Optical read-out of Coulomb staircases in a moiré superlattice via trapped interlayer trions

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

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

Bright and Dark Quadrupolar Excitons in the WSe_{2}/MoSe_{2}/WSe_{2} Heterotrilayer

Transition metal dichalcogenide heterostructures have been extensively studied as a platform for investigating exciton physics. While heterobilayers such as WSe_{2}/MoSe_{2} have received significant attention, there has been comparatively less research on heterotrilayers, which may offer new excitonic species and phases, as well as unique physical properties. In this Letter, we present theoretical and experimental investigations on the emission properties of quadrupolar excitons (QXs), a newly predicted type of exciton, in a WSe_{2}/MoSe_{2}/WSe_{2} heterotrilayer device. Our findings reveal that the optical brightness or darkness of QXs is determined by horizontal mirror symmetry and valley and spin selection rules. Additionally, the emission intensity and energy of both bright and dark QXs can be adjusted by applying an out-of-plane electric field, due to changes in hole distribution and the Stark effect. These results not only provide experimental evidence for the existence of QXs in heterotrilayers but also uncover their novel properties, which have the potential to drive the development of new exciton-based applications.

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.

Quadrupolar excitons and hybridized interlayer Mott insulator in a trilayer moiré superlattice

Transition metal dichalcogenide (TMDC) moiré superlattices, owing to the moiré flatbands and strong correlation, can host periodic electron crystals and fascinating correlated physics. The TMDC heterojunctions in the type-II alignment also enable long-lived interlayer excitons that are promising for correlated bosonic states, while the interaction is dictated by the asymmetry of the heterojunction. Here we demonstrate a new excitonic state, quadrupolar exciton, in a symmetric WSe₂-WS₂-WSe₂ trilayer moiré superlattice. The quadrupolar excitons exhibit a quadratic dependence on the electric field, distinctively different from the linear Stark shift of the dipolar excitons in heterobilayers. This quadrupolar exciton stems from the hybridization of WSe₂ valence moiré flatbands. The same mechanism also gives rise to an interlayer Mott insulator state, in which the two WSe₂ layers share one hole laterally confined in one moiré unit cell. In contrast, the hole occupation probability in each layer can be continuously tuned via an out-of-plane electric field, reaching 100% in the top or bottom WSe₂ under a large electric field, accompanying the transition from quadrupolar excitons to dipolar excitons. Our work demonstrates a trilayer moiré system as a new exciting playground for realizing novel correlated states and engineering quantum phase transitions.

Dynamics of Moiré Trion and Its Valley Polarization in a Microfabricated WSe2/MoSe2 Heterobilayer

The moiré potential, induced by stacking two monolayer semiconductors with slightly different lattice mismatches, acts as periodic quantum confinement for optically generated excitons, resulting in spatially ordered zero-dimensional quantum systems. However, there are limitations to exploring intrinsic optical properties of moiré excitons due to ensemble emissions and broadened emissions from many peaks caused by the inhomogeneity of the moiré potential. In this study, we proposed a microfabrication technique based on focused Ga⁺ ion beams, which enables us to control the number of peaks originating from the moiré potential and thus explore unknown moiré optical characteristics of WSe₂/MoSe₂ heterobilayer. By taking advantage of this approach, we reveal emissions from a single moiré exciton and charged moiré exciton (trion) under electrostatic doping conditions. We show the momentum dark moiré trion state above the bright trion state with a splitting energy of approximately 4 meV and clarify that the dynamics are determined by the initial trion population in the bright state. Furthermore, the degree of negative circularly polarized emissions and their valley dynamics of moiré trions are dominated by a very long valley relaxation process lasting ∼700 ns. Our findings on microfabricated heterobilayer could be viewed as an extension of our groundbreaking efforts in the field of quantum optics application using moiré superlattices.

Layer-dependent correlated phases in WSe2/MoS2 moiré superlattice

Electron correlation plays an essential role in the macroscopic quantum phenomena in the moiré heterostructure, such as antiferromagnetism and correlated insulating phases. Unlike the phenomena where the interaction involves only electrons in one layer, the interaction of distinct phases in two or more layers represents a new horizon forward, such as the one in the Kondo lattice model. Here, using interlayer excitons as a probe, we show that the interlayer interactions in heterobilayers of tungsten diselenide and molybdenum disulfide (WSe₂/MoS₂) can be electrically switched on and off, resulting in a layer-dependent correlated phase diagram, including single-layer, layer-selective, excitonic-insulator and layer-hybridized regions. We demonstrate that these correlated phases affect the interlayer exciton non-radiative decay pathways. These results reveal the role of strong correlation on interlayer exciton dynamics and pave the way for studying the layer-resolved strong correlation behaviour in moiré heterostructures.

Strong Interlayer Coupling in Twisted Transition Metal Dichalcogenide Moiré Superlattices

Moiré superlattices in twisted van der Waals materials offer a powerful platform for exploring light-matter interactions. The periodic moiré potentials in moiré superlattices can induce strongly correlated quantum phenomena that depend on the moiré potential associated with interlayer coupling at the interface. However, moiré superlattices are primarily prepared by mechanical exfoliation and manual stacking, where the transfer methods easily cause interfacial contamination, and the preparation of high-quality bilayer 2D materials with small twist angles by growth methods remains a significant challenge. In this work, WSe₂ /WSe₂ homobilayers with different twist angles by chemical vapor deposition (CVD), using a heteroatom-assisted growth technique, are synthesized. Using low-frequency Raman scattering, the uniformity of the moiré superlattices is mapped to demonstrate the strong interfacial coupling of the CVD-fabricated twist-angle homobilayers. The moiré potential depths of the CVD-grown and artificially stacked homostructures with twist angles of 1.5° are 115 and 45 meV (an increase of 155%), indicating that the depth of moiré potential can be modulated by the interfacial coupling. These results open a new avenue to study the modulation of moiré potential by strong interlayer coupling and provide a foundation for the development of twistronics.

Structure modulation of two-dimensional transition metal chalcogenides: recent advances in methodology, mechanism and applications

Together with the development of two-dimensional (2D) materials, transition metal dichalcogenides (TMDs) have become one of the most popular series of model materials for fundamental sciences and practical applications. Due to the ever-growing requirements of customization and multi-function, dozens of modulated structures have been introduced in TMDs. In this review, we present a systematic and comprehensive overview of the structure modulation of TMDs, including point, linear and out-of-plane structures, following and updating the conventional classification for silicon and related bulk semiconductors. In particular, we focus on the structural characteristics of modulated TMD structures and analyse the corresponding root causes. We also summarize the recent progress in modulating methods, mechanisms, properties and applications based on modulated TMD structures. Finally, we demonstrate challenges and prospects in the structure modulation of TMDs and forecast potential directions about what and how breakthroughs can be achieved.

Optical Microscope Based Universal Parameter for Identifying Layer Number in Two-Dimensional Materials

Optical contrast is the most common preliminary method to identify layer number of two-dimensional (2D) materials, but it is seldom used as a confirmatory technique. We explain the reason for variation of optical contrast between imaging systems, motivating system-independent measurement of optical contrast as a critical need. We describe a universal method to quantify the layer number using the RGB (red-green-blue) and RAW optical images. For RGB images, the slope of 2D flake (MoS₂, WSe₂, graphene) intensity vs substrate intensity is extracted from optical images with varying lamp power. The intensity slope identifies layer number and is system independent. For RAW images, intensity slopes and intensity ratios are completely system and intensity independent. Intensity slope (for RGB) and intensity ratio (for RAW) are thus universal parameters for identifying layer number. The RAW format is not present in all imaging systems, but it can confirm layer number using a single optical image, making it a rapid and system-independent universal method. A Fresnel-reflectance-based optical model provides an excellent match with experiments. Furthermore, we have created a MATLAB-based graphical user interface that can identify layer number rapidly. This technique is expected to accelerate the preparation of heterostructures and to fulfill a prolonged need for universal optical contrast method.

Localized interlayer excitons in MoSe2-WSe2 heterostructures without a moiré potential

Interlayer excitons (IXs) in MoSe₂–WSe₂ heterobilayers have generated interest as highly tunable light emitters in transition metal dichalcogenide (TMD) heterostructures. Previous reports of spectrally narrow (<1 meV) photoluminescence (PL) emission lines at low temperature have been attributed to IXs localized by the moiré potential between the TMD layers. We show that spectrally narrow IX PL lines are present even when the moiré potential is suppressed by inserting a bilayer hexagonal boron nitride (hBN) spacer between the TMD layers. We compare the doping, electric field, magnetic field, and temperature dependence of IXs in a directly contacted MoSe₂–WSe₂ region to those in a region separated by bilayer hBN. The doping, electric field, and temperature dependence of the narrow IX lines are similar for both regions, but their excitonic g-factors have opposite signs, indicating that the origin of narrow IX PL is not the moiré potential.

The spectrally narrow photoluminescence lines occurring in transition metal dichalcogenides (TMD) heterostructures at low temperature have been attributed to interlayer excitons (IXs) localized by the moiré potential between the TMD layers. Here, the authors show that these lines are present even when the moiré potential is suppressed by inserting an hBN spacer between the TMD layers.

The Magnetic Genome of Two-Dimensional van der Waals Materials

Magnetism in two-dimensional (2D) van der Waals (vdW) materials has recently emerged as one of the most promising areas in condensed matter research, with many exciting emerging properties and significant potential for applications ranging from topological magnonics to low-power spintronics, quantum computing, and optical communications. In the brief time after their discovery, 2D magnets have blossomed into a rich area for investigation, where fundamental concepts in magnetism are challenged by the behavior of spins that can develop at the single layer limit. However, much effort is still needed in multiple fronts before 2D magnets can be routinely used for practical implementations. In this comprehensive review, prominent authors with expertise in complementary fields of 2D magnetism (i.e., synthesis, device engineering, magneto-optics, imaging, transport, mechanics, spin excitations, and theory and simulations) have joined together to provide a genome of current knowledge and a guideline for future developments in 2D magnetic materials research.

Theory of Excitons in Atomically Thin Semiconductors: Tight-Binding Approach

Atomically thin semiconductors from the transition metal dichalcogenide family are materials in which the optical response is dominated by strongly bound excitonic complexes. Here, we present a theory of excitons in two-dimensional semiconductors using a tight-binding model of the electronic structure. In the first part, we review extensive literature on 2D van der Waals materials, with particular focus on their optical response from both experimental and theoretical points of view. In the second part, we discuss our ab initio calculations of the electronic structure of MoS2, representative of a wide class of materials, and review our minimal tight-binding model, which reproduces low-energy physics around the Fermi level and, at the same time, allows for the understanding of their electronic structure. Next, we describe how electron-hole pair excitations from the mean-field-level ground state are constructed. The electron-electron interactions mix the electron-hole pair excitations, resulting in excitonic wave functions and energies obtained by solving the Bethe-Salpeter equation. This is enabled by the efficient computation of the Coulomb matrix elements optimized for two-dimensional crystals. Next, we discuss non-local screening in various geometries usually used in experiments. We conclude with a discussion of the fine structure and excited excitonic spectra. In particular, we discuss the effect of band nesting on the exciton fine structure; Coulomb interactions; and the topology of the wave functions, screening and dielectric environment. Finally, we follow by adding another layer and discuss excitons in heterostructures built from two-dimensional semiconductors.

Scalable Moiré Lattice with Oriented TMD Monolayers

Moiré lattice in artificially stacked monolayers of two-dimensional (2D) materials effectively modulates the electronic structures of materials, which is widely highlighted. Formation of the electronic Moiré superlattice promises the prospect of uniformity among different moiré cells across the lattice, enabling a new platform for novel properties, such as unconventional superconductivity, and scalable quantum emitters. Recently, epitaxial growth of the monolayer transition metal dichalcogenide (TMD) is achieved on the sapphire substrate by chemical vapor deposition (CVD) to realize scalable growth of highly-oriented monolayers. However, fabrication of the scalable Moiré lattice remains challenging due to the lack of essential manipulation of the well-aligned monolayers for clean interface quality and precise twisting angle control. Here, scalable and highly-oriented monolayers of TMD are realized on the sapphire substrates by using the customized CVD process. Controlled growth of the epitaxial monolayers is achieved by promoting the rotation of the nuclei-like domains in the initial growth stage, enabling aligned domains for further grain growth in the steady-state stage. A full coverage and distribution of the highly-oriented domains are verified by second-harmonic generation (SHG) microscopy. By developing the method for clean monolayer manipulation, hetero-stacked bilayer (epi-WS₂/epi-MoS₂) is fabricated with the specific angular alignment of the two major oriented monolayers at the edge direction of 0°/ ± 60°. On account of the optimization for scalable Moiré lattice with a high-quality interface, the observation of interlayer exciton at low temperature illustrates the feasibility of scalable Moiré superlattice based on the oriented monolayers.