Evidence for moiré excitons in van der Waals heterostructures

Superior Thermoelectric Properties of Twist-Angle Superlattice Borophene Induced by Interlayer Electrons Transport

In this paper, the energy bands, interlayer interactions and thermoelectric effects of twisted bilayer borophene (TBB) synthesized on Ag (111) are studied theoretically. The results manifest the advantages of twistronics, where the high electrical conductivity and the large Seebeck coefficient are regulated to the same range, which lead to the significantly increase of figure of merit ZT than that of bilayer borophene (BB) without twist, where the BB without twist is successfully synthesized on Ag (111) film is recently experimental report [Nat. Mater. 2022, 21, 35]. For the TBB synthesized of on Ag (111) film, theoretical analysis demonstrates that TBB and Ag are relatively strongly coupled, and TBB becomes a metallic 2D material, where the top and bottom borophene layers are semiconducting and metallic, respectively. TBB exhibits excellent thermoelectric efficiency due to the charge transfer bonding between the layers, less electron localization, and the regulation of Seebeck coefficient, electrical conductivity, and ZT at the same region of chemical potential and the same temperature by twistronics. The structure-property relationship offers the possibility of applying TBB in thermoelectric devices.

Dynamic Generation of Spin Spirals of Moiré Trapped Carriers via Exciton Mediated Spin Interactions

Stacking transition metal dichalcogenides (TMDs) to form moiré superlattices has provided exciting opportunities to explore many-body correlation phenomena of the moiré trapped carriers. TMD bilayers, on the other hand, host long-lived interlayer exciton (IX), an elementary excitation of long spin-valley lifetime that can be optically or electrically injected. Here we find that, through the Coulomb exchange between mobile IXs and carriers, the IX bath can mediate both Heisenberg and Dzyaloshinskii-Moriya type spin interactions between moiré trapped carriers, controllable by exciton density and exciton spin current, respectively. We show the strong Heisenberg interaction and the extraordinarily long-ranged Dzyaloshinskii-Moriya interaction here can jointly establish robust spin spiral magnetic orders in Mott-Wigner crystal states at various filling factors, with the spiral direction controlled by the exciton current.

Preparation, properties and applications of two-dimensional superlattices

As a combination concept of a 2D material and a superlattice, two-dimensional superlattices (2DSs) have attracted increasing attention recently. The natural advantages of 2D materials in their properties, dimension, diversity and compatibility, and their gradually improved technologies for preparation and device fabrication serve as solid foundations for the development of 2DSs. Compared with the existing 2D materials and even their heterostructures, 2DSs relate to more materials and elaborate architectures, leading to novel systems with more degrees of freedom to modulate material properties at the nanoscale. Here, three typical types of 2DSs, including the component, strain-induced and moiré superlattices, are reviewed. The preparation methods, properties and state-of-the-art applications of each type are summarized. An outlook of the challenges and future developments is also presented. We hope that this work can provide a reference for the development of 2DS-related research.

Ferroelectric Domain Control of Nonlinear Light Polarization in MoS2 via PbZr0.2 Ti0.8 O3 Thin Films and Free-Standing Membranes

Two-dimensional (2D) transition metal dichalcogenides (TMDCs) such as MoS₂ exhibit exceptionally strong nonlinear optical responses, while nanoscale control of the amplitude, polar orientation, and phase of the nonlinear light in TMDCs remains challenging. In this work, by interfacing monolayer MoS₂ with epitaxial PbZr_0.2 Ti_0.8 O₃ (PZT) thin films and free-standing PZT membranes, the amplitude and polarization of the second harmonic generation (SHG) signal are modulated via ferroelectric domain patterning, which demonstrates that PZT membranes can lead to in-operando programming of nonlinear light polarization. The interfacial coupling of the MoS₂ polar axis with either the out-of-plane polar domains of PZT or the in-plane polarization of domain walls tailors the SHG light polarization into different patterns with distinct symmetries, which are modeled via nonlinear electromagnetic theory. This study provides a new material platform that enables reconfigurable design of light polarization at the nanoscale, paving the path for developing novel optical information processing, smart light modulators, and integrated photonic circuits.

Two Dimensional Heterostructures for Optoelectronics: Current Status and Future Perspective

Researchers have found various families of two-dimensional (2D) materials and associated heterostructures through detailed theoretical work and experimental efforts. Such primitive studies provide a framework to investigate novel physical/chemical characteristics and technological aspects from micro to nano and pico scale. Two-dimensional van der Waals (vdW) materials and their heterostructures can be obtained to enable high-frequency broadband through a sophisticated combination of stacking order, orientation, and interlayer interactions. These heterostructures have been the focus of much recent research due to their potential applications in optoelectronics. Growing the layers of one kind of 2D material over the other, controlling absorption spectra via external bias, and external doping proposes an additional degree of freedom to modulate the properties of such materials. This mini review focuses on current state-of-the-art material design, manufacturing techniques, and strategies to design novel heterostructures. In addition to a discussion of fabrication techniques, it includes a comprehensive analysis of the electrical and optical properties of vdW heterostructures (vdWHs), particularly emphasizing the energy-band alignment. In the following sections, we discuss specific optoelectronic devices, such as light-emitting diodes (LEDs), photovoltaics, acoustic cavities, and biomedical photodetectors. Furthermore, this also includes a discussion of four different 2D-based photodetector configurations according to their stacking order. Moreover, we discuss the challenges that remain to be addressed in order to realize the full potential of these materials for optoelectronics applications. Finally, as future perspectives, we present some key directions and express our subjective assessment of upcoming trends in the field.

Wrinkles, Ridges, Miura-Ori, and Moiré Patterns in MoSe2 Using Neural Networks

Effects of lateral compression on out-of-plane deformation of two-dimensional MoSe₂ layers are investigated. A MoSe₂ monolayer develops periodic wrinkles under uniaxial compression and Miura-Ori patterns under biaxial compression. When a flat MoSe₂ monolayer is placed on top of a wrinkled MoSe₂ layer, the van der Waals (vdW) interaction transforms wrinkles into ridges and generates mixed 2H and 1T phases and chain-like defects. Under a biaxial strain, the vdW interaction induces regions of Miura-Ori patterns in bilayers. Strained systems analyzed using a convolutional neural network show that the compressed system consists of semiconducting 2H and metallic 1T phases. The energetics, mechanical response, defect structure, and dynamics are analyzed as bilayers undergo wrinkle-ridge transformations under uniaxial compression and moiré transformations under biaxial compression. Our results indicate that in-plane compression can induce self-assembly of out-of-plane metasurfaces with controllable semiconducting and metallic phases and moiré patterns with unique optoelectronic properties.

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.

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.

A primer on twistronics: a massless Dirac fermion's journey to moiré patterns and flat bands in twisted bilayer graphene

The recent discovery of superconductivity in magic-angle twisted bilayer graphene (TBLG) has sparked a renewed interest in the strongly-correlated physics ofsp²carbons, in stark contrast to preliminary investigations which were dominated by the one-body physics of the massless Dirac fermions. We thus provide a self-contained, theoretical perspective of the journey of graphene from its single-particle physics-dominated regime to the strongly-correlated physics of the flat bands. Beginning from the origin of the Dirac points in condensed matter systems, we discuss the effect of the superlattice on the Fermi velocity and Van Hove singularities in graphene and how it leads naturally to investigations of the moiré pattern in van der Waals heterostructures exemplified by graphene-hexagonal boron-nitride and TBLG. Subsequently, we illuminate the origin of flat bands in TBLG at the magic angles by elaborating on a broad range of prominent theoretical works in a pedagogical way while linking them to available experimental support, where appropriate. We conclude by providing a list of topics in the study of the electronic properties of TBLG not covered by this review but may readily be approached with the help of this primer.

Unveiling Electronic Behaviors in Heterochiral Charge-Density-Wave Twisted Stacking Materials with 1.25 nm Unit Dependence

Layered charge-density-wave (CDW) materials have gained increasing interest due to their CDW stacking-dependent electronic properties for practical applications. Among the large family of CDW materials, those with star of David (SOD) patterns are very important due to the potentials for quantum spin liquid and related device applications. However, the spatial extension and the spin coupling information down to the nanoscale remain elusive. Here, we report the study of heterochiral CDW stackings in bilayer (BL) NbSe₂ with high spatial resolution. We reveal that there exist well-defined heterochiral stackings, which have inhomogeneous electronic states among neighboring CDW units (star of David, SOD), significantly different from the homogeneous electronic states in the homochiral stackings. Intriguingly, the different electronic behaviors are spatially localized within each SOD with a unit size of 1.25 nm, and the gap sizes are determined by the different types of SOD stackings. Density functional theory (DFT) calculations match the experimental measurements well and reveal the SOD-stacking-dependent correlated electronic states and antiferromagnetic/ferromagnetic couplings. Our findings give a deep understanding of the spatial distribution of interlayer stacking and the delicate modulation of the spintronic states, which is very helpful for CDW-based nanoelectronic devices.

Spin-polarized spatially indirect excitons in a topological insulator

The exciton, a bound state of an electron and a hole, is a fundamental quasiparticle induced by coherent light-matter interactions in semiconductors. When the electrons and holes are in distinct spatial locations, spatially indirect excitons are formed with a much longer lifetime and a higher condensation temperature. One of the ultimate frontiers in this field is to create long-lived excitonic topological quasiparticles by driving exciton states with topological properties, to simultaneously leverage both topological effects and correlation^1,2. Here we reveal the existence of a transient excitonic topological surface state (TSS) in a topological insulator, Bi₂Te₃. By using time-, spin- and angle-resolved photoemission spectroscopy, we directly follow the formation of a long-lived exciton state as revealed by an intensity buildup below the bulk-TSS mixing point and an anomalous band renormalization of the continuously connected TSS in the momentum space. Such a state inherits the spin-polarization of the TSS and is spatially indirect along the z axis, as it couples photoinduced surface electrons and bulk holes in the same momentum range, which ultimately leads to an excitonic state of the TSS. These results establish Bi₂Te₃ as a possible candidate for the excitonic condensation of TSSs³ and, in general, opens up a new paradigm for exploring the momentum space emergence of other spatially indirect excitons, such as moiré and quantum well excitons^4-6, and for the study of non-equilibrium many-body topological physics.

The Promise of Soft-Matter-Enabled Quantum Materials

The field of quantum materials has experienced rapid growth over the past decade, driven by exciting new discoveries with immense transformative potential. Traditional synthetic methods to quantum materials have, however, limited the exploration of architectural control beyond the atomic scale. By contrast, soft matter self-assembly can be used to tailor material structure over a large range of length scales, with a vast array of possible form factors, promising emerging quantum material properties at the mesoscale. This review explores opportunities for soft matter science to impact the synthesis of quantum materials with advanced properties. Existing work at the interface of these two fields is highlighted, and perspectives are provided on possible future directions by discussing the potential benefits and challenges which can arise from their bridging.

Layer-Structured Anisotropic Metal Chalcogenides: Recent Advances in Synthesis, Modulation, and Applications

The unique electronic and catalytic properties emerging from low symmetry anisotropic (1D and 2D) metal chalcogenides (MCs) have generated tremendous interest for use in next generation electronics, optoelectronics, electrochemical energy storage devices, and chemical sensing devices. Despite many proof-of-concept demonstrations so far, the full potential of anisotropic chalcogenides has yet to be investigated. This article provides a comprehensive overview of the recent progress made in the synthesis, mechanistic understanding, property modulation strategies, and applications of the anisotropic chalcogenides. It begins with an introduction to the basic crystal structures, and then the unique physical and chemical properties of 1D and 2D MCs. Controlled synthetic routes for anisotropic MC crystals are summarized with example advances in the solution-phase synthesis, vapor-phase synthesis, and exfoliation. Several important approaches to modulate dimensions, phases, compositions, defects, and heterostructures of anisotropic MCs are discussed. Recent significant advances in applications are highlighted for electronics, optoelectronic devices, catalysts, batteries, supercapacitors, sensing platforms, and thermoelectric devices. The article ends with prospects for future opportunities and challenges to be addressed in the academic research and practical engineering of anisotropic MCs.

Interlayer exciton landscape in WS2/tetracene heterostructures

The vertical stacking of two-dimensional materials into heterostructures gives rise to a plethora of intriguing optoelectronic properties and presents an unprecedented potential for technological development. While much progress has been made combining different monolayers of transition metal dichalcogenides (TMDs), little is known about TMD-based heterostructures including organic layers of molecules. Here, we present a joint theory-experiment study on a TMD/tetracene heterostructure demonstrating clear signatures of spatially separated interlayer excitons in low temperature photoluminescence spectra. Here, the Coulomb-bound electrons and holes are localized either in the TMD or in the molecule layer, respectively. We reveal both in theory and experiment signatures of the entire intra- and interlayer exciton landscape in the photoluminescence spectra. In particular, we find both in theory and experiment a pronounced transfer of intensity from the intralayer TMD exciton to a series of energetically lower interlayer excitons with decreasing temperature. In addition, we find signatures of phonon-sidebands stemming from these interlayer exciton states. Our findings shed light on the microscopic nature of interlayer excitons in TMD/molecule heterostructures and could have important implications for technological applications of these materials.

Efficient modulation of thermal transport in two-dimensional materials for thermal management in device applications

With the development of chip technology, the density of transistors on integrated circuits is increasing and the size is gradually shrinking to the micro-/nanoscale, with the consequent problem of heat dissipation on chips becoming increasingly serious. For device applications, efficient heat dissipation and thermal management play a key role in ensuring device operation reliability. In this review, we summarize the thermal management applications based on 2D materials from both theoretical and experimental perspectives. The regulation approaches of thermal transport can be divided into two main types: intrinsic structure engineering (acting on the intrinsic structure) and non-structure engineering (applying external fields). On one hand, the thermal transport properties of 2D materials can be modulated by defects and disorders, size effect (including length, width, and the number of layers), heterostructures, structure regulation, doping, alloy, functionalizing, and isotope purity. On the other hand, strain engineering, electric field, and substrate can also modulate thermal transport efficiently without changing the intrinsic structure of the materials. Furthermore, we propose a perspective on the topic of using magnetism and light field to modulate the thermal transport properties of 2D materials. In short, we comprehensively review the existing thermal management modulation applications as well as the latest research progress, and conclude with a discussion and perspective on the applications of 2D materials in thermal management, which will be of great significance to the development of next-generation nanoelectronic devices.

Time- and angle-resolved photoemission spectroscopy (TR-ARPES) of TMDC monolayers and bilayers

Many unique properties in two-dimensional (2D) materials and their heterostructures rely on charge excitation, scattering, transfer, and relaxation dynamics across different points in the momentum space. Understanding these dynamics is crucial in both the fundamental study of 2D physics and their incorporation in optoelectronic and quantum devices. A direct method to probe charge carrier dynamics with momentum resolution is time- and angle-resolved photoemission spectroscopy (TR-ARPES). Such measurements have been challenging, since photoexcited carriers in many 2D monolayers reside at high crystal momenta, requiring probe photon energies in the extreme UV (EUV) regime. These challenges have been recently addressed by development of table-top pulsed EUV sources based on high harmonic generation, and the successful integration into a TR-ARPES and/or time-resolved momentum microscope. Such experiments will allow direct imaging of photoelectrons with superior time, energy, and crystal momentum resolution, with unique advantage over traditional optical measurements. Recently, TR-ARPES experiments of 2D transition metal dichalcogenide (TMDC) monolayers and bilayers have created unprecedented opportunities to reveal many intrinsic dynamics of 2D materials, such as bandgap renormalization, charge carrier scattering, relaxation, and wavefunction localization in moiré patterns. This perspective aims to give a short review of recent discoveries and discuss the challenges and opportunities of such techniques in the future.

Inversion Symmetry and Exotic Interlayer Exciton Behavior in Twisted Trilayer MoS2 Produced by Vapor Deposition

Two-dimensional materials (2DMs) that are stacked vertically with a certain twist angle provide new degrees of freedom for designing novel physical properties. Twist-related properties of homogeneous bilayer and heterogeneous bilayer 2DMs, such as excitons and phonons, have been described in many pioneering works. However, twist-related properties of homogeneous trilayer 2DMs have been rarely reported. In this work, trilayer MoS₂ with the twisted angle of 12° by optimized vapor deposition rather than the conventional mechanical stacking method was successfully fabricated. The inversion symmetry of trilayer MoS₂ is changed by twist. Phonons and excitons produced by twist have an enormous influence on the interlayer interaction of trilayer MoS₂, making trilayer MoS₂ appear to have exotic optical properties. Compared with monolayer MoS₂, the phonon vibration and photoluminescence intensity of trilayer MoS₂ with one-interlayer-twisted are significantly improved, and the second harmonic generation response in the non-twist region of trilayer MoS₂ is ∼3 times that of monolayer MoS₂. In addition, interlayer coupling, inversion symmetry, and exciton behavior of the twist region show regional differences. This work provides a new way for designing twist and exploring the influence of twist on the structures of 2DMs with few layers.

Twist-Dependent Intra- and Interlayer Excitons in Moiré MoSe_{2} Homobilayers

Optoelectronic properties of van der Waals homostructures can be selectively engineered by the relative twist angle between layers. Here, we study the twist-dependent moiré coupling in MoSe_{2} homobilayers. For small angles, we find a pronounced redshift of the K-K and Γ-K excitons accompanied by a transition from K-K to Γ-K emission. Both effects can be traced back to the underlying moiré pattern in the MoSe_{2} homobilayers, as confirmed by our low-energy continuum model for different moiré excitons. We identify two distinct intralayer moiré excitons for R stacking, while H stacking yields two degenerate intralayer excitons due to inversion symmetry. In both cases, bright interlayer excitons are found at higher energies. The performed calculations are in excellent agreement with experiment and allow us to characterize the observed exciton resonances, providing insight about the layer composition and relevant stacking configuration of different moiré exciton species.

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.

Phonon-assisted upconversion in twisted two-dimensional semiconductors

Phonon-assisted photon upconversion (UPC) is an anti-Stokes process in which incident photons achieve higher energy emission by absorbing phonons. This letter studies phonon-assisted UPC in twisted 2D semiconductors, in which an inverted contrast between UPC and conventional photoluminescence (PL) of WSe₂ twisted bilayer is emergent. A 4-fold UPC enhancement is achieved in 5.5° twisted bilayer while PL weakens by half. Reduced interlayer exciton conversion efficiency driven by lattice relaxation, along with enhanced pump efficiency resulting from spectral redshift, lead to the rotation-angle-dependent UPC enhancement. The counterintuitive phenomenon provides a novel insight into a unique way that twisted angle affects UPC and light-matter interactions in 2D semiconductors. Furthermore, the UPC enhancement platform with various superimposable means offers an effective method for lighting bilayers and expanding the application prospect of 2D stacked van der Waals devices.

Strong Structural and Electronic Coupling in Metavalent PbS Moiré Superlattices

Moiré superlattices are twisted bilayer materials in which the tunable interlayer quantum confinement offers access to new physics and novel device functionalities. Previously, moiré superlattices were built exclusively using materials with weak van der Waals interactions, and synthesizing moiré superlattices with strong interlayer chemical bonding was considered to be impractical. Here, using lead sulfide (PbS) as an example, we report a strategy for synthesizing moiré superlattices coupled by strong chemical bonding. We use water-soluble ligands as a removable template to obtain free-standing ultrathin PbS nanosheets and assemble them into direct-contact bilayers with various twist angles. Atomic-resolution imaging shows the moiré periodic structural reconstruction at the superlattice interface due to the strong metavalent coupling. Electron energy loss spectroscopy and theoretical calculations collectively reveal the twist-angle-dependent electronic structure, especially the emergent separation of flat bands at small twist angles. The localized states of flat bands are similar to well-arranged quantum dots, promising an application in devices. This study opens a new door to the exploration of deep energy modulations within moiré superlattices alternative to van der Waals twistronics.

Extraordinary Phonon Displacement and Giant Resonance Raman Enhancement in WSe2/WS2 Moiré Heterostructures

Twisted van der Waals heterostructures are known to induce surprisingly diverse and intriguing phenomena, such as correlated electronic phase and unconventional optical properties. This can be realized by controlled rotation of adjacent atomic planes, which provides an uncommon way to manipulate inelastic light-matter interactions. Here, we discover an extraordinary blue shift of 5-6 wavenumbers for high-frequency phonon modes in WS₂/WSe₂ twisted heterobilayers, captured meticulously using Raman spectroscopy. Phonon spectra displace rapidly over a subtle change in interlayer twist angle owing to heterostrain and atomic reconstruction from the Moiré pattern. First-order linear coefficients of the phonon modes in twisted heterostructures are further found to increase largely compared to their monolayer counterpart and vary immensely with the twist angle. Exceptional and extravagant enhancement of up to 50-fold is observed in the Raman vibrational intensity at a specific twist angle; this is largely influenced by the resonance process derived from a simple critical twist angle model. In addition, we depict how the resonance can be modulated by changing the thermal conditions and also the stacking angle. Therefore, our work further highlights the twist-driven phonon dynamics in pristine two-dimensional heterostructures, adding vital insight into Moiré physics and promoting comprehensive understanding of structural and optical properties in Moiré superlattices.

Spatially Dependent Electronic Structures and Excitons in a Marginally Twisted Moiré Superlattice of Spiral WS2

Twisted two-dimensional transition metal dichalcogenide (TMD) moiré superlattices provide an additional degree of freedom to engineer electronic and optical properties. Nevertheless, controllable synthesis of marginally twisted homo TMD moiré superlattices is still a challenge. Here, physical vapor deposition grown spiral WS₂ nanosheets are demonstrated to be a marginally twisted moiré superlattice using scanning tunneling microscopy and spectroscopy. Periodic moiré superlattices are found on the third layer (3L) and 4L of the spiral WS₂ nanosheet owing to the marginally twisted alignment between two neighboring layers, resulting in a highly localized flat band near the valence band maximum. Their bandgap depends on atomic stacking configurations, which gives a good interpretation for split moiré excitons using photoluminescence at 77 K. This work can benefit the development of twisted homo TMD moiré superlattices and could promote the profound research of twisted TMDs in the prospective field, such as strongly correlated physics and twistronics.

Light driven magnetic transitions in transition metal dichalcogenide heterobilayers

Motivated by the recent excitement around the physics of twisted transition metal dichalcogenide (TMD) multilayer systems, we study strongly correlated phases of TMD heterobilayers under the influence of light. We consider both waveguide light and circularly polarized light. The former allows for longitudinally polarized light, which in the high frequency limit can be used to selectively modify interlayer hoppings in a tight-binding model. We argue based on quasi-degenerate perturbation theory that changes to the interlayer hoppings can be captured as a modulation to the strength of the moiré potential in a continuum model. As a consequence, waveguide light can be used to drive transitions between a myriad of different magnetic phases, including a transition from a 120^∘Neel phase to a stripe ordered magnetic phase, or from a spin density wave phase to a paramagnetic phase, among others. When the system is subjected to circularly polarized light we find that the effective mass of the active TMD layer is modified by an applied electromagnetic field. By simultaneously applying waveguide light and circularly polarized light to a system, one has a high level of control in moving through the phase diagram in-situ. Lastly, we comment on the experimental feasibility of Floquet state preparation and argue that it is within reach of available techniques when the system is coupled to a judiciously chosen bath.

Tunable electronic properties and related functional devices for ferroelectric In2Se3/MoSSe van der Waals heterostructures

In recent years, two-dimensional (2D) materials have attracted increasing attraction in a number of scientific research fields. In particular, ferroelectric materials with reversible spontaneous electric polarization and Janus transition metal dichalcogenides (TMDs) with intrinsic dipoles exhibit novel properties for many practical applications. Here, the electronic properties of van der Waals (vdW) heterostructures consisting of In₂Se₃ and MoSSe were investigated based on a first-principles approach. It was demonstrated that four studied In₂Se₃/MoSSe heterostructures exhibited obvious band gap (E _g) differences, ranging 0.13 to 0.90 eV for PBE (0.47 to 1.50 eV for HSE06) owing to the reversible spontaneous electric polarization of In₂Se₃ and different intrinsic dipole of MoSSe, and different band alignments of type-I or type-II could also be obtained. The energy bands of the four vdW heterostructures could be obviously regulated by varying degrees of vertical (horizontal) strain and vertical interface electric field, and the E _g varied from zero to 1.27 eV. Then, M4-based mechanical switching devices and ferroelectric diodes were designed based on the significant strain and electric field function. These results provide one possible mechanism for how the polarization direction regulates the physical properties of the system due to the different charges on the two surfaces of the out-of-plane polarized ferroelectric material, which may lead to different proximity effects on the face of the material.

Hyperspectral imaging of exciton confinement within a moiré unit cell with a subnanometer electron probe

Electronic and optical excitations in two-dimensional systems are distinctly sensitive to the presence of a moiré superlattice. We used cryogenic transmission electron microscopy and spectroscopy to simultaneously image the structural reconstruction and associated localization of the lowest-energy intralayer exciton in a rotationally aligned WS₂-WSe₂ moiré superlattice. In conjunction with optical spectroscopy and ab initio calculations, we determined that the exciton center-of-mass wave function is confined to a radius of approximately 2 nanometers around the highest-energy stacking site in the moiré unit cell. Our results provide direct evidence that atomic reconstructions lead to the strongly confining moiré potentials and that engineering strain at the nanoscale will enable new types of excitonic lattices.

Recent progress of two-dimensional heterostructures for thermoelectric applications

The rapid development of synthesis and fabrication techniques has opened up a research upsurge in two-dimensional (2D) material heterostructures, which have received extensive attention due to their superior physical and chemical properties. Currently, thermoelectric energy conversion is an effective means to deal with the energy crisis and increasingly serious environmental pollution. Therefore, an in-depth understanding of thermoelectric transport properties in 2D heterostructures is crucial for the development of micro-nano energy devices. In this review, the recent progress of 2D heterostructures for thermoelectric applications is summarized in detail. Firstly, we systematically introduce diverse theoretical simulations and experimental measurements of the thermoelectric properties of 2D heterostructures. Then, the thermoelectric applications and performance regulation of several common 2D materials, as well as in-plane heterostructures and van der Waals heterostructures, are also discussed. Finally, the challenges of improving the thermoelectric performance of 2D heterostructures materials are summarized, and related prospects are described.

Signature of Cascade Transitions between Interlayer Excitons in a Moiré Superlattice

A moiré superlattice in transition metal dichalcogenides heterostructure provides an exciting platform for studying strongly correlated electronics and excitonic physics, such as multiple interlayer exciton (IX) energy bands. However, the correlations between these IXs remain elusive. Here, we demonstrate the cascade transitions between IXs in a moiré superlattice by performing energy- and time-resolved photoluminescence measurements in the MoS_{2}/WSe_{2} heterostructure. Furthermore, we show that the lower-energy IX can be excited to higher-energy ones, facilitating IX population inversion. Our finding of cascade transitions between IXs contributes to the fundamental understanding of the IX dynamics in moiré superlattices and may have important applications, such as in exciton condensate, quantum information protocols, and quantum cascade lasers.

Breaking Rotational Symmetry in Supertwisted WS2 Spirals via Moiré Magnification of Intrinsic Heterostrain

Twisted stacking of van der Waals materials with moiré superlattices offers a new way to tailor their physical properties via engineering of the crystal symmetry. Unlike well-studied twisted bilayers, little is known about the overall symmetry and symmetry-driven physical properties of continuously supertwisted multilayer structures. Here, using polarization-resolved second harmonic generation (SHG) microscopy, we report threefold (C₃) rotational symmetry breaking in supertwisted WS₂ spirals grown on non-Euclidean surfaces, contrasting the intact symmetry of individual monolayers. This symmetry breaking is attributed to a geometrical magnifying effect in which small relative strain between adjacent twisted layers (heterostrain), verified by Raman spectroscopy and multiphysics simulations, generates significant distortion in the moiré pattern. Density-functional theory calculations can explain the C₃ symmetry breaking and unusual SHG response by the interlayer wave function coupling. These findings thus pave the way for further developments in the so-called "3D twistronics".

Thickness- and Twist-Angle-Dependent Interlayer Excitons in Metal Monochalcogenide Heterostructures

Interlayer excitons, or bound electron-hole pairs whose constituent quasiparticles are located in distinct stacked semiconducting layers, are being intensively studied in heterobilayers of two-dimensional semiconductors. They owe their existence to an intrinsic type-II band alignment between both layers that convert these into p-n junctions. Here, we unveil a pronounced interlayer exciton (IX) in heterobilayers of metal monochalcogenides, namely, γ-InSe on ε-GaSe, whose pronounced emission is adjustable just by varying their thicknesses given their number of layers dependent direct band gaps. Time-dependent photoluminescense spectroscopy unveils considerably longer interlayer exciton lifetimes with respect to intralayer ones, thus confirming their nature. The linear Stark effect yields a bound electron-hole pair whose separation d is just (3.6 ± 0.1) Å with d being very close to d_Se = 3.4 Å which is the calculated interfacial Se separation. The envelope of IX is twist-angle-dependent and describable by superimposed emissions that are nearly equally spaced in energy, as if quantized due to localization induced by the small moiré periodicity. These heterostacks are characterized by extremely flat interfacial valence bands making them prime candidates for the observation of magnetism or other correlated electronic phases upon carrier doping.

Distinctive g-Factor of Moiré-Confined Excitons in van der Waals Heterostructures

We investigated the valley Zeeman splitting of excitonic peaks in the microphotoluminescence (μPL) spectra of high-quality hBN/WS₂/MoSe₂/hBN heterostructures under perpendicular magnetic fields up to 20 T. We identify two neutral exciton peaks in the μPL spectra; the lower-energy peak exhibits a reduced g-factor relative to that of the higher energy peak and much lower than the recently reported values for interlayer excitons in other van der Waals (vdW) heterostructures. We provide evidence that such a discernible g-factor stems from the spatial confinement of the exciton in the potential landscape created by the moiré pattern due to lattice mismatch or interlayer twist in heterobilayers. This renders magneto-μPL an important tool to reach a deeper understanding of the effect of moiré patterns on excitonic confinement in vdW heterostructures.

Raman Fingerprint of Interlayer Coupling in 2D TMDCs

Vertical stacking of two-dimensional (2D) homo- and heterostructures are intriguing research objects, as they are essential for fundamental studies and a key towards 2D device applications. It is paramount to understand the interlayer coupling in 2D materials and to find a fast yet precise characteristic signature. In this work, we report on a Raman fingerprint of interlayer coupling in 2D transition metal dichalcogenides (TMDCs). We observed that the out-of-plane B2g vibrational mode is absent when two monolayers form a vertical stack yet remain uncoupled but emerges after strong coupling. Using systematic Raman, photoluminescence (PL), and atomic force microscopy (AFM) studies of WSe2/WSe2 homo-bilayers and MoSe2/WSe2 hetero-bilayers, we conclude that the B2g vibrational mode is a distinct Raman fingerprint of interlayer coupling in 2D TMDCs. Our results propose an easy, fast, precise, and reliable measure to evaluate the interlayer coupling in 2D TMDCs.

Valley Relaxation of the Moiré Excitons in a WSe2/MoSe2 Heterobilayer

The moiré superlattice consisting of lattice- or angular-mismatched van der Waals heterostructures drastically changes the physical properties of constituent atomically thin materials by confinement of the exciton by the moiré potential, which is promising for next-generation quantum optics. The moiré superlattice also affects the valley degrees of freedom of the monolayer transition-metal dichalcogenides (TMDs) and the valley-dependent optical selection rule, which results in the characteristic circular polarized light emission of the moiré exciton. However, the valley relaxation process of excitons in the moiré superlattice remains to be understood. Here, we studied valley relaxation of moiré excitons in a twisted WSe₂/MoSe₂ heterobilayer by circularly polarized photoluminescence and photoluminescence excitation (PLE) spectroscopy. The experimentally observed circularly polarized emission strongly depends on the excitation power density, which contrasts with the case of two-dimensional monolayer TMDs. The excitation power-dependent circularly polarized emission suggests the characteristic valley relaxation of the moiré exciton with a small density of states in zero-dimensional systems. In addition, the resonant PLE measurement reveals the intravalley relaxation process from the triplet to singlet state of the moiré exciton via Γ₅ phonon emission. Our findings clarified the valley relaxation of the moiré excitons, which would lead to the application of the circularly polarized quantum light emitter in twisted semiconducting heterobilayers.

Emergent Moiré Phonons Due to Zone Folding in WSe2-WS2 Van der Waals Heterostructures

Bilayers of 2D materials offer opportunities for creating devices with tunable electronic, optical, and mechanical properties. In van der Waals heterostructures (vdWHs) where the constituent monolayers have different lattice constants, a moiré superlattice forms with a length scale larger than the lattice constant of either constituent material regardless of twist angle. Here, we report the appearance of moiré Raman modes from nearly aligned WSe₂-WS₂ vdWHs in the range of 240-260 cm^-1, which are absent in both monolayers and homobilayers of WSe₂ and WS₂ and in largely misaligned WSe₂-WS₂ vdWHs. Using first-principles calculations and geometric arguments, we show that these moiré Raman modes are a consequence of the large moiré length scale, which results in zone-folded phonon modes that are Raman active. These modes are sensitive to changes in twist angle, but notably, they occur at identical frequencies for a given small twist angle away from either the 0-degree or 60-degree aligned heterostructure. Our measurements also show a strong Raman intensity modulation in the frequency range of interest, with near 0 and near 60-degree vdWHs exhibiting a markedly different dependence on excitation energy. In near 0-degree aligned WSe₂-WS₂ vdWHs, a nearly complete suppression of both the moiré Raman modes and the WSe₂ A_1g Raman mode (∼250 cm^-1) is observed when exciting with a 532 nm CW laser at room temperature. Temperature-dependent reflectance contrast measurements demonstrate the significant Raman intensity modulation arises from resonant Raman effects.

Criterion for photonic topological transition in two-dimensional heterostructures

The anisotropic van der Waals material α-MoO₃ has recently attracted considerable attention because of the ability to support ellipse and hyperbolic phonon polaritons with extreme field confinement and long lifetimes, which can be used in topological transition and transformation polaritonics. However, the dispersion theory of some phonon polaritons in complex heterojunctions often requires tedious computation, which makes it difficult to simply judge and analyze the physical process of the photonic topological transition. Here we obtain the equivalent permittivity distribution of two-dimensional (2D) heterostructures by the effective medium theory and analyze the rotation-induced topological transitions and stack-dependent topological transitions of phonon polaritons. Unlike the previous discussion, we can predict the topological transition points by a parameter ɛ_x/y(i.e., the permittivity ratio along the in-plane crystal axis of the equivalent medium) and design precisely the phonon polaritons in the stacked materials by controlling the equivalent permittivity after simple calculation. The feasibility of the effective medium theory is verified based on the 2D approximation model and the non-2D approximation model under the limit of an ultrathin slab. Meanwhile, we compare the field distributions and dispersions of the 2D heterostructures and the corresponding equivalent structure. The simulation suggests that the elliptic/hyperbolic responses of the stacked materials depend on the sign of ɛ_x/y. The new, to the best of our knowledge, method not only provides an easier and clearer criterion for the study of photonic topological transition in anisotropic polaritons, but also shows great potential in designing some multilayer 2D heterostructures.

Enhanced interactions of interlayer excitons in free-standing heterobilayers

Strong, long-range dipole-dipole interactions between interlayer excitons (IXs) can lead to new multiparticle correlation regimes^1,2, which drive the system into distinct quantum and classical phases^2-5, including dipolar liquids, crystals and superfluids. Both repulsive and attractive dipole-dipole interactions have been theoretically predicted between IXs in a semiconductor bilayer^2,6-8, but only repulsive interactions have been reported experimentally so far^3,9-16. This study investigated free-standing, twisted (51°, 53°, 45°) tungsten diselenide/tungsten disulfide (WSe₂/WS₂) heterobilayers, in which we observed a transition in the nature of dipolar interactions among IXs, from repulsive to attractive. This was caused by quantum-exchange-correlation effects, leading to the appearance of a robust interlayer biexciton phase (formed by two IXs), which has been theoretically predicted^6-8 but never observed before in experiments. The reduced dielectric screening in a free-standing heterobilayer not only resulted in a much higher formation efficiency of IXs, but also led to strongly enhanced dipole-dipole interactions, which enabled us to observe the many-body correlations of pristine IXs at the two-dimensional quantum limit. In addition, we firstly observed several emission peaks from moiré-trapped IXs at room temperature in a well-aligned, free-standing WSe₂/WS₂ heterobilayer. Our findings open avenues for exploring new quantum phases with potential for applications in non-linear optics.

Tuning moiré excitons in Janus heterobilayers for high-temperature Bose-Einstein condensation

Using first-principles calculations, we predict that moiré excitons in twisted Janus heterobilayers could realize tunable and high-temperature Bose-Einstein condensation (BEC). The electric dipole in the Janus heterobilayers leads to charge-transfer interlayer and intralayer moiré excitons with exceptionally long lifetimes, in the absence of spacer layers. The electric dipole is also expected to enhance exciton-exciton repulsions at high exciton densities and can modulate moiré potentials that trap excitons for their condensation. The key parameters for exciton condensation, including exciton Bohr radius, binding energy, effective mass, and critical Mott density, are examined as a function of the twist angle. Last, exciton phase diagrams for the Janus heterobilayers are constructed from which one can estimate the BEC (>100 K) and superfluid (~30 K) transition temperatures. In addition to indirect interlayer excitons, we find that direct intralayer excitons can also condense at high temperatures, consistent with experiments.

Magnetic moiré effects and two types of topological transition in a twisted-bilayer hyperbolic metasurface with double-split ring arrays

Moiré configurations have recently attracted much attention due to their ability to enhance photonic responses and manipulate surface waves in the subwavelength ranges. However, previous studies have usually been focused on natural hyperbolic materials with limitations on patterning procedures, controlling rotation angles, and merely manipulating electric surface plasmons. Here, we theoretically and numerically investigate a novel magnetic moiré hyperbolic metasurface in the terahertz region, which enables two types of topological transition and a plethora of unusual magnetic moiré effects (magnetic surface wave manipulation, dispersion engineering, magic angles, spacer-dependent topological transition, and local field enhancement). This work extends twistronics and moiré physics to the terahertz region and magnetic polaritons, with potential applications in quantum physics, energy transfer, and planarized magnetic plasmonic devices.

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.

An image interaction approach to quantum-phase engineering of two-dimensional materials

Tuning electrical, optical, and thermal material properties is central for engineering and understanding solid-state systems. In this scenario, atomically thin materials are appealing because of their sensitivity to electric and magnetic gating, as well as to interlayer hybridization. Here, we introduce a radically different approach to material engineering relying on the image interaction experienced by electrons in a two-dimensional material when placed in proximity of an electrically neutral structure. We theoretically show that electrons in a semiconductor atomic layer acquire a quantum phase resulting from the image potential induced by the presence of a neighboring periodic array of conducting ribbons, which in turn modifies the optical, electrical, and thermal properties of the monolayer, giving rise to additional interband optical absorption, plasmon hybridization, and metal-insulator transitions. Beyond its fundamental interest, material engineering based on the image interaction represents a disruptive approach to tailor the properties of atomic layers for application in nanodevices.

Observation of moiré excitons in the twisted WS2/WS2 homostructure

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

Intralayer charge-transfer moiré excitons in van der Waals superlattices

Moiré patterns of transition metal dichalcogenide heterobilayers have proved to be an ideal platform on which to host unusual correlated electronic phases, emerging magnetism and correlated exciton physics. Whereas the existence of new moiré excitonic states is established^1-4 through optical measurements, the microscopic nature of these states is still poorly understood, often relying on empirically fit models. Here, combining large-scale first-principles GW (where G and W denote the one-particle Green's function and the screened Coulomb interaction, respectively) plus Bethe-Salpeter calculations and micro-reflection spectroscopy, we identify the nature of the exciton resonances in WSe₂/WS₂ moiré superlattices, discovering a rich set of moiré excitons that cannot be captured by prevailing continuum models. Our calculations show moiré excitons with distinct characters, including modulated Wannier excitons and previously unidentified intralayer charge-transfer excitons. Signatures of these distinct excitonic characters are confirmed experimentally by the unique carrier-density and magnetic-field dependences of different moiré exciton resonances. Our study highlights the highly non-trivial exciton states that can emerge in transition metal dichalcogenide moiré superlattices, and suggests new ways of tuning many-body physics in moiré systems by engineering excited-states with specific spatial characters.

Molding Broadband Dispersion in Twisted Trilayer Hyperbolic Polaritonic Surfaces

Recent advancement in twisted layered metasurfaces can be employed to control the nanoscale flow of light, including the exotic hyperbolic-to-elliptic topological transitions in twisted bilayers (tBL). Such topological transitions can only occur to limited frequency ranges, restricted by the intrinsic in-plane dispersion of individual hyperbolic surfaces. Here, we report that, by controlling interlayer evanescent coupling in twisted polaritonic trilayers, moldable topological transitions of light can be achieved in broadband. We reveal that the required minimum open angle of the individual hyperbolic polaritonic surface for open-to-close topological transitions can be significantly lowered compared to that of the twisted bilayer counterpart. This increases the degree of freedom to enhance and control near-field light-matter interactions and energy management. As an example, we demonstrate a knob to manipulate near-field radiative heat transfer (NFRHT). By rotating the relative angles of trilayers, exotic and tunable thermal conductance can be achieved. Our findings enrich the controllability of light at the nanoscale in broadband, bringing twisted optical materials one step closer to practical applications.

One-Dimensional Strain Solitons Manipulated Superlubricity on Graphene Interface

The frictional properties of a uniaxial tensile strained graphene interface are studied using molecular dynamics simulations. A misfit interval statistical method (MISM) is applied to characterize the atomistic misfits at the interface and strain soliton pattern. During sliding along both armchair and zigzag directions, the lateral force depends on the ratio of graphene flake length (L) to strain soliton spacing (L_s) and becomes nearly zero when L is an integer multiple of 3L_s. Furthermore, the strain solitons propagate along the armchair sliding direction dynamically, while fission and fusion are repeatedly evidenced along the zigzag sliding direction. The underlying superlubric mechanism is revealed by a single-atom quasi-static model. The cancellation of lateral force for the contacting atoms exhibits a dynamic balance when sliding along the armchair direction but a quasi-static balance along the zigzag direction. A diagram of flake length with respect to tensile strain (L-ε) is proposed to predict the critical condition for the transition from nonsuperlubricity to superlubricity. Our results provide insights on the design of superlubric devices.

Uncovering Topological Edge States in Twisted Bilayer Graphene

Twisted bilayer graphene (t-BLG) has recently been introduced as a rich physical platform displaying flat electronic bands, strongly correlated states, and unconventional superconductivity. Studies have hinted at an unusual Z₂ topology of the moiré Dirac bands of t-BLG. However, direct experimental evidence of this moiré band topology and associated edge states is still lacking. Herein, using superconducting quantum interferometry, we reconstructed the spatial supercurrent distribution in t-BLG Josephson junctions and revealed the presence of edge states located in the superlattice band gaps. The absence of edge conduction in high resistance regions just outside the superlattice band gap confirms that the edge transport originates from the filling of electronic states located inside the band gap and further allows us to exclude several other edge conduction mechanisms. These results confirm the unusual moiré band topology of twisted bilayer graphene and will stimulate further research to explore its consequences.

Deep Quantum-Dot Arrays in Moiré Superlattices of Non-van der Waals Materials

Recently, moiré superlattices of twisted van der Waals (vdW) materials have attracted substantial interest due to their strongly correlated properties. However, the vdW interlayer interaction is intrinsically weak, such that many desired properties can only exist at low temperature. Here, we theoretically predict some unusual properties stemming from the chemical bonding between twisted PbS nanosheets as an example of non-vdW moiré superlattices. The strong interlayer coupling in such systems results in giant strain vortices and dipole vortices at the interface. The modified electronic structures become a series of dispersionless bands and artificial-atom states. In real space, these states are analogous to arrays of well-positioned quantum dots, which may be promising for use in single-electron devices. In theory, if the materials are doped with a low concentration of electrons, a Wigner crystal will form even without any magnetic field. To confirm the accessibility and stability of non-vdW moiré superlattices in experiment, we synthesized PbS moiré superlattices with different twist angles. Our transmission-electron-microscope observations reveal the resemblance of the small-angle-twisted structures with the square matrices of quantum dots, which is in good accordance with our calculations.