Broken mirror symmetry in excitonic response of reconstructed domains in twisted MoSe2/MoSe2 bilayers

Excitonic signatures of ferroelectric order in parallel-stacked MoS2

Interfacial ferroelectricity, prevalent in various parallel-stacked layered materials, allows switching of out-of-plane ferroelectric order by in-plane sliding of adjacent layers. Its resilience against doping potentially enables next-generation storage and logic devices. However, studies have been limited to indirect sensing or visualization of ferroelectricity. For transition metal dichalcogenides, there is little knowledge about the influence of ferroelectric order on their intrinsic valley and excitonic properties. Here, we report direct probing of ferroelectricity in few-layer 3R-MoS2 using reflectance contrast spectroscopy. Contrary to a simple electrostatic perception, layer-hybridized excitons with out-of-plane electric dipole moment remain decoupled from ferroelectric ordering, while intralayer excitons with in-plane dipole orientation are sensitive to it. Ab initio calculations identify stacking-specific interlayer hybridization leading to this asymmetric response. Exploiting this sensitivity, we demonstrate optical readout and control of multi-state polarization with hysteretic switching in a field-effect device. Time-resolved Kerr ellipticity reveals direct correspondence between spin-valley dynamics and stacking order.

Synthesis, Modulation, and Application of Two-Dimensional TMD Heterostructures

Two-dimensional (2D) transition metal dichalcogenide (TMD) heterostructures have attracted a lot of attention due to their rich material diversity and stack geometry, precise controllability of structure and properties, and potential practical applications. These heterostructures not only overcome the inherent limitations of individual materials but also enable the realization of new properties through appropriate combinations, establishing a platform to explore new physical and chemical properties at micro-nano-pico scales. In this review, we systematically summarize the latest research progress in the synthesis, modulation, and application of 2D TMD heterostructures. We first introduce the latest techniques for fabricating 2D TMD heterostructures, examining the rationale, mechanisms, advantages, and disadvantages of each strategy. Furthermore, we emphasize the importance of characteristic modulation in 2D TMD heterostructures and discuss some approaches to achieve novel functionalities. Then, we summarize the representative applications of 2D TMD heterostructures. Finally, we highlight the challenges and future perspectives in the synthesis and device fabrication of 2D TMD heterostructures and provide some feasible solutions.

Heterostrain-Induced Zeeman-like Splitting in h-BN-Encapsulated Bilayer WSe2

Heterostrain is predicted to induce exceptionally rich physics in atomically thin two-dimensional structures by modifying the symmetry and optical selection rules. In this work, we introduce heterostrain into WSe2 bilayers by combining h-BN encapsulation and high-temperature vacuum annealing. Nonvolatile heterostrain gives rise to a Zeeman-like splitting associated with the elliptically polarized optical emission of interlayer K-K excitons. Further manipulation of the interlayer exciton emission in an external magnetic field reveals that the Zeeman-like splitting cannot be eliminated even in a magnetic field of up to ±6 T. We propose a microscopic picture with respect to the layer and valley pseudospin to interpret the results. Our findings imply an intriguing way to encode binary information with the layer pseudospin enabled by the heterostrain and open a venue for manipulating the layer pseudospin with heterostrain engineering, optical pseudospin injection, and an external magnetic field.

Manipulation of Moiré Superlattice in Twisted Monolayer-multilayer Graphene by Moving Nanobubbles

In the heterostructure of two-dimensional (2D) materials, many novel physics phenomena are strongly dependent on the Moiré superlattice. How to achieve the continuous manipulation of the Moiré superlattice in the same sample is very important to study the evolution of various physical properties. Here, in minimally twisted monolayer-multilayer graphene, we found that bubble-induced strain has a huge impact on the Moiré superlattice. By employing the AFM tip to dynamically and continuously move the nanobubble, we realized the modulation of the Moiré superlattice, like the evolution of regular triangular domains into long strip domain structures with single or double domain walls. We also achieved controllable modulation of the Moiré superlattice by moving multiple nanobubbles and establishing the coupling of nanobubbles. Our work presents a flexible method for continuous and controllable manipulation of Moiré superlattices, which will be widely used to study novel physical properties in 2D heterostructures.

Electrical Control and Transport of Tightly Bound Interlayer Excitons in a MoSe_{2}/hBN/MoSe_{2} Heterostructure

Controlling interlayer excitons in Van der Waals heterostructures holds promise for exploring Bose-Einstein condensates and developing novel optoelectronic applications, such as excitonic integrated circuits. Despite intensive studies, several key fundamental properties of interlayer excitons, such as their binding energies and interactions with charges, remain not well understood. Here we report the formation of momentum-direct interlayer excitons in a high-quality MoSe_{2}/hBN/MoSe_{2} heterostructure under an electric field, characterized by bright photoluminescence (PL) emission with high quantum yield and a narrow linewidth of less than 4 meV. These interlayer excitons show electrically tunable emission energy spanning ∼180  meV through the Stark effect, and exhibit a sizable binding energy of ∼81  meV in the intrinsic regime, along with trion binding energies of a few millielectronvolts. Remarkably, we demonstrate the long-range transport of interlayer excitons with a characteristic diffusion length exceeding 10  μm, which can be attributed, in part, to their dipolar repulsive interactions. Spatially and polarization-resolved spectroscopic studies reveal rich exciton physics in the system, such as valley polarization, local trapping, and the possible existence of dark interlayer excitons. The formation and transport of tightly bound interlayer excitons with narrow linewidth, coupled with the ability to electrically manipulate their properties, open exciting new avenues for exploring quantum many-body physics, including excitonic condensate and superfluidity, and for developing novel optoelectronic devices, such as exciton and photon routers.

Phase Engineering of Nanomaterials: Transition Metal Dichalcogenides

Crystal phase, a critical structural characteristic beyond the morphology, size, dimension, facet, etc., determines the physicochemical properties of nanomaterials. As a group of layered nanomaterials with polymorphs, transition metal dichalcogenides (TMDs) have attracted intensive research attention due to their phase-dependent properties. Therefore, great efforts have been devoted to the phase engineering of TMDs to synthesize TMDs with controlled phases, especially unconventional/metastable phases, for various applications in electronics, optoelectronics, catalysis, biomedicine, energy storage and conversion, and ferroelectrics. Considering the significant progress in the synthesis and applications of TMDs, we believe that a comprehensive review on the phase engineering of TMDs is critical to promote their fundamental studies and practical applications. This Review aims to provide a comprehensive introduction and discussion on the crystal structures, synthetic strategies, and phase-dependent properties and applications of TMDs. Finally, our perspectives on the challenges and opportunities in phase engineering of TMDs will also be discussed.

Resonant Tunneling-Enhanced Photoresponsivity in a Twisted Graphene van der Waals Heterostructure

Leveraging its ultrahigh carrier mobility, zero-bandgap linear dispersion, and extremely short response time, graphene exhibits remarkable potential in ultrafast broad-band photodetection. Nonetheless, the inherently low responsivity of graphene photodetectors, due to the low photogenerated carrier density, significantly impedes the development of practical devices. In this study, we present an improved photoresponse within a graphene-hexagonal boron nitride-graphene vertical tunnel junction device, where the crystallographic orientation of the two graphene electrodes is aligned. Through meticulous device structure design and the adjustment of bias and gate voltages, we observe a 2 orders of magnitude increase in tunneling photocurrent, which is attributed to the momentum-conserving resonant electron tunneling. The enhanced external photoresponsivity is evident across a wide temperature and spectral range and achieves 0.7 A/W for visible light excitation. This characteristic, coupled with the device's negative differential conductance, suggests a novel avenue for highly efficient photodetection and high-frequency, logic-based optoelectronics using van der Waals heterostructures.

Non-volatile electrical polarization switching via domain wall release in 3R-MoS2 bilayer

Understanding the nature of sliding ferroelectricity is of fundamental importance for the discovery and application of two-dimensional ferroelectric materials. In this work, we investigate the phenomenon of switchable polarization in a bilayer MoS2 with natural rhombohedral stacking, where the spontaneous polarization is coupled with excitonic effects through asymmetric interlayer coupling. Using optical spectroscopy and imaging techniques, we observe how a released domain wall switches the polarization of a large single domain. Our results highlight the importance of domain walls in the polarization switching of non-twisted rhombohedral transition metal dichalcogenides and open new opportunities for the non-volatile control of their optical response.

Competition of Moiré Network Sites to Form Electronic Quantum Dots in Reconstructed MoX2/WX2 Heterostructures

Twisted bilayers of two-dimensional semiconductors offer a versatile platform for engineering quantum states for charge carriers using moiré superlattice effects. Among the systems of recent interest are twistronic MoX2/WX2 heterostructures (X = Se or S), which undergo reconstruction into preferential stacking domains and highly strained domain wall networks, determining the electron/hole localization across moiré superlattices. Here, we present a catalogue of options for the formation of self-organized quantum dots and wires in lattice-reconstructed marginally twisted MoX2/WX2 bilayers with a relative lattice mismatch δ ≪ 1 for twist angles ranging from perfect alignment to θ ∼ 1°. On the basis of multiscale modeling taking into account twirling of domain wall networks, we analyze bilayers with both parallel and antiparallel orientations of their unit cells and describe crossovers between different positioning of band edges for electrons and holes across moiré superlattices when θ < δ and θ > δ.

Recent Strategies for the Synthesis of Phase-Pure Ultrathin 1T/1T' Transition Metal Dichalcogenide Nanosheets

The past few decades have witnessed a notable increase in transition metal dichalcogenide (TMD) related research not only because of the large family of TMD candidates but also because of the various polytypes that arise from the monolayer configuration and layer stacking order. The peculiar physicochemical properties of TMD nanosheets enable an enormous range of applications from fundamental science to industrial technologies based on the preparation of high-quality TMDs. For polymorphic TMDs, the 1T/1T' phase is particularly intriguing because of the enriched density of states, and thus facilitates fruitful chemistry. Herein, we comprehensively discuss the most recent strategies for direct synthesis of phase-pure 1T/1T' TMD nanosheets such as mechanical exfoliation, chemical vapor deposition, wet chemical synthesis, atomic layer deposition, and more. We also review frequently adopted methods for phase engineering in TMD nanosheets ranging from chemical doping and alloying, to charge injection, and irradiation with optical or charged particle beams. Prior to the synthesis methods, we discuss the configuration of TMDs as well as the characterization tools mostly used in experiments. Finally, we discuss the current challenges and opportunities as well as emphasize the promising fields for the future development.

Quantifying Strain in Moiré Superlattice

In twisted van der Waals (vdW) bilayers, intrinsic strain associated with the moiré superlattice and unintentionally introduced uniaxial strain may be present simultaneously. Both strains are able to lift the degeneracy of the E2g phonon modes in Raman spectra. Because of the different rotation symmetry of the two types of strain, the corresponding Raman intensity exhibits a distinct polarization dependence. We compare a 2.5° twisted MoS2 bilayer, in which the maximal intrinsic moiré strain is anticipated, and a natural MoS2 bilayer with an intentionally introduced uniaxial strain. By analyzing the frequency shift of the E2g doublet and their polarization dependence, we can not only determine the direction of unintentional uniaxial strain in the twisted bilayer but also quantify both strain components. This simple strain characterization method based on far-field Raman spectra will facilitate the studies of electronic properties of moiré superlattices under the influence of combined intrinsic and external strains.

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.

Tuning and exploiting interlayer coupling in two-dimensional van der Waals heterostructures

Two-dimensional (2D) layered materials can stack into new material systems, with van der Waals (vdW) interaction between the adjacent constituent layers. This stacking process of 2D atomic layers creates a new degree of freedom-interlayer interface between two adjacent layers-that can be independently studied and tuned from the intralayer degree of freedom. In such heterostructures (HSs), the physical properties are largely determined by the vdW interaction between the individual layers,i.e.interlayer coupling, which can be effectively tuned by a number of means. In this review, we summarize and discuss a number of such approaches, including stacking order, electric field, intercalation, and pressure, with both their experimental demonstrations and theoretical predictions. A comprehensive overview of the modulation on structural, optical, electrical, and magnetic properties by these four approaches are also presented. We conclude this review by discussing several prospective research directions in 2D HSs field, including fundamental physics study, property tuning techniques, and future applications.

Twirling and Spontaneous Symmetry Breaking of Domain Wall Networks in Lattice-Reconstructed Heterostructures of Two-Dimensional Materials

Lattice relaxation in twistronic bilayers with close lattice parameters and almost perfect crystallographic alignment of the layers results in the transformation of the moiré pattern into a sequence of preferential stacking domains and domain wall networks. Here, we show that reconstructed moiré superlattices of the perfectly aligned heterobilayers of same chalcogen transition metal dichalcogenides have broken-symmetry structures featuring twisted nodes ("twirls") of domain wall networks. The analysis of twist-angle dependence of strain characteristics for the broken-symmetry structures shows that the formation of twirl reduces the amount of hydrostatic strain around the nodes, potentially weakening their influence on the band edge energies of electrons and holes.

Visualizing moiré ferroelectricity via plasmons and nano-photocurrent in graphene/twisted-WSe2 structures

Ferroelectricity, a spontaneous and reversible electric polarization, is found in certain classes of van der Waals (vdW) materials. The discovery of ferroelectricity in twisted vdW layers provides new opportunities to engineer spatially dependent electric and optical properties associated with the configuration of moiré superlattice domains and the network of domain walls. Here, we employ near-field infrared nano-imaging and nano-photocurrent measurements to study ferroelectricity in minimally twisted WSe2. The ferroelectric domains are visualized through the imaging of the plasmonic response in a graphene monolayer adjacent to the moiré WSe2 bilayers. Specifically, we find that the ferroelectric polarization in moiré domains is imprinted on the plasmonic response of the graphene. Complementary nano-photocurrent measurements demonstrate that the optoelectronic properties of graphene are also modulated by the proximal ferroelectric domains. Our approach represents an alternative strategy for studying moiré ferroelectricity at native length scales and opens promising prospects for (opto)electronic devices.

Sequential order dependent dark-exciton modulation in bi-layered TMD heterostructure

We report the emergence of dark-excitons in transition-metal-dichalcogenide (TMD) heterostructures that strongly rely on the stacking sequence, i.e., momentum-dark K-Q exciton located exclusively at the top layer of the heterostructure. The feature stems from band renormalization and is distinct from those of typical neutral excitons or trions, regardless of materials, substrates, and even homogeneous bilayers, which is further confirmed by scanning tunneling spectroscopy. To understand the unusual stacking sequence, we introduce the excitonic Elliot formula by imposing strain exclusively on the top layer that could be a consequence of the stacking process. We further find that the intensity ratio of Q- to K-excitons in the same layer is inversely proportional to laser power, unlike for conventional K-K excitons. This can be a metric for engineering the intensity of dark K-Q excitons in TMD heterostructures, which could be useful for optical power switches in solar panels.

Operando electron microscopy investigation of polar domain dynamics in twisted van der Waals homobilayers

Conventional antiferroelectric materials with atomic-scale anti-aligned dipoles undergo a transition to a ferroelectric (FE) phase under strong electric fields. The moiré superlattice formed in the twisted stacks of van der Waals crystals exhibits polar domains alternating in moiré length with anti-aligned dipoles. In this moiré domain antiferroelectic (MDAF) arrangement, the distribution of electric dipoles is distinguished from that of two-dimensional FEs, suggesting dissimilar domain dynamics. Here we performed an operando transmission electron microscopy investigation on twisted bilayer WSe2 to observe the polar domain dynamics in real time. We find that the topological protection, provided by the domain wall network, prevents the MDAF-to-FE transition. As one decreases the twist angle, however, this transition occurs as the domain wall network disappears. Exploiting stroboscopic operando transmission electron microscopy on the FE phase, we measure a maximum domain wall velocity of 300 μm s-1. Domain wall pinnings by various disorders limit the domain wall velocity and cause Barkhausen noises in the polarization hysteresis loop. Atomic-scale analysis of the pinning disorders provides structural insight on how to improve the switching speed of van der Waals FEs.

Programming correlated magnetic states with gate-controlled moiré geometry

The ability to control the underlying lattice geometry of a system may enable transitions between emergent quantum ground states. Here, we report in-situ gate switching between honeycomb and triangular lattice geometries of an electron many-body Hamiltonian in R-stacked MoTe₂ moiré bilayers, resulting in switchable magnetic exchange interactions. At zero electric field, we observe a correlated ferromagnetic insulator near one hole per moiré unit cell with a widely tunable Curie temperature up to 14K. Applying an electric field switches the system into a half-filled triangular lattice with antiferromagnetic interactions; further doping this layer-polarized superlattice tunes the antiferromagnetic exchange interaction back to ferromagnetic. Our work demonstrates R-stacked MoTe₂ moirés to be a laboratory for engineering correlated states with nontrivial topology.

Excitons in mesoscopically reconstructed moiré heterostructures

Moiré effects in vertical stacks of two-dimensional crystals give rise to new quantum materials with rich transport and optical phenomena that originate from modulations of atomic registries within moiré supercells. Due to finite elasticity, however, the superlattices can transform from moiré-type to periodically reconstructed patterns. Here we expand the notion of such nanoscale lattice reconstruction to the mesoscopic scale of laterally extended samples and demonstrate rich consequences in optical studies of excitons in MoSe₂-WSe₂ heterostructures with parallel and antiparallel alignments. Our results provide a unified perspective on moiré excitons in near-commensurate semiconductor heterostructures with small twist angles by identifying domains with exciton properties of distinct effective dimensionality, and establish mesoscopic reconstruction as a compelling feature of real samples and devices with inherent finite size effects and disorder. Generalized to stacks of other two-dimensional materials, this notion of mesoscale domain formation with emergent topological defects and percolation networks will instructively expand the understanding of fundamental electronic, optical and magnetic properties of van der Waals heterostructures.

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.

Sliding ferroelectricity in van der Waals layered γ-InSe semiconductor

Two-dimensional (2D) van-der-Waals (vdW) layered ferroelectric semiconductors are highly desired for in-memory computing and ferroelectric photovoltaics or detectors. Beneficial from the weak interlayer vdW-force, controlling the structure by interlayer twist/translation or doping is an effective strategy to manipulate the fundamental properties of 2D-vdW semiconductors, which has contributed to the newly-emerging sliding ferroelectricity. Here, we report unconventional room-temperature ferroelectricity, both out-of-plane and in-plane, in vdW-layered γ-InSe semiconductor triggered by yttrium-doping (InSe:Y). We determine an effective piezoelectric constant of ∼7.5 pm/V for InSe:Y flakes with thickness of ∼50 nm, about one order of magnitude larger than earlier reports. We directly visualize the enhanced sliding switchable polarization originating from the fantastic microstructure modifications including the stacking-faults elimination and a subtle rhombohedral distortion due to the intralayer compression and continuous interlayer pre-sliding. Our investigations provide new freedom degrees of structure manipulation for intrinsic properties in 2D-vdW-layered semiconductors to expand ferroelectric candidates for next-generation nanoelectronics.

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.

Ultrafast response of spontaneous photovoltaic effect in 3R-MoS2-based heterostructures

Rhombohedrally stacked MoS₂ has been shown to exhibit spontaneous polarization down to the bilayer limit and can sustain a strong depolarization field when sandwiched between graphene. Such a field gives rise to a spontaneous photovoltaic effect without needing any p-n junction. In this work, we show that the photovoltaic effect has an external quantum efficiency of 10% for devices with only two atomic layers of MoS₂ at low temperatures, and identify a picosecond-fast photocurrent response, which translates to an intrinsic device bandwidth at ∼100-GHz level. To this end, we have developed a nondegenerate pump-probe photocurrent spectroscopy technique to deconvolute the thermal and charge-transfer processes, thus successfully revealing the multicomponent nature of the photocurrent dynamics. The fast component approaches the limit of the charge-transfer speed at the graphene-MoS₂ interface. The remarkable efficiency and ultrafast photoresponse in the graphene-3R-MoS₂ devices support the use of ferroelectric van der Waals materials for future high-performance optoelectronic applications.

Cumulative polarization in conductive interfacial ferroelectrics

Ferroelectricity in atomically thin bilayer structures has been recently predicted¹ and measured^2-4 in two-dimensional materials with hexagonal non-centrosymmetric unit-cells. The crystal symmetry translates lateral shifts between parallel two-dimensional layers to sign changes in their out-of-plane electric polarization, a mechanism termed 'slide-tronics'⁴. These observations have been restricted to switching between only two polarization states under low charge carrier densities^5-12, limiting the practical application of the revealed phenomena¹³. To overcome these issues, one should explore the nature of polarization in multi-layered van der Waals stacks, how it is governed by intra- and interlayer charge redistribution and to what extent it survives the addition of mobile charge carriers¹⁴. To explore these questions, we conduct surface potential measurements of parallel WSe₂ and MoS₂ multi-layers with aligned and anti-aligned configurations of the polar interfaces. We find evenly spaced, nearly decoupled potential steps, indicating highly confined interfacial electric fields that provide a means to design multi-state 'ladder-ferroelectrics'. Furthermore, we find that the internal polarization remains notable on electrostatic doping of mobile charge carrier densities as high as 10¹³ cm^-2, with substantial in-plane conductivity. Using density functional theory calculations, we trace the extra charge redistribution in real and momentum spaces and identify an eventual doping-induced depolarization mechanism.

Capacitively and Inductively Coupled Excitons in Bilayer MoS_{2}

The coupling of intralayer A and B excitons and interlayer excitons (IE) is studied in a two-dimensional semiconductor, homobilayer MoS_{2}. It is shown that the measured optical susceptibility reveals both the magnitude and the phase of the coupling constants. The IE and B excitons couple via a 0-phase (capacitive) coupling; the IE and A excitons couple via a π-phase (inductive) coupling. The IE-B and IE-A coupling mechanisms are interpreted as hole tunneling and electron-hole exchange, respectively. The couplings imply that even in a monolayer, the A and B excitons have mixed spin states. Using the IE as a sensor, the A-B intravalley exchange coupling is determined. Finally, we realize a bright and highly tunable lowest-energy momentum-direct exciton at high electric fields.

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

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

Electrically Tunable Localized versus Delocalized Intralayer Moiré Excitons and Trions in a Twisted MoS2 Bilayer

Moiré superlattice (mSL)-induced sub-bands in twisted van der Waals homo- and heterostructures govern their optical and electrical properties, rendering additional degrees of freedom such as twist angle. Here, we demonstrate the moiré superlattice effects on the intralayer excitons and trions in a twisted bilayer of MoS₂ of H-type stacking at marginal twist angles. We identify the emissions from localized and delocalized sub-bands of intralayer moiré excitons and show their electrical modulation by the corresponding trion formation. The electrical control of the oscillator strength of the moiré excitons also results in the strong tunability of resonant Raman scattering. We find that the gate-induced doping significantly modulates the electronic moiré potential; however, leaves the excitonic moiré confinement unaltered. This effect, coupled with variable moiré trap filling by tuning the optical excitation density, allows us to delineate the different phases of localized and delocalized moiré trions. We demonstrate that the moiré excitons exhibit strong valley coherence that changes in a striking nonmonotonic W-shape with gating due to motional narrowing. These observations from the simultaneous electrostatic control of quasiparticle-dependent moiré potential will lead to exciting effects of tunable many-body phenomena in moiré superlattices.

Dynamic Tuning of Moiré Superlattice Morphology by Laser Modification

In artificial van der Waals (vdW) layered devices, twisting the stacking angle has emerged as an effective strategy to regulate the electronic phases and optical properties of these systems. Along with the twist registry, the lattice reconstruction arising from vdW interlayer interaction has also inspired significant research interests. The control of twist angles is significantly important because the moiré periodicity determines the electron propagation length on the lattice and the interlayer electron-electron interactions. However, the moiré periodicity is hard to be modified after the device has been fabricated. In this work, we have demonstrated that the moiré periodicity can be precisely modulated with a localized laser annealing technique. This is achieved with regulating the interlayer lattice mismatch by the mismatched lattice constant, which originates from the variable density of sulfur vacancy generated during laser modification. The existence of sulfur vacancy is further verified by excitonic emission energy and lifetime in photoluminescence measurements. Furthermore, we also discover that the mismatched lattice constant has the equivalent contribution as the twist angle for determining the lattice mismatch. Theoretical modeling elaborates the moiré-wavelength-dependent energy variations at the interface and mimics the evolution of moiré morphology.

Interfacial ferroelectricity in marginally twisted 2D semiconductors

Twisted heterostructures of two-dimensional crystals offer almost unlimited scope for the design of new metamaterials. Here we demonstrate a room temperature ferroelectric semiconductor that is assembled using mono- or few-layer MoS₂. These van der Waals heterostructures feature broken inversion symmetry, which, together with the asymmetry of atomic arrangement at the interface of two 2D crystals, enables ferroelectric domains with alternating out-of-plane polarization arranged into a twist-controlled network. The last can be moved by applying out-of-plane electrical fields, as visualized in situ using channelling contrast electron microscopy. The observed interfacial charge transfer, movement of domain walls and their bending rigidity agree well with theoretical calculations. Furthermore, we demonstrate proof-of-principle field-effect transistors, where the channel resistance exhibits a pronounced hysteresis governed by pinning of ferroelectric domain walls. Our results show a potential avenue towards room temperature electronic and optoelectronic semiconductor devices with built-in ferroelectric memory functions.

Interfacial ferroelectricity in rhombohedral-stacked bilayer transition metal dichalcogenides

van der Waals materials have greatly expanded our design space of heterostructures by allowing individual layers to be stacked at non-equilibrium configurations, for example via control of the twist angle. Such heterostructures not only combine characteristics of the individual building blocks, but can also exhibit physical properties absent in the parent compounds through interlayer interactions¹. Here we report on a new family of nanometre-thick, two-dimensional (2D) ferroelectric semiconductors, where the individual constituents are well-studied non-ferroelectric monolayer transition metal dichalcogenides (TMDs), namely WSe₂, MoSe₂, WS₂ and MoS₂. By stacking two identical monolayer TMDs in parallel, we obtain electrically switchable rhombohedral-stacking configurations, with out-of-plane polarization that is flipped by in-plane sliding motion. Fabricating nearly parallel-stacked bilayers enables the visualization of moiré ferroelectric domains as well as electric field-induced domain wall motion with piezoelectric force microscopy. Furthermore, by using a nearby graphene electronic sensor in a ferroelectric field transistor geometry, we quantify the ferroelectric built-in interlayer potential, in good agreement with first-principles calculations. The new semiconducting ferroelectric properties of these four new TMDs opens up the possibility of studying the interplay between ferroelectricity and their rich electric and optical properties^2-5.

Electrically Switchable Intervalley Excitons with Strong Two-Phonon Scattering in Bilayer WSe2

We report the observation of QΓ intervalley exciton in bilayer WSe₂ devices encapsulated by boron nitride. The QΓ exciton resides at ∼18 meV below the QK exciton. The QΓ and QK excitons exhibit different Stark shifts under an out-of-plane electric field due to their different interlayer dipole moments. By controlling the electric field, we can switch their energy ordering and control which exciton dominates the luminescence of bilayer WSe₂. Remarkably, both QΓ and QK excitons exhibit unusually strong two-phonon replicas, which are comparable to or even stronger than the one-phonon replicas. By detailed theoretical simulation, we reveal the existence of numerous (≥14) two-phonon scattering paths involving (nearly) resonant exciton-phonon scattering in bilayer WSe₂. To our knowledge, such electric-field-switchable intervalley excitons with strong two-phonon replicas have not been found in any other two-dimensional semiconductors. These make bilayer WSe₂ a distinctive valleytronic material with potential novel applications.

Excitons in semiconductor moiré superlattices

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

A Scalable Network Model for Electrically Tunable Ferroelectric Domain Structure in Twistronic Bilayers of Two-Dimensional Semiconductors

Moiré structures in small-angle-twisted bilayers of two-dimensional (2D) semiconductors with a broken-symmetry interface form arrays of ferroelectric (FE) domains with periodically alternating out-of-plane polarization. Here, we propose a network theory for the tunability of such FE domain structure by applying an electric field perpendicular to the 2D crystal. Using multiscale analysis, we derive a fully parametrized string-theory-like description of the domain wall network (DWN) and show that it undergoes a qualitative change, after the arcs of partial dislocation (PD) like domain walls merge (near the network nodes) into streaks of perfect screw dislocations (PSD), which happens at a threshold displacement field dependent on the DWN period.

Optomechanical Properties of MoSe2 Nanosheets as Revealed by In Situ Transmission Electron Microscopy

Free-standing few-layered MoSe₂ nanosheet stacks optoelectronic signatures are analyzed by using light compatible in situ transmission electron microscopy (TEM) utilizing an optical TEM holder allowing for the simultaneous mechanical deformation, electrical probing and light illumination of a sample. Two types of deformation, namely, (i) bending of nanosheets perpendicular to their basal atomic planes and (ii) edge deformation parallel to the basal atomic planes, lead to two distinctly different optomechanical performances of the nanosheet stacks. The former deformation induces a stable but rather marginal increase in photocurrent, whereas the latter mode is prone to unstable nonsystematic photocurrent value changes and a red-shifted photocurrent spectrum. The experimental results are verified by ab initio calculations using density functional theory (DFT).

Emergence and Tuning of Multiple Flat Bands in Twisted Bilayer γ-Graphyne

Using twisted bilayer γ-graphyne (TBGY) as an example, we show that it is possible to create multiple flat bands in carbon allotropes without the requirement of a specified magic angle. The origin of the flat bands can be understood by a simple two-level coupling model. The narrow bandwidth and strong localization of the flat band states might lead to strong correlation effects, which make TBGY a good platform for studying correlation physics. On the basis of the two-level coupling model, we further propose that the width and extent of localization of flat bands can be tuned by an energy mismatch ΔE between the two layers of TBGY, which can be realized by either applying a perpendicular electric field or introducing a heterostrain. This allows continuous modulation of TBGY from the strong-correlation regime to the medium- or weak-correlation regime, which could be utilized to study the quantum phase transition.

Topology and geometry under the nonlinear electromagnetic spotlight

For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their wavefunctions. A key challenge is to identify and implement experiments that probe or control these quantum properties. In this Review, we describe recent progress in this direction, focusing on nonlinear electromagnetic responses that arise directly from quantum geometry and topology. We give an overview of the field by discussing theoretical ideas, experiments and the materials that drive them. We conclude by discussing how these techniques can be combined with device architectures to uncover, probe and ultimately control quantum phases with emergent topological and correlated properties.

Direct visualization of magnetic domains and moiré magnetism in twisted 2D magnets

[Figure: see text].

Moiré trions in MoSe2/WSe2 heterobilayers

Transition metal dichalcogenide moiré bilayers with spatially periodic potentials have emerged as a highly tunable platform for studying both electronic^1-6 and excitonic^4,7-13 phenomena. The power of these systems lies in the combination of strong Coulomb interactions with the capability of controlling the charge number in a moiré potential trap. Electronically, exotic charge orders at both integer and fractional fillings have been discovered^2,5. However, the impact of charging effects on excitons trapped in moiré potentials is poorly understood. Here, we report the observation of moiré trions and their doping-dependent photoluminescence polarization in H-stacked MoSe₂/WSe₂ heterobilayers. We find that as moiré traps are filled with either electrons or holes, new sets of interlayer exciton photoluminescence peaks with narrow linewidths emerge about 7 meV below the energy of the neutral moiré excitons. Circularly polarized photoluminescence reveals switching from co-circular to cross-circular polarizations as moiré excitons go from being negatively charged and neutral to positively charged. This switching results from the competition between valley-flip and spin-flip energy relaxation pathways of photo-excited electrons during interlayer trion formation. Our results offer a starting point for engineering both bosonic and fermionic many-body effects based on moiré excitons¹⁴.

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

Moiré patterns with a superlattice potential can be formed by vertically stacking two layered materials with a relative twist or lattice constant mismatch. In transition metal dichalcogenide-based systems, the moiré potential landscape can trap interlayer excitons (IXs) at specific atomic registries. Here, we report that spatially isolated trapped IXs in a molybdenum diselenide/tungsten diselenide heterobilayer device provide a sensitive optical probe of carrier filling in their immediate environment. By mapping the spatial positions of individual trapped IXs, we are able to spectrally track the emitters as the moiré lattice is filled with excess carriers. Upon initial doping of the heterobilayer, neutral trapped IXs form charged IXs (IX trions) uniformly with a binding energy of ~7 meV. Upon further doping, the empty superlattice sites sequentially fill, creating a Coulomb staircase: stepwise changes in the IX trion emission energy due to Coulomb interactions with carriers at nearest-neighbour moiré sites. This non-invasive, highly local technique can complement transport and non-local optical sensing techniques to characterize Coulomb interaction energies, visualize charge correlated states, or probe local disorder in a moiré superlattice.

Excitons and emergent quantum phenomena in stacked 2D semiconductors

The design and control of material interfaces is a foundational approach to realize technologically useful effects and engineer material properties. This is especially true for two-dimensional (2D) materials, where van der Waals stacking allows disparate materials to be freely stacked together to form highly customizable interfaces. This has underpinned a recent wave of discoveries based on excitons in stacked double layers of transition metal dichalcogenides (TMDs), the archetypal family of 2D semiconductors. In such double-layer structures, the elegant interplay of charge, spin and moiré superlattice structure with many-body effects gives rise to diverse excitonic phenomena and correlated physics. Here we review some of the recent discoveries that highlight the versatility of TMD double layers to explore quantum optics and many-body effects. We identify outstanding challenges in the field and present a roadmap for unlocking the full potential of excitonic physics in TMD double layers and beyond, such as incorporating newly discovered ferroelectric and magnetic materials to engineer symmetries and add a new level of control to these remarkable engineered materials.

Dynamic Tuning of Moiré Excitons in a WSe2/WS2 Heterostructure via Mechanical Deformation

Moiré superlattices in van der Waals (vdW) heterostructures form by stacking atomically thin layers on top of one another with a twist angle or lattice mismatch. The resulting moiré potential leads to a strong modification of the band structure, which can give rise to exotic quantum phenomena ranging from correlated insulators and superconductors to moiré excitons and Wigner crystals. Here, we demonstrate the dynamic tuning of moiré potential in a WSe₂/WS₂ heterostructure at cryogenic temperature. We utilize the optical fiber tip of a cryogenic scanning near-field optical microscope (SNOM) to locally deform the heterostructure and measure its near-field optical response simultaneously. The deformation of the heterostructure increases the moiré potential, which leads to a red shift of the moiré exciton resonances. We observe the interlayer exciton resonance shifts up to 20 meV, while the intralayer exciton resonances shift up to 17 meV.

Phonon-Assisted Intervalley Scattering Determines Ultrafast Exciton Dynamics in MoSe_{2} Bilayers

While valleys (energy extrema) are present in all band structures of solids, their preeminent role in determining exciton resonances and dynamics in atomically thin transition metal dichalcogenides (TMDC) is unique. Using two-dimensional coherent electronic spectroscopy, we find that exciton decoherence occurs on a much faster timescale in MoSe_{2} bilayers than that in the monolayers. We further identify two population relaxation channels in the bilayer, a coherent and an incoherent one. Our microscopic model reveals that phonon-emission processes facilitate scattering events from the K valley to other lower-energy Γ and Λ valleys in the bilayer. Our combined experimental and theoretical studies unequivocally establish different microscopic mechanisms that determine exciton quantum dynamics in TMDC monolayers and bilayers. Understanding exciton quantum dynamics provides critical guidance to the manipulation of spin-valley degrees of freedom in TMDC bilayers.

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

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

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

Identification of twist-angle-dependent excitons in WS2/WSe2 heterobilayers

Stacking atomically thin films enables artificial construction of van der Waals heterostructures with exotic functionalities such as superconductivity, the quantum Hall effect, and engineered light-matter interactions. In particular, heterobilayers composed of monolayer transition metal dichalcogenides have attracted significant interest due to their controllable interlayer coupling and trapped valley excitons in moiré superlattices. However, the identification of twist-angle-modulated optical transitions in heterobilayers is sometimes controversial since both momentum-direct (K-K) and -indirect excitons reside on the low energy side of the bright exciton in the monolayer constituents. Here, we attribute the optical transition at approximately 1.35 eV in the WS2/WSe2 heterobilayer to an indirect Γ-K transition based on a systematic analysis and comparison of experimental PL spectra with theoretical calculations. The exciton wavefunction obtained by the state-of-the-art GW-Bethe-Salpeter equation (GW-BSE) approach indicates that both the electron and hole of the exciton are contributed by the WS2 layer. Polarization-resolved k-space imaging further confirms that the transition dipole moment of this optical transition is dominantly in-plane and is independent of the twist angle. The calculated absorption spectrum predicts that the usually called interlayer exciton peak coming from the K-K transition is located at 1.06 eV, but with a much weaker amplitude. Our work provides new insights into understanding the steady-state and dynamic properties of twist-angle-dependent excitons in van der Waals heterostructures.

Bilayer Wigner crystals in a transition metal dichalcogenide heterostructure

One of the first theoretically predicted manifestations of strong interactions in many-electron systems was the Wigner crystal^1-3, in which electrons crystallize into a regular lattice. The crystal can melt via either thermal or quantum fluctuations⁴. Quantum melting of the Wigner crystal is predicted to produce exotic intermediate phases^5,6 and quantum magnetism^7,8 because of the intricate interplay of Coulomb interactions and kinetic energy. However, studying two-dimensional Wigner crystals in the quantum regime has often required a strong magnetic field^9-11 or a moiré superlattice potential^12-15, thus limiting access to the full phase diagram of the interacting electron liquid. Here we report the observation of bilayer Wigner crystals without magnetic fields or moiré potentials in an atomically thin transition metal dichalcogenide heterostructure, which consists of two MoSe₂ monolayers separated by hexagonal boron nitride. We observe optical signatures of robust correlated insulating states at symmetric (1:1) and asymmetric (3:1, 4:1 and 7:1) electron doping of the two MoSe₂ layers at cryogenic temperatures. We attribute these features to bilayer Wigner crystals composed of two interlocked commensurate triangular electron lattices, stabilized by inter-layer interaction¹⁶. The Wigner crystal phases are remarkably stable, and undergo quantum and thermal melting transitions at electron densities of up to 6 × 10¹² per square centimetre and at temperatures of up to about 40 kelvin. Our results demonstrate that an atomically thin heterostructure is a highly tunable platform for realizing many-body electronic states and probing their liquid-solid and magnetic quantum phase transitions^4-8,17.

Weak ferroelectric charge transfer in layer-asymmetric bilayers of 2D semiconductors

In bilayers of two-dimensional semiconductors with stacking arrangements which lack inversion symmetry charge transfer between the layers due to layer-asymmetric interband hybridisation can generate a potential difference between the layers. We analyse bilayers of transition metal dichalcogenides (TMDs)—in particular, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {WSe}_2$$\end{document}WSe2—for which we find a substantial stacking-dependent charge transfer, and InSe, for which the charge transfer is found to be negligibly small. The information obtained about TMDs is then used to map potentials generated by the interlayer charge transfer across the moiré superlattice in twistronic bilayers.

Interfacial ferroelectricity by van der Waals sliding

Despite their partial ionic nature, many layered diatomic crystals avoid internal electric polarization by forming a centrosymmetric lattice at their optimal van-der-Waals stacking. Here, we report a stable ferroelectric order emerging at the interface between two naturally-grown flakes of hexagonal-boron-nitride, which are stacked together in a metastable non-centrosymmetric parallel orientation. We observe alternating domains of inverted normal polarization, caused by a lateral shift of one lattice site between the domains. Reversible polarization switching coupled to lateral sliding is achieved by scanning a biased tip above the surface. Our calculations trace the origin of the phenomenon to a subtle interplay between charge redistribution and ionic displacement, and provide intuitive insights to explore the interfacial polarization and its unique "slidetronics" switching mechanism.

Moiré superlattices and related moiré excitons in twisted van der Waals heterostructures

Recent advances in moiré superlattices and moiré excitons, such as quantum emission arrays, low-energy flat bands, and Mott insulators, have rapidly attracted attention in the fields of optoelectronics, materials, and energy research. The interlayer twist turns into a degree of freedom that alters the properties of the systems of materials, and the realization of moiré excitons also offers the feasibility of making artificial exciton crystals. Moreover, moiré excitons exhibit many exciting properties under the regulation of various external conditions, including spatial polarisation, alternating dipolar to alternating dipolar moments and gate-dependence to gate voltage dependence; all are pertinent to their applications in nano-photonics and quantum information. But the lag in theoretical development and the low-efficiency of processing technologies significantly limit the potential of moiré superlattice applications. In this review, we systematically summarise and discuss the recent progress in moiré superlattices and moiré excitons, and analyze the current challenges, and put forward relevant recommendations. There is no doubt that further research will lead to breakthroughs in their application and promote reforms and innovations in traditional solid-state physics and materials science.

Stacking-engineered ferroelectricity in bilayer boron nitride

2D ferroelectrics with robust polarization down to atomic thicknesses provide building blocks for functional heterostructures. Experimental realization remains challenging because of the requirement of a layered polar crystal. Here, we demonstrate a rational design approach to engineering 2D ferroelectrics from a non-ferroelectric parent compound via employing van der Waals assembly. Parallel-stacked bilayer boron nitride exhibits out-of-plane electric polarization that reverses depending on the stacking order. The polarization switching is probed via the resistance of an adjacently stacked graphene sheet. Twisting the boron nitride sheets by a small angle changes the dynamics of switching thanks to the formation of moiré ferroelectricity with staggered polarization. The ferroelectricity persists to room temperature while keeping the high mobility of graphene, paving the way for potential ultrathin nonvolatile memory applications.