establishes moiré phonons as a sensitive probe of the moiré potential as well as the electronic structures of moiré systems.

Ferroic Phases in Two-Dimensional Materials

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

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

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

Moiré-Pattern Modulated Electronic Structures of GaSe/HOPG Heterostructure

Conventional two-dimensional electron gas (2DEG) typically occurs at the interface of semiconductor heterostructures and noble metal surfaces, but it is scarcely observed in individual 2D semiconductors. In this study, few-layer gallium selenide (GaSe) grown on highly ordered pyrolytic graphite (HOPG) is demonstrated using scanning tunneling microscopy and spectroscopy (STM/STS), revealing that the coexistence of quantum well states (QWS) and 2DEG. The QWS are located in the valence bands and exhibit a peak feature, with the number of quantum wells being equal to the number of atomic layers. Meanwhile, the 2DEG is located in the conduction bands and exhibits a standing-wave feature. Additionally, monolayer GaSe/HOPG heterostructures with different stacking angles (0°, 33°, 8°) form distinct moiré patterns that arise from lattice mismatch and angular rotation between adjacent atomic layers in 2D materials, which effectively modulate the electron effective mass, charge redistribution, and band gap of GaSe. Overall, this work reveals a paradigm of band engineering based on layer numbers and moiré patterns that can modulate the electronic properties of 2D materials.

Flattening conduction and valence bands for interlayer excitons in a moiré MoS2/WSe2 heterobilayer

We explore the flatness of conduction and valence bands of interlayer excitons in MoS2/WSe2 van der Waals heterobilayers, tuned by interlayer twist angle, pressure, and external electric field. We employ an efficient continuum model where the moiré pattern from lattice mismatch and/or twisting is represented by an equivalent mesoscopic periodic potential. We demonstrate that the mismatch moiré potential is too weak to produce significant flattening. Moreover, we draw attention to the fact that the quasi-particle effective masses around the Γ-point and the band flattening are reduced with twisting. As an alternative approach, we show (i) that reducing the interlayer distance by uniform vertical pressure can significantly increase the effective mass of the moiré hole, and (ii) that the moiré depth and its band flattening effects are strongly enhanced by accessible electric gating fields perpendicular to the heterobilayer, with resulting electron and hole effective masses increased by more than an order of magnitude - leading to record-flat bands. These findings impose boundaries on the commonly generalized benefits of moiré twistronics, while also revealing alternative feasible routes to achieve truly flat electron and hole bands to carry us to strongly correlated excitonic phenomena on demand.

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.

Twist-angle-dependent momentum-space direct and indirect interlayer excitons in WSe2/WS2 heterostructure

Interlayer excitons (ILEs) in the van der Waals (vdW) heterostructures of type-II band alignment transition metal dichalcogenides (TMDCs) have attracted significant interest owing to their unique exciton properties and potential in quantum information applications. However, the new dimension that emerges with the stacking of structures with a twist angle leads to a more complex fine structure of ILEs, presenting both an opportunity and a challenge for the regulation of the interlayer excitons. In this study, we report the evolution of interlayer excitons with the twist angle in the WSe₂/WS₂ heterostructure and identify the direct (indirect) interlayer excitons by combining photoluminescence (PL) and density functional theory (DFT) calculations. Two interlayer excitons with opposite circular polarization assigned to the different transition paths of K-K and Q-K were observed. The nature of the direct (indirect) interlayer exciton was confirmed by circular polarization PL measurement, excitation power-dependent PL measurement and DFT calculations. Furthermore, by applying an external electric field to regulate the band structure of the WSe₂/WS₂ heterostructure and control the transition path of the interlayer excitons, we could successfully realize the regulation of interlayer exciton emission. This study provides more evidence for the twist-angle-based control of heterostructure properties.