Control of Exciton Valley Coherence in Transition Metal Dichalcogenide Monolayers

Large-Area Epitaxial Growth of Transition Metal Dichalcogenides

Over the past decade, research on atomically thin two-dimensional (2D) transition metal dichalcogenides (TMDs) has expanded rapidly due to their unique properties such as high carrier mobility, significant excitonic effects, and strong spin-orbit couplings. Considerable attention from both scientific and industrial communities has fully fueled the exploration of TMDs toward practical applications. Proposed scenarios, such as ultrascaled transistors, on-chip photonics, flexible optoelectronics, and efficient electrocatalysis, critically depend on the scalable production of large-area TMD films. Correspondingly, substantial efforts have been devoted to refining the synthesizing methodology of 2D TMDs, which brought the field to a stage that necessitates a comprehensive summary. In this Review, we give a systematic overview of the basic designs and significant advancements in large-area epitaxial growth of TMDs. We first sketch out their fundamental structures and diverse properties. Subsequent discussion encompasses the state-of-the-art wafer-scale production designs, single-crystal epitaxial strategies, and techniques for structure modification and postprocessing. Additionally, we highlight the future directions for application-driven material fabrication and persistent challenges, aiming to inspire ongoing exploration along a revolution in the modern semiconductor industry.

Giant Optical Anisotropy Induced by Magnetic Order in FePS3/WSe2 Heterostructures

Magnetic 2D materials offer a promising platform for manipulating quantum states at the nanoscale. Recent studies have underscored the significant influence of 2D magnetic materials on the optical behaviors of transition-metal dichalcogenides (TMDs), revealing phenomena such as interlayer exciton-magnon interactions, magnetization-dependent valley polarization, and an enhanced Zeeman effect. However, the controlled manipulation of anisotropic optical properties in TMDs via magnetism remains challenging. Here, the magnetic ordering in FePS3 profoundly impacts the optical characteristics of WSe2, achieving a giant linear polarization degree of 5.1 in exciton emission is demonstrated. This is supported by a detailed analysis of low-temperature photoluminescence (PL) and Raman spectra from nL-FePS3/WSe2 heterostructures. These findings indicate that a phase transition in FePS3 from paramagnetic to antiferromagnetic enhances interlayer Coulomb interactions, inducing a transition from non-polar to polar behavior in the heterostructures. Additionally, valley-polarized PL spectra under magnetic fields from -9 to 9 T reveal the influence of FePS3 on valley polarization and Zeeman splitting of excitons in monolayer WSe2. These results present a novel strategy for tailoring the optoelectronic properties of 2D magnetic van der Waals heterostructures, paving the way for advancements in nanoscale device design.

Metasurface of Strongly Coupled Excitons and Nanoplasmonic Arrays

Metasurfaces allow light to be manipulated at the nanoscale. Integrating metasurfaces with transition metal dichalcogenide monolayers provides additional functionality to ultrathin optics, including tunable optical properties with enhanced light-matter interactions. In this work, we demonstrate the realization of a polaritonic metasurface utilizing the sizable light-matter coupling of excitons in monolayer WSe2 and the collective lattice resonances of nanoplasmonic gold arrays. We developed a novel fabrication method to integrate gold nanodisk arrays in hexagonal boron nitride and thus simultaneously ensure spectrally narrow exciton transitions and their immediate proximity to the near-field of array surface lattice resonances. In the regime of strong light-matter coupling, the resulting van der Waals metasurface exhibits all key characteristics of lattice polaritons, with a directional and linearly polarized far-field emission profile dictated by the underlying nanoplasmonic lattice. Our work can be straightforwardly adapted to other lattice geometries, establishing structured van der Waals metasurfaces as means to engineer polaritonic lattices.

Emergence of Optical Anisotropy in Moiré Superlattice via Heterointerface Engineering

The interaction between light and moiré superlattices presents a platform for exploring unique light-matter phenomena. Tailoring these optical properties holds immense potential for advancing the utilization of moiré superlattices in photonics, optoelectronics, and valleytronics. However, the control of the optical polarization state in moiré superlattices, particularly in the presence of moiré effects, remains elusive. Here, we unveil the emergence of optical anisotropy in moiré superlattices by constructing twisted WSe2/WSe2/SiP heterostructures. We report a linear polarization degree of ∼70% for moiré excitons, attributed to the spatially nonuniform charge distribution, corroborated by first-principles calculations. Furthermore, we demonstrate the modulation of this linear polarization state via the application of a magnetic field, resulting in polarization angle rotation and a magnetic-field-dependent linear polarization degree, influenced by valley coherence and moiré potential effects. Our findings demonstrate an efficient strategy for tuning the optical polarization state of moiré superlattices using heterointerface engineering.

Motion of Two-Dimensional Excitons in Momentum Space Leads to Pseudospin Distribution Narrowing on the Bloch Sphere

Motional narrowing implies narrowing induced by motion; for example, in nuclear magnetic resonance, the thermally induced random motion of the nuclei in an inhomogeneous environment leads to a counterintuitive narrowing of the resonance line. Similarly, the excitons in monolayer semiconductors experience magnetic inhomogeneity: the electron-hole spin-exchange interaction manifests as an in-plane pseudomagnetic field with a periodically varying orientation inside the exciton band. The excitons undergo random momentum scattering and pseudospin precession repeatedly in this inhomogeneous magnetic environment, typically resulting in fast exciton depolarization. On the contrary, we show that such magnetic inhomogeneity averages out at high scattering rates due to motional narrowing. Physically, a faster exciton scattering leads to a narrower pseudospin distribution on the Bloch sphere, implying a nontrivial improvement in exciton polarization. The in-plane nature of the pseudomagnetic field enforces a contrasting scattering dependence between the circularly and linearly polarized excitons, providing a spectroscopic way to gauge the sample quality.

Spatial Imaging and Control of Dark Excitons in Monolayer Transition Metal Dichalcogenides

Dark excitons play a vital role in exciton condensation and optical properties of monolayer transition metal dichalcogenides (MTMDs). Previous literature mainly focuses on the detection of the energy of the dark exciton, while spatial detection and control are equally important but are less studied. Here we report that for MTMD embedded in a semiconductor microcavity and under a uniform in-plane magnetic field the spatial distribution of the dark exciton can be probed by measuring that of the cavity photon for small exciton-exciton interaction energy. Further, we propose to realize the anomalous exciton Hall effect by exploiting spatially inhomogeneous coupling of the bright and dark excitons under a Gaussian excitation beam. This effect occurs regardless of the exciton-exciton interaction, which will strengthen the diffusion of excitons in the excitation region. These results provide an improved understanding of the excitons in MTMDs, thereby facilitating their potential practical applications.

Tunneling Valley Hall Effect Driven by Tilted Dirac Fermions

Valleytronics is a research field utilizing a valley degree of freedom of electrons for information processing and storage. A strong valley polarization is critical for realistic valleytronic applications. Here, we predict a tunneling valley Hall effect (TVHE) driven by tilted Dirac fermions in all-in-one tunnel junctions based on a two-dimensional (2D) valley material. Different doping of the electrode and spacer regions in these tunnel junctions results in momentum filtering of the tunneling Dirac fermions, generating a strong transverse valley Hall current dependent on the Dirac-cone tilting. Using the parameters of an existing 2D valley material, we demonstrate that such a strong TVHE can host a giant valley Hall angle even in the absence of the Berry curvature. Finally, we predict that resonant tunneling can occur in a tunnel junction with properly engineered device parameters such as the spacer width and transport direction, providing significant enhancement of the valley Hall angle. Our work opens a new approach to generate valley polarization in realistic valleytronic systems.

Large Biaxial Compressive Strain Tuning of Neutral and Charged Excitons in Single-Layer Transition Metal Dichalcogenides

The absorption and emission of light in single-layer transition metal dichalcogenides are governed by the formation of excitonic quasiparticles. Strain provides a powerful technique to tune the optoelectronic properties of two-dimensional materials and thus to adjust their exciton energies. The effects of large compressive strain in the optical spectrum of two-dimensional (2D) semiconductors remain rather unexplored compared to those of tensile strain, mainly due to experimental constraints. Here, we induced large, uniform, biaxial compressive strain (∼1.2%) by cooling, down to 10 K, single-layer WS2, MoS2, WSe2, and MoSe2 deposited on polycarbonate substrates. We observed a significant strain-induced modulation of neutral exciton energies, with blue shifts up to 160 meV, larger than in any previous experiments. Our results indicate a remarkably efficient transfer of compressive strain, demonstrated by gauge factor values exceeding previous results and approaching theoretical expectations. At low temperatures, we investigated the effect of compressive strain on the resonances associated with the formation of charged excitons. In WS2, a notable reduction of gauge factors for charged compared to neutral excitons suggests an increase in their binding energy, which likely results from the effects of strain added to the influence of the polymeric substrate.

Observation of ~100% valley-coherent excitons in monolayer MoS2 through giant enhancement of valley coherence time

In monolayer transition metal dichalcogenide semiconductors, valley coherence degrades rapidly due to a combination of fast scattering and inter-valley exchange interaction. This leads to a sub-picosecond valley coherence time, making coherent manipulation of exciton a highly challenging task. Using monolayer MoS₂ sandwiched between top and bottom graphene, here we demonstrate fully valley-coherent excitons by observing ~100% degree of linear polarization in steady state photoluminescence. This is achieved in this unique design through a combined effect of (a) suppression in exchange interaction due to enhanced dielectric screening, (b) reduction in exciton lifetime due to a fast inter-layer transfer to graphene, and (c) operating in the motional narrowing regime. We disentangle the role of the key parameters affecting valley coherence by using a combination of calculation (solutions of Bethe-Salpeter and Maialle-Silva-Sham equations) and a careful choice of design of experiments using four different stacks with systematic variation of screening and exciton lifetime. To the best of our knowledge, this is the first report in which the excitons are found to be valley coherent in the entire lifetime in monolayer semiconductors, allowing optical readout of valley coherence possible.

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

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

Transition Metal Dichalcogenides (TMDCs) Heterostructures: Synthesis, Excitons and Photoelectric Properties

Transition metal dichalcogenides (TMDCs) have good flexibility, light absorption, and carrier mobility, and can be used to fabricate wearable devices and photodetectors. In addition, the band gaps of these materials are adjustable, which are related to the number of stacking layers. The the material properties can be changed by vertically stacking TMDCs to form van der Waals (vdW) heterostructures. Compared with single-layer TMDC, the vdW heterostructure has better light response and more efficient photoelectric conversion. Interlayer excitons formed in vdW heterostructure have a longer exciton lifetime and unique valley selectivity compared with intralayer excitons, which promotes the research on TMDCs materials in photoelectric field, valley electronics, carrier dynamics, etc. In this paper, the methods of synthesizing heterostructures are introduced. Photoelectric properties, valley dynamics, electronic properties and related applications of TMDCs vdW heterostructures are also discussed. Heterostructures stacked with different materials, stacking modes, and twist angles all can affect the properties. Hence, it brings more creativity and research direction to the material field.

Enhanced light-matter interaction in two-dimensional transition metal dichalcogenides

Two-dimensional (2D) transition metal dichalcogenide (TMDC) materials, such as MoS₂, WS₂, MoSe₂, and WSe₂, have received extensive attention in the past decade due to their extraordinary electronic, optical and thermal properties. They evolve from indirect bandgap semiconductors to direct bandgap semiconductors while their layer number is reduced from a few layers to a monolayer limit. Consequently, there is strong photoluminescence in a monolayer (1L) TMDC due to the large quantum yield. Moreover, such monolayer semiconductors have two other exciting properties: large binding energy of excitons and valley polarization. These properties make them become ideal materials for various electronic, photonic and optoelectronic devices. However, their performance is limited by the relatively weak light-matter interactions due to their atomically thin form factor. Resonant nanophotonic structures provide a viable way to address this issue and enhance light-matter interactions in 2D TMDCs. Here, we provide an overview of this research area, showcasing relevant applications, including exotic light emission, absorption and scattering features. We start by overviewing the concept of excitons in 1L-TMDC and the fundamental theory of cavity-enhanced emission, followed by a discussion on the recent progress of enhanced light emission, strong coupling and valleytronics. The atomically thin nature of 1L-TMDC enables a broad range of ways to tune its electric and optical properties. Thus, we continue by reviewing advances in TMDC-based tunable photonic devices. Next, we survey the recent progress in enhanced light absorption over narrow and broad bandwidths using 1L or few-layer TMDCs, and their applications for photovoltaics and photodetectors. We also review recent efforts of engineering light scattering, e.g., inducing Fano resonances, wavefront engineering in 1L or few-layer TMDCs by either integrating resonant structures, such as plasmonic/Mie resonant metasurfaces, or directly patterning monolayer/few layers TMDCs. We then overview the intriguing physical properties of different van der Waals heterostructures, and their applications in optoelectronic and photonic devices. Finally, we draw our opinion on potential opportunities and challenges in this rapidly developing field of research.

Observation of quantum-confined exciton states in monolayer WS2 quantum dots by ultrafast spectroscopy

Monolayer transition metal dichalcogenide quantum dots (TMDC QDs) could exhibit unique photophysical properties, because of both lateral quantum confinement effect and edge effect. However, there is little fundamental study on the quantum-confined exciton dynamics in monolayer TMDC QDs, to date. Here, by selective excitations of monolayer WS₂ QDs in broadband transient absorption (TA) spectroscopy experiments, the excitation-wavelength-dependent ground state bleaching signals corresponding to the quantum-confined exciton states are directly observed. Compared to the time-resolved photophysical properties of WS₂ nanosheets, the selected monolayer WS₂ QDs only show one ground state bleaching peak with larger initial values for the linear polarization anisotropy of band-edge excitons, probably due to the expired spin-orbit coupling. This suggests a complete change of the band structure for monolayer WS₂ QDs. In the femtosecond time-resolved circular polarization anisotropy experiments, a valley depolarization time of ∼100 fs is observed for WS₂ nanosheets at room temperature, which is not observed for monolayer WS₂ QDs. Our findings suggest a strong state-mixing of band-edge valley excitons responsible for the large linear polarization in monolayer WS₂ QDs, which could be helpful for understanding the exciton relaxation mechanisms in colloidal monolayer TMDC QDs.

Linearly Polarized Electroluminescence from MoS2 Monolayers Deposited on Metal Nanoparticles: Toward Tunable Room-Temperature Single-Photon Sources

Break junctions in noble-metal films can exhibit electroluminescence (EL) through inelastic electron tunneling. The EL spectrum can be tuned by depositing a single-layer crystal of a transition-metal dichalcogenide (TMDC) on top. Whereas the emission from the gaps between silver or gold nanoparticles formed in the break junction is spectrally broad, the hybrid metal/TMDC structure shows distinct luminescence from the TMDC material. The EL from individual hotspots is found to be linearly polarized, with a polarization axis apparently oriented randomly. Surprisingly, the degree of polarization is retained in the EL from the TMDC monolayer at room temperature. In analogy to polarized photoluminescence experiments, such polarized EL can be interpreted as a signature of valley-selective transitions, suggesting that spin-flip transitions and dephasing for excitons in the K valleys are of limited importance. However, polarized EL may also originate from the metal nanoparticles formed under electromigration which constitute optical antenna structures. Such antennae can apparently change over time since jumps in the polarization are observed in bare silver-nanoparticle films. Remarkably, photon-correlation spectroscopy reveals that gold-nanoparticle films exhibit signatures of deterministic single-photon emission in the EL, suggesting a route to designing room-temperature polarized single-photon sources with tunable photon energy through the choice of TMDC overlayer.

Valley manipulation in monolayer transition metal dichalcogenides and their hybrid systems: status and challenges

Recently, the emerging conceptual valley-related devices have attracted much attention due to the progress on generating, controlling, and detecting the valley degree of freedom in the transition metal dichalcogenide (TMD) monolayers. In general, it is known that achieving valley degree of freedom with long valley lifetime is crucial in the implementation of valleytronic devices. Here, we provide a brief introduction of the basic understandings of valley degree of freedom. We as well review the recent experimental advancement in the modulation of valley degree of freedom. The strategies include optical/magnetic/electric field tuning, moiré patterns, plasmonic metasurface, defects and strain engineering. In addition, we summarize the corresponding mechanisms, which can help to obtain large degree of polarization and long valley lifetimes in monolayer TMDs. Based on these methods, two-dimensional valley-optoelectronic systems based on TMD heterostructures can be constructed, providing opportunities for such as the new paradigm in data processing and transmission. Challenges and perspectives on the development of valleytronics are highlighted as well.

Enhanced Faraday rotation in proximitized monolayer transition metal dichalcogenides

Monolayer transition metal dichalcogenides (TMDCs) under the application of a magnetic exchange field carry the nontrivial optical Hall conductivity and thus exhibit the nonzero Faraday rotation (FR) angle. However, the tradeoff between the FR angle and transmission hinders their possible applications in magnetic-optical (MO) devices. Here, we theoretically show that a heterostructure of two photonic crystals with proximitized monolayer TMDCs enables the enhancement of the FR angle and transmission simultaneously through the combination of a four-band Hamiltonian model, Kubo formula and transfer matrix method. The MO improvement in the hybrid structure in both the FR angle and transmission is determined by the combined effects from the localized electromagnetic field at the interface between the two photonic crystals and the satisfaction of the phase match condition. Our work opens up an alternative opportunity to use TMDCs in two-dimensional MO fields in the visible frequency range.

Skew Scattering and Side Jump Drive Exciton Valley Hall Effect in Two-Dimensional Crystals

Exciton valley Hall effect is the spatial separation of the valley-tagged excitons by a drag force. Usually, the effect is associated with the anomalous velocity acquired by the particles due to the Berry curvature of the Bloch bands. Here we show that the anomalous velocity plays no role in the exciton valley Hall effect, which is governed by the side-jump and skew scattering. We develop a microscopic theory of the exciton valley Hall effect in the presence of a synthetic electric field and phonon drag and calculate all relevant contributions to the valley Hall current also demonstrating the cancellation of the anomalous velocity. The sensitivity of the effect to the origin of the drag force and to the scattering processes is shown. We extend the drift-diffusion model to account for the valley Hall effect and calculate the exciton density and valley polarization profiles.

Room-Temperature Valley Polarization in Atomically Thin Semiconductors via Chalcogenide Alloying

Room-temperature manipulation and processing of information encoded in the electronic valley pseudospin and spin degrees of freedoms lie at the heart of the next technological quantum revolution. In atomically thin layers of transition-metal dichalcogenides (TMDs) with hexagonal lattices, valley-polarized excitations and valley quantum coherence can be generated by simply shining with adequately polarized light. In turn, the polarization states of light can induce topological Hall currents in the absence of an external magnetic field, which underlies the fundamental principle of opto-valleytronics devices. However, demonstration of optical generation of valley polarization at room temperature has remained challenging and not well understood. Here, we demonstrate control of strong valley polarization (valley quantum coherence) at room temperature of up to ∼50% (∼20%) by strategically designing Coulomb forces and spin-orbit interactions in atomically thin TMDs via chalcogenide alloying. We show that tailor making the carrier density and the relative order between optically active (bright) and forbidden (dark) states by key variations on the chalcogenide atom ratio allows full control of valley pseudospin dynamics. Our findings set a comprehensive approach for intrinsic and efficient manipulation of valley pseudospin and spin degree of freedom toward realistic opto-valleytronics devices.

Retro-normal reflection and specular Andreev reflection in a transition metal dichalcogenides superconducting heterojunction

Based on the Bogoliubov-de Gennes equation, the spin-resolved scattering problem through a transition metal dichalcogenides normal metal/superconductor has been investigated. It is shown that the tunneling conductances have a close relationship with the nontrivial Rashba metallic states. Without the Rashba spin-orbit interaction (RSOI), the tunneling conductances exhibit clear characteristic features for detecting the normal Rashba metal state (NRMS) and the anomalous Rashba metal state (ARMS). While in the presence of RSOI, the oscillation, hump structure, and the reentrant behavior of the tunneling conductances can be served as a smoking gun to distinguish the Rashba ring metal state (RRMS) from those nontrivial metallic states. Fundamentally, in sharp contrast to the NRMS and the ARMS where only the normal reflection and the retro-Andreev reflection can occur, the additional scattering processes of the retro-normal reflection (RNR) and the specular Andreev reflection (SAR) can take place in the present junction with the RRMS. Thus the obtained results offer a feasible way to determine the RNR, the SAR, and the nontrivial Rashba metallic states based on the transition metal dichalcogenides superconducting heterojunction.

Enhancing and controlling valley magnetic response in MoS2/WS2 heterostructures by all-optical route

Van der Waals heterostructures of transition metal dichalcogenides with interlayer coupling offer an exotic platform to realize fascinating phenomena. Due to the type II band alignment of these heterostructures, electrons and holes are separated into different layers. The localized electrons induced doping in one layer, in principle, would lift the Fermi level to cross the spin-polarized upper conduction band and lead to strong manipulation of valley magnetic response. Here, we report the significantly enhanced valley Zeeman splitting and magnetic tuning of polarization for the direct optical transition of MoS₂ in MoS₂/WS₂ heterostructures. Such strong enhancement of valley magnetic response in MoS₂ stems from the change of the spin-valley degeneracy from 2 to 4 and strong many-body Coulomb interactions induced by ultrafast charge transfer. Moreover, the magnetic splitting can be tuned monotonically by laser power, providing an effective all-optical route towards engineering and manipulating of valleytronic devices and quantum-computation.

Van der Waals heterostructures may offer a suitable platform for all-optical manipulation of valleytronic devices. Here, the authors observe a strong enhancement of the valley magnetic response in MoS₂, and magnetic tuning of the polarization of MoS₂ direct optical transition

Probing and Manipulating Valley Coherence of Dark Excitons in Monolayer WSe_{2}

Monolayers of semiconducting transition metal dichalcogenides are two-dimensional direct-gap systems which host tightly bound excitons with an internal degree of freedom corresponding to the valley of the constituting carriers. Strong spin-orbit interaction and the resulting ordering of the spin-split subbands in the valence and conduction bands makes the lowest-lying excitons in WX_{2} (X being S or Se) spin forbidden and optically dark. With polarization-resolved photoluminescence experiments performed on a WSe_{2} monolayer encapsulated in a hexagonal boron nitride, we show how the intrinsic exchange interaction in combination with the applied in-plane and/or out-of-plane magnetic fields enables one to probe and manipulate the valley degree of freedom of the dark excitons.

Optical valley Hall effect for highly valley-coherent exciton-polaritons in an atomically thin semiconductor

Spin-orbit coupling is a fundamental mechanism that connects the spin of a charge carrier with its momentum. In the optical domain, an analogous synthetic spin-orbit coupling is accessible by engineering optical anisotropies in photonic materials. Both yield the possibility of creating devices that directly harness spin and polarization as information carriers. Atomically thin transition metal dichalcogenides promise intrinsic spin-valley Hall features for free carriers, excitons and photons. Here we demonstrate spin- and valley-selective propagation of exciton-polaritons in a monolayer of MoSe₂ that is strongly coupled to a microcavity photon mode. In a wire-like device we trace the flow and helicity of exciton-polaritons expanding along its channel. By exciting a coherent superposition of K and K' tagged polaritons, we observe valley-selective expansion of the polariton cloud without either an external magnetic field or coherent Rayleigh scattering. The observed optical valley Hall effect occurs on a macroscopic scale, offering the potential for applications in spin-valley-locked photonic devices.

Room-temperature valley coherence in a polaritonic system

The emerging field of valleytronics aims to coherently manipulate an electron and/or hole’s valley pseudospin as an information bearing degree of freedom (DOF). Monolayer transition metal dichalcogenides, due to their strongly bound excitons, their degenerate valleys and their seamless interfacing with photons are a promising candidate for room temperature valleytronics. Although the exciton binding energy suggests room temperature valley coherence should be possible, it has been elusive to-date. A potential solution involves the formation of half-light, half-matter cavity polaritons based on 2D material excitons. It has recently been discovered that cavity polaritons can inherit the valley DOF. Here, we demonstrate the room temperature valley coherence of valley-polaritons by embedding a monolayer of tungsten diselenide in a monolithic dielectric cavity. The extra decay path introduced by the exciton-cavity coupling, which is free from decoherence, is the key to room temperature valley coherence preservation. These observations paves the way for practical valleytronic devices.

Owing to the presence of strongly bound excitons and degenerate valleys, monolayer transition metal dichalcogenides show promise for valleytronic applications. Here, the authors embed monolayer WSe₂ in a monolithic dielectric cavity, and observe room-temperature valley coherence of valley-polaritons.

Dark-exciton valley dynamics in transition metal dichalcogenide alloy monolayers

We report a comprehensive theory to describe exciton and biexciton valley dynamics in monolayer Mo_1−xW_xSe₂ alloys. To probe the impact of different excitonic channels, including bright and dark excitons, intravalley biexcitons, intervalley scattering between bright excitons, as well as bright biexcitons, we have performed a systematic study from the simplest system to the most complex one. In contrast to the binary WSe₂ monolayer with weak photoluminescence (PL) and high valley polarization at low temperatures and the MoSe₂, that presents high PL intensity, but low valley polarization, our results demonstrate that it is possible to set up a ternary alloy with intermediate W-concentration that holds simultaneously a considerably robust light emission and an efficient optical orientation of the valley pseudospin. We find the critical value of W-concentration, x_c, that turns alloys from bright to darkish. The dependence of the PL intensity on temperature shows three regimes: while bright monolayer alloys display a usual temperature dependence in which the intensity decreases with rising temperature, the darkish alloys exhibit the opposite behavior, and the alloys with x around x_c show a non-monotonic temperature response. Remarkably, we observe that the biexciton enhances significantly the stability of the exciton emission against fluctuations of W-concentration for bright alloys. Our findings pave the way for developing high-performance valleytronic and photo-emitting devices.

Valley coherent exciton-polaritons in a monolayer semiconductor

Two-dimensional transition metal dichalcogenides (TMDs) provide a unique possibility to generate and read-out excitonic valley coherence using linearly polarized light, opening the way to valley information transfer between distant systems. However, these excitons have short lifetimes (ps) and efficiently lose their valley coherence via the electron-hole exchange interaction. Here, we show that control of these processes can be gained by embedding a monolayer of WSe₂ in an optical microcavity, forming part-light-part-matter exciton-polaritons. We demonstrate optical initialization of valley coherent polariton populations, exhibiting luminescence with a linear polarization degree up to 3 times higher than displayed by bare excitons. We utilize an external magnetic field alongside selective exciton-cavity-mode detuning to control the polariton valley pseudospin vector rotation, which reaches 45° at B = 8 T. This work provides unique insight into the decoherence mechanisms in TMDs and demonstrates the potential for engineering the valley pseudospin dynamics in monolayer semiconductors embedded in photonic structures.

The short exciton life time in atomically thin transition metal dichalcogenides poses limitations to efficient control of the valley pseudospin and coherence. Here, the authors manipulate the exciton coherence in a WSe₂ monolayer embedded in an optical microcavity in the strong light-matter coupling regime.

Interlayer valley excitons in heterobilayers of transition metal dichalcogenides

Stacking different two-dimensional crystals into van der Waals heterostructures provides an exciting approach to designing quantum materials that can harness and extend the already fascinating properties of the constituents. Heterobilayers of transition metal dichalcogenides are particularly attractive for low-dimensional semiconductor optics because they host interlayer excitons-with electrons and holes localized in different layers-which inherit valley-contrasting physics from the monolayers and thereby possess various novel and appealing properties compared to other solid-state nanostructures. This Review presents the contemporary experimental and theoretical understanding of these interlayer excitons. We discuss their unique optical properties arising from the underlying valley physics, the strong many-body interactions and electrical control resulting from the electric dipole moment, and the unique effects of a moiré superlattice on the interlayer exciton potential landscape and optical properties.

Defect-Induced Modification of Low-Lying Excitons and Valley Selectivity in Monolayer Transition Metal Dichalcogenides

We study the effect of point-defect chalcogen vacancies on the optical properties of monolayer transition metal dichalcogenides using ab initio GW and Bethe-Salpeter equation calculations. We find that chalcogen vacancies introduce unoccupied in-gap states and occupied resonant defect states within the quasiparticle continuum of the valence band. These defect states give rise to a number of strongly bound defect excitons and hybridize with excitons of the pristine system, reducing the valley-selective circular dichroism. Our results suggest a pathway to tune spin-valley polarization and other optical properties through defect engineering.

Spontaneous Exciton Valley Coherence in Transition Metal Dichalcogenide Monolayers Interfaced with an Anisotropic Metasurface

The control of the exciton intervalley coherence renders transition metal dichalcogenides monolayers promising candidates for quantum information science. So far, generating intervalley coherence has the need for an external coherent field. Here, we theoretically demonstrate spontaneous generation (i.e., without any external field) of exciton intervalley coherence. We achieve this by manipulating the vacuum field in the vicinity of the monolayer with a designed polarization-dependent metasurface, inducing an anisotropic decay rate for in-plane excitonic dipoles. Harnessing quantum coherence and interference effects in two-dimensional materials may provide the route for novel quantum valleytronic devices.

Valleytronics: Opportunities, Challenges, and Paths Forward

A lack of inversion symmetry coupled with the presence of time-reversal symmetry endows 2D transition metal dichalcogenides with individually addressable valleys in momentum space at the K and K' points in the first Brillouin zone. This valley addressability opens up the possibility of using the momentum state of electrons, holes, or excitons as a completely new paradigm in information processing. The opportunities and challenges associated with manipulation of the valley degree of freedom for practical quantum and classical information processing applications were analyzed during the 2017 Workshop on Valleytronic Materials, Architectures, and Devices; this Review presents the major findings of the workshop.

Microsecond Valley Lifetime of Defect-Bound Excitons in Monolayer WSe_{2}

In atomically thin two-dimensional semiconductors such as transition metal dichalcogenides (TMDs), controlling the density and type of defects promises to be an effective approach for engineering light-matter interactions. We demonstrate that electron-beam irradiation is a simple tool for selectively introducing defect-bound exciton states associated with chalcogen vacancies in TMDs. Our first-principles calculations and time-resolved spectroscopy measurements of monolayer WSe_{2} reveal that these defect-bound excitons exhibit exceptional optical properties including a recombination lifetime approaching 200 ns and a valley lifetime longer than 1  μs. The ability to engineer the crystal lattice through electron irradiation provides a new approach for tailoring the optical response of TMDs for photonics, quantum optics, and valleytronics applications.

Optically dark excitonic states mediated exciton and biexciton valley dynamics in monolayer WSe2

We present a theory to address the photoluminescence (PL) intensity and valley polarization (VP) dynamics in monolayer WSe₂, under the impact of excitonic dark states of both excitons and biexcitons. We find that the PL intensity of all excitonic channels including intravalley exciton (X_b), intravalley biexciton (XX_k,k) and intervalley biexciton (XX[Formula: see text]) in particular for the XX_k,k PL is enhanced by laser excitation fluence. In addition, our results indicate the anomalous temperature dependence of PL, i.e. increasing with temperature, as a result of favored phonon assisted dark-to-bright scatterings at high temperatures. Moreover, we observe that the PL is almost immune to intervalley scatterings, which trigger the exchange of excitonic states between the two valleys. As far as the valley polarization is concerned, we find that the VP of X_b shrinks as temperature increases, exhibiting opposite temperature response to PL, while the intravalley XX_k,k VP is found almost independent of temperature. In contrast to both X_b and XX_k,k, the intervalley XX[Formula: see text] VP identically vanishes, because of equal populations of excitons in the K and [Formula: see text] valleys bounded to form intervalley biexcitons. Notably, it is found that the X_b VP much more strongly depends on bright-dark scattering than that of XX_k,k, making dark state act as a robust reservoir for valley polarization against intervalley scatterings for X_b at strong bright-dark scatterings, but not for XX_k,k. Dark excitonic states enabled enhancement of VP benefits quantum technology for information processing based on the valley degree of freedom in valleytronic devices. Furthermore, the VP has strong dependence on intervalley scattering but maintains essentially constant with excitation fluence. Finally, the dependence of time evolution of PL and VP on temperature and excitation fluence is discussed.

Valley Manipulation by Optically Tuning the Magnetic Proximity Effect in WSe2/CrI3 Heterostructures

Monolayer valley semiconductors, such as tungsten diselenide (WSe₂), possess valley pseudospin degrees of freedom that are optically addressable but degenerate in energy. Lifting the energy degeneracy by breaking time-reversal symmetry is vital for valley manipulation. This has been realized by directly applying magnetic fields or via pseudomagnetic fields generated by intense circularly polarized optical pulses. However, sweeping large magnetic fields is impractical for devices, and the pseudomagnetic fields are only effective in the presence of ultrafast laser pulses. The recent rise of two-dimensional (2D) magnets unlocks new approaches to controlling valley physics via van der Waals heterostructure engineering. Here, we demonstrate the wide continuous tuning of the valley polarization and valley Zeeman splitting with small changes in the laser-excitation power in heterostructures formed by monolayer WSe₂ and 2D magnetic chromium triiodide (CrI₃). The valley manipulation is realized via the optical control of the CrI₃ magnetization, which tunes the magnetic exchange field over a range of 20 T. Our results reveal a convenient new path toward the optical control of valley pseudospins and van der Waals magnetic heterostructures.

Theory and Ab Initio Computation of the Anisotropic Light Emission in Monolayer Transition Metal Dichalcogenides

Monolayer transition metal dichalcogenides (TMDCs) are direct gap semiconductors with a unique potential for use in ultrathin light emitters. However, their photoluminescence (PL) is not completely understood. We develop an approach to compute the radiative recombination rate in monolayer TMDCs as a function of photon emission direction and polarization. Using exciton wavefunctions and energies obtained with the ab initio Bethe-Salpeter equation, we obtain polar plots of the PL for different scenarios. Our results can explain the PL anisotropy and polarization dependence measured in recent experiments and predict that light is emitted with a peak intensity normal to the exciton dipole in monolayer TMDCs. We show that excitons emit light anisotropically upon recombination when they are in any quantum superposition state of the K and K' inequivalent valleys. When averaged over the emission angle and exciton momentum, our new treatment recovers the temperature-dependent radiative lifetimes that we previously derived. Our work demonstrates a generally applicable first-principles approach to studying anisotropic light emission in two-dimensional materials.

Lightwave valleytronics in a monolayer of tungsten diselenide

As conventional electronics is approaching its ultimate limits1, nanoscience has urgently sought for novel fast control concepts of electrons at the fundamental quantum level2. Lightwave electronics3 – the foundation of attosecond science4 – utilizes the oscillating carrier wave of intense light pulses to control the translational motion of the electron’s charge faster than a single cycle of light5–15. Despite being particularly promising information carriers, the internal quantum attributes of spin16 and valley pseudospin17–19 have not been switchable on the subcycle scale20–21. Here we demonstrate lightwave-driven changes of the valley pseudospin and introduce distinct signatures in the optical read out. Photogenerated electron–hole pairs in a monolayer of tungsten diselenide are accelerated and collided by a strong lightwave. The emergence of high odd-order sidebands and anomalous changes in their polarization direction directly attest to the ultrafast pseudospin dynamics. Quantitative computations combining density-functional theory with a non-perturbative quantum many-body approach assign the polarization of the sidebands to a lightwave-induced change of the valley pseudospin and confirm that the process is coherent and adiabatic. Our work opens the door to systematic valleytronic logic at optical clock rates.

Ultrafast quantum beats of anisotropic excitons in atomically thin ReS2

Quantum beats, periodic oscillations arising from coherent superposition states, have enabled exploration of novel coherent phenomena. Originating from strong Coulomb interactions and reduced dielectric screening, two-dimensional transition metal dichalcogenides exhibit strongly bound excitons either in a single structure or hetero-counterpart; however, quantum coherence between excitons is barely known to date. Here we observe exciton quantum beats in atomically thin ReS2 and further modulate the intensity of the quantum beats signal. Surprisingly, linearly polarized excitons behave like a coherently coupled three-level system exhibiting quantum beats, even though they exhibit anisotropic exciton orientations and optical selection rules. Theoretical studies are also provided to clarify that the observed quantum beats originate from pure quantum coherence, not from classical interference. Furthermore, we modulate on/off quantum beats only by laser polarization. This work provides an ideal laboratory toward polarization-controlled exciton quantum beats in two-dimensional materials.

Charge-Stripe Order and Superconductivity in Ir1-xPtxTe2

A combined resistivity and hard x-ray diffraction study of superconductivity and charge ordering in Ir Ir_1−xPt_xTe₂, as a function of Pt substitution and externally applied hydrostatic pressure, is presented. Experiments are focused on samples near the critical composition x_c ~ 0.045 where competition and switching between charge order and superconductivity is established. We show that charge order as a function of pressure in Ir_0.95Pt_0.05Te₂ is preempted — and hence triggered — by a structural transition. Charge ordering appears uniaxially along the short crystallographic (1, 0, 1) domain axis with a (1/5, 0, 1/5) modulation. Based on these results we draw a charge-order phase diagram and discuss the relation between stripe ordering and superconductivity.

Zeeman splitting via spin-valley-layer coupling in bilayer MoTe2

Atomically thin monolayer transition metal dichalcogenides possess coupling of spin and valley degrees of freedom. The chirality is locked to identical valleys as a consequence of spin-orbit coupling and inversion symmetry breaking, leading to a valley analog of the Zeeman effect in presence of an out-of-plane magnetic field. Owing to the inversion symmetry in bilayers, the photoluminescence helicity should no longer be locked to the valleys. Here we show that the Zeeman splitting, however, persists in 2H-MoTe₂ bilayers, as a result of an additional degree of freedom, namely the layer pseudospin, and spin-valley-layer locking. Unlike monolayers, the Zeeman splitting in bilayers occurs without lifting valley degeneracy. The degree of circularly polarized photoluminescence is tuned with magnetic field from -37% to 37%. Our results demonstrate the control of degree of freedom in bilayer with magnetic field, which makes bilayer a promising platform for spin-valley quantum gates based on magnetoelectric effects.Monolayer transition metal dichalcogenides host a valley splitting in magnetic field analogous to the Zeeman effect. Here, the authors report that the Zeeman splitting still persists in bilayers of MoTe₂ without lifting the valley degeneracy, due to spin-valley-layer coupling.

Control of Coherently Coupled Exciton Polaritons in Monolayer Tungsten Disulphide

Monolayer transition metal dichalcogenides (TMD) with confined 2D Wannier-Mott excitons are intriguing for the fundamental study of strong light-matter interactions and the exploration of exciton polaritons at high temperatures. However, the research of 2D exciton polaritons has been hindered because the polaritons in these atomically thin semiconductors discovered so far can hardly support strong nonlinear interactions and quantum coherence due to uncontrollable polariton dynamics and weakened coherent coupling. In this work, we demonstrate, for the first time, a precisely controlled hybrid composition with angular dependence and dispersion-correlated polariton emission by tuning the polariton dispersion in TMD over a broad temperature range of 110-230 K in a single cavity. This tamed polariton emission is achieved by the realization of robust coherent exciton-photon coupling in monolayer tungsten disulphide (WS_{2}) with large splitting-to-linewidth ratios (>3.3). The unprecedented ability to manipulate the dispersion and correlated properties of TMD exciton polaritons at will offers new possibilities to explore important quantum phenomena such as inversionless lasing, Bose-Einstein condensation, and superfluidity.

Trion Valley Coherence in Monolayer Semiconductors

The emerging field of valleytronics aims to exploit the valley pseudospin of electrons residing near Bloch band extrema as an information carrier. Recent experiments demonstrating optical generation and manipulation of exciton valley coherence (the superposition of electron-hole pairs at opposite valleys) in monolayer transition metal dichalcogenides (TMDs) provide a critical step towards control of this quantum degree of freedom. The charged exciton (trion) in TMDs is an intriguing alternative to the neutral exciton for control of valley pseudospin because of its long spontaneous recombination lifetime, its robust valley polarization, and its coupling to residual electronic spin. Trion valley coherence has however been unexplored due to experimental challenges in accessing it spectroscopically. In this work, we employ ultrafast two-dimensional coherent spectroscopy to resonantly generate and detect trion valley coherence in monolayer MoSe₂ demonstrating that it persists for a few-hundred femtoseconds. We conclude that the underlying mechanisms limiting trion valley coherence are fundamentally different from those applicable to exciton valley coherence.

Tunable spin and valley dependent magneto-optical absorption in molybdenum disulfide quantum dots

Photonic quantum computer, quantum communication, quantum metrology and quantum optical technologies rely on the single-photon source (SPS). However, the SPS with valley-polarization remains elusive and the tunability of magneto-optical transition frequency and emission/absorption intensity is restricted, in spite of being highly in demand for valleytronic applications. Here we report a new class of SPSs based on carriers spatially localized in two-dimensional monolayer transition metal dichalcogenide quantum dots (QDs). We demonstrate that the photons are absorbed (or emitted) in the QDs with distinct energy but definite valley-polarization. The spin-coupled valley-polarization is invariant under either spatial or magnetic quantum quantization. However, the magneto-optical absorption peaks undergo a blue shift as the quantization is enhanced. Moreover, the absorption spectrum pattern changes considerably with a variation of Fermi energy. This together with the controllability of absorption spectrum by spatial and magnetic quantizations, offers the possibility of tuning the magneto-optical properties at will, subject to the robust spin-coupled valley polarization.