Valley susceptibility of an interacting two-dimensional electron system

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.

Nematic Metal in a Multivalley Electron Gas: Variational Monte Carlo Analysis and Application to AlAs

The two-dimensional electron gas is of fundamental importance in quantum many-body physics. We study a minimal extension of this model with C_{4} (as opposed to full rotational) symmetry and an electronic dispersion with two valleys with anisotropic effective masses. Electrons in our model interact via Coulomb repulsion, screened by distant metallic gates. Using variational Monte Carlo simulations, we find a broad intermediate range of densities with a metallic valley-polarized, spin-unpolarized ground state. Our results are of direct relevance to the recently discovered "nematic" state in AlAs quantum wells. For the effective mass anisotropy relevant to this system, m_{x}/m_{y}≈5.2, we obtain a transition from an anisotropic metal to a valley-polarized metal at r_{s}≈12 (where r_{s} is the dimensionless Wigner-Seitz radius). At still lower densities, we find a (possibly metastable) valley and spin-polarized state with a reduced electronic anisotropy.

Valley-Polarized Quantum Hall Phase in a Strain-Controlled Dirac System

In multivalley systems, the valley pseudospin offers rich physics going from encoding of information by its polarization (valleytronics), to exploring novel phases of matter when its degeneracy is changed. Here, by strain engineering, we reveal fully valley-polarized quantum Hall phases in the Pb_{1-x}Sn_{x}Se Dirac system. Remarkably, when the valley energy splitting exceeds the fundamental band gap, we observe a "bipolar quantum Hall phase," heralded by the coexistence of hole and electron chiral edge states at distinct valleys in the same quantum well. This suggests that spatially overlaid counterpropagating chiral edge states emerging at different valleys do not interfere with each other.

Influence of electronic correlation on the valley and topological properties of VSiGeP4 monolayer

Valley is used as a new degree of freedom for information encoding and storage. In this work, the valley and topological properties of the VSiGeP4 monolayer were studied by adjusting the U value based on first-principles calculations. The VSiGeP4 monolayer remains in a ferromagnetic ground state regardless of the change in the U value. The magnetic anisotropy of the VSiGeP4 monolayer is initially in-plane, and then turns out-of-plane with the increase in the U value. Moreover, a topological phase transition is observed in the present VSiGeP4 monolayer with the increase in U value from 0 to 3 eV, i.e., the VSiGeP4 monolayer behaves as a bipolar magnetic semiconductor, a ferrovalley semiconductor, a half-valley metal characteristic, and a quantum anomalous Hall state. The mechanism of the topological phase transition behavior of the VSiGeP4 monolayer was analyzed. It was found that the variation in U values would change the strength of the electronic correlation effect, resulting in the valley and topological properties. In addition, carrier doping was studied to design a valleytronic device using this VSiGeP4 monolayer. By doping 0.05 electrons per f.u., the VSiGeP4 monolayer with a U value of 3 eV exhibits 100% spin polarization. This study indicates that the VSiGeP4 monolayer has potential applications in spintronic, valleytronic, and topological electronic nanodevices.

Tunable valley polarization effect and second-order topological state in monolayer FeClSH

In two-dimensional (2D) materials, breaking the inversion symmetry plays an important role in valleytronics. Ferrovalley (FV) materials can achieve spontaneous valley polarization (VP) without additional modulation due to the magnetic exchange interaction and strong spin-orbit coupling. Using first-principles calculations, we predict a new 2D material, Janus FeClSH, which exhibits a large spontaneous VP. This monolayer is a perfect FV material, where the valence band maximum and conduction band minimum are located at the K/K' point. A large VP of 102.95 meV is spontaneously generated for the case of out-of-plane magnetization. Additionally, we propose that the irradiating circularly polarized light can be used to realize VP for the case of in-plane magnetization. Remarkably, a triangular nanoflake of FeClSH with armchair edges can show nontrivial corner states, exhibiting a second-order topological insulator (SOTI) state. The VP effect and SOTI state are tunable with the Hubbard U parameter, making the FeClSH monolayer promising for the study of the coupling between VP and SOTI.

Ferroic Phases in Two-Dimensional Materials

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

Room temperature valley polarization via spin selective charge transfer

The two degenerate valleys in transition metal dichalcogenides can be used to store and process information for quantum information science and technology. A major challenge is maintaining valley polarization at room temperature where phonon-induced intervalley scattering is prominent. Here we demonstrate room temperature valley polarization in heterostructures of monolayer MoS2 and naphthylethylammine based one-dimensional chiral lead halide perovskite. By optically exciting the heterostructures with linearly polarized light close to resonance and measuring the helicity resolved photoluminescence, we obtain a degree of polarization of up to -7% and 8% in MoS2/right-handed (R-(+)-) and left-handed (S-(-)-) 1-(1-naphthyl)ethylammonium lead iodide perovskite, respectively. We attribute this to spin selective charge transfer from MoS2 to the chiral perovskites, where the perovskites act as a spin filter due to their chiral nature. Our study provides a simple, yet robust route to obtain room temperature valley polarization, paving the way for practical valleytronics devices.

Distinct ferrovalley characteristics of the Janus RuClX (X = F, Br) monolayer

Two-dimensional ferrovalley materials should simultaneously possess three characteristics, that is, a Curie temperature beyond atmospheric temperature, perpendicular magnetic anisotropy, and large valley polarization for potential commercial applications. In this report, we predict two ferrovalley Janus RuClX (X = F, Br) monolayers by first-principles calculations and Monte Carlo simulations. The RuClF monolayer exhibited a valley-splitting energy as large as 194 meV, perpendicular magnetic anisotropy energy of 187 μeV per f.u., and Curie temperature of 320 K. Thus, spontaneous valley polarization at room temperature will be present in the RuClF monolayer, which is nonvolatile for spintronic and valleytronic devices. Although the valley-splitting energy of the RuClBr monolayer was as high as 226 meV with magnetic anisotropy energy of 1.852 meV per f.u., the magnetic anisotropy of the RuClBr monolayer was in-plane, and its Curie temperature was only 179 K. The orbital-resolved magnetic anisotropy energy revealed that the interaction between the occupied spin-up states of d_yz and the unoccupied spin-down states of d_z² dominated the out-of-plane magnetic anisotropy in the RuClF monolayer, but the in-plane magnetic anisotropy of the RuClBr monolayer was mostly contributed by the coupling of the d_xy and d_x²-y² orbitals. Interestingly, the valley polarizations in the Janus RuClF and RuClBr monolayers appeared in their valence band and conduction band, respectively. Thus, two anomalous valley Hall devices are proposed using the present Janus RuClF and RuClBr monolayers with hole and electron doping, respectively. This study provides interesting and alternative candidate materials for the development of valleytronic devices.

Layer-polarized anomalous Hall effects in valleytronic van der Waals bilayers

The layer-polarized anomalous Hall effect (LP-AHE), derived from the coupling between the Berry curvature and the layer degree of freedom, is of importance for both fundamental physics and device applications. Nonetheless, the current research paradigm is rooted in topological systems, rendering such a phenomenon rather scarce. Here, through model analysis, we propose an alternative, but general, mechanism for realizing the LP-AHE in valleytronic van der Waals bilayers by interlayer sliding. The interaction between out-of-plane ferroelectricity and A-type antiferromagnetism gives rise to the layer-locked Berry curvature and thus the long-sought LP-AHE in bilayer systems. The LP-AHE can be strongly coupled with sliding ferroelectricity, rendering it ferroelectrically controllable and reversible. The mechanism is demonstrated in a series of real valleytronic materials, including bilayer VSi₂P₄, VSi₂N₄, FeCl₂, RuBr₂ and VClBr. The new mechanism and phenomena provide a significant new direction to realize the LP-AHE and explore its application in electronics.

Nonvolatile Electrical Valley Manipulation in WS2 by Ferroelectric Gating

Valleytronics in transition metal dichalcogenides has been intensively investigated for potential applications in next-generation information storage, data processing, and signal transmission devices. Here a ferroelectric gating approach is engaged in achieving nonvolatile electrical tuning of the valley-excitonic properties of monolayer and bilayer WS₂. The gating effects include carrier doping and ferroelectric coupling, which are further distinguished by comparing two geometries where the gate electrodes are in direct contact with or insulated from the WS₂ crystal. The results show that the carrier doping from gate electrodes acts on WS₂ through carrier screening, which only moderately alters the valley polarization. In contrast, the ferroelectric gating promotes electron-phonon interaction, introduces a strong surface polarization field, and controls the interfacial charge trapping/detrapping, causing a Stark shift in exciton energy and strongly enhancing room-temperature valley polarization. In bilayer WS₂, the intralayer-interlayer exciton transition is further induced, contributing to even higher valley polarization. The ferroelectric coupling effect can still be maintained after the removal of gate voltage, showing its nonvolatile nature. The role of ferroelectricity is further verified by the anomalous temperature dependence in valley polarization. This work has revealed effective electrical control over valley excitons in semiconductors through interaction with ferroelectric materials. The reported high room-temperature valley polarization in WS₂ will boost the development of valleytronics devices.

2D electrene LaH2monolayer: an ideal ferrovalley direct semiconductor with room-temperature ferromagnetic stability

In developing nonvolatile valleytronic devices, ferromagnetic (FM) ferrovalley semiconductors are critically needed due to the existence of spontaneous valley polarization. At present, however, the known real materials have various drawbacks towards practical applications, including the in-plane FM ground state, low Curie temperature (TC), small valley polarization, narrow energy window with clean polarized valley, and indirect bandgap. From first-principles calculations, here we predict anideal ferrovalley semiconductor, honeycomb LaH₂monolayer (ML), whose intrinsic properties can overcome all these shortcomings. We demonstrate that LaH₂ML, having satisfied structural stability, is a FM half-semiconducting electrene (La3+2H-⋅e-) with its magnetic moments localized at the lattice interstitial sites rather than La atoms. At the same time, LaH₂ML holds the following desired attributes: a robust out-of-plane FM ground state with a highTC(334 K), a sizable valley polarization (166 meV), a wide energy window (137 meV) harboring clean single-valley carriers, and a direct bandgap. These results identify a much needed ideal ferrovalley semiconductor candidate, holding the promising application potential in valleytronics and spintronics devices.

Phonon-Limited Valley Polarization in Transition-Metal Dichalcogenides

The ability to selectively photoexcite at different Brillouin zone valleys forms the basis of valleytronics and other valley-related physics. Symmetry arguments combined with static lattice first-principles calculations suggest an ideal 100% valley polarization in transition-metal dichalcogenides under circularly polarized light. However, experimental reports of the valley polarization range from 32% to almost 100%. Possible explanations for this discrepancy include phonon-mediated transitions, which would place a fundamental limit to valley polarization, and defect-mediated transitions, which could, in principle, be reduced with cleaner samples. We explore the phonon-mediated fundamental limit by performing calculations of phonon-mediated optical absorption for circularly polarized light entirely from the first principles. We also use group theory to reveal the microscopic mechanisms behind the phonon-mediated excitations, discovering contributions from several individual phonon modes and from multiphonon processes. Overall, our calculations show that the phonon-limited valley polarization is around 70% at room temperature for state-of-the-art valleytronic materials including MoSe_{2}, MoS_{2}, WS_{2}, WSe_{2}, and MoTe_{2}. This fundamental limit implies that sufficiently pure transition-metal dichalcogenides are ideal candidates for valleytronics applications.

Strain engineering of electronic properties and anomalous valley hall conductivity of transition metal dichalcogenide nanoribbons

Strain engineering is a powerful technique for tuning electronic properties and valley degree of freedom in honeycomb structure of two-dimensional crystals. Carriers in + k and − k (opposite Berry curvature) in transition metal dichalcogenide (TMD) with broken inversion symmetry act as effective magnetic fields, where this polarized valleys are suitable for encoding information. In this work, we study the strained TMD nanoribbons by Slater-Koster tight-binding model, which acquires electronic bands in whole Brillouin zone. From this, we derive a generic profile of strain effect on the electronic band structure of TMD nanoribbons, which shows indirect band gap, and also exhibits a phase transition from semiconductor to metallic by applying uniaxial X-tensile and Y-arc type of strain. Midgap states in strained TMD nanoribbons are determined by calculation of localized density of electron states. Moreover, our findings of anomalous valley Hall conductivity reveal that the creation of pseudogauge fields using strained TMD nanoribbons affect the Dirac electrons, which generate the new quantized Landau level. Furthermore, we demonstrate in strained TMD nanoribbons that strain field can effectively tune both the magnitude and sign of valley Hall conductivity. Our work elucidates the valley Hall transport in strained TMDs due to pseudo-electric and pseudo-magnetic filed will be applicable as information carries for future electronics and valleytronics.

Intrinsic Valley Splitting and Direct-to-Indirect Band Gap Transition in Monolayer HfZrSiCO2

Both a reasonably large valley splitting (VS) and a sufficiently long valley exciton lifetime are crucial in valleytronics device applications. Currently, no single system possesses both attributes simultaneously. Herein, we demonstrate that a Janus monolayer HfZrSiCO2 concurrently hosts a giant intrinsic VS and excitonic quasi-particles with long valley lifetime due to valley-sublayer coupling and built-in electric field. In addition, the band structure of the monolayer HfZrSiCO2 can be continuously manipulated by either an external electric field or a biaxial strain, giving rise to a tunable VS and driving a direct-to-indirect band gap transition. Moreover, the system exhibits valley-contrasting linear dichroism in exciton absorption. These results suggest that the Janus monolayer HfZrSiCO2 is a promising candidate for information applications.

Electrical Switching of the Off-Resonance Room-Temperature Valley Polarization in Monolayer MoS2 by a Double-Resonance Chiral Microstructure

Enhancing and expanding the manipulated range of room-temperature valley polarization at off-resonance wavelength is extremely crucial to developing various functional valleytronic devices. Although these have been realized through the double-resonance strategy or twist-angle engineering, the demand for electrical control over the concepts remains elusive. Here, we fabricate a gate-tunable double-resonance chiral microstructure using a molybdenum disulfides (MoS₂) monolayer. On the basis of the varied interface charge density, we demonstrate the huge photoluminescence (PL) tuning ability of this configuration. Furthermore, benefiting predominately from the screening of long-range e-h exchange interactions and the chiral Purcell effect, the electrical switching of the room-temperature valley polarization at off-resonance wavelength is also realized. Our work enriches the functions of TMDs-based optoelectronic devices and may create important applications in future valley-polarized encode and information processing devices.

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.

Long-Range Directional Routing and Spatial Selection of High-Spin-Purity Valley Trion Emission in Monolayer WS2

Valley-dependent excitation and emission in transition metal dichalcogenides (TMDCs) have recently emerged as a new avenue for optical data manipulation, quantum optical technologies, and chiral photonics. The valley-polarized electronic states can be optically addressed through photonic spin-orbit interaction of excitonic emission, typically with plasmonic nanostructures, but their performance is limited by the low quantum yield of neutral excitons in TMDC multilayers and the large Ohmic loss of plasmonic systems. Here, we demonstrate a valleytronic system based on the trion emission in high-quantum-yield WS₂ monolayers chirally coupled to a low-loss microfiber. The integrated system uses the spin properties of the waveguided modes to achieve long-range directional routing of valley excitations and also provides an approach to selectively address valley-dependent emission from different spatial locations around the microfiber. This valleytronic interface can be integrated with fiber communication devices, allowing for merging valley polarization and chiral photonics as an alternative mechanism for optical information transport and manipulation in classical and quantum regimes.

The magnetic proximity effect at the MoS2/CrI3interface

The vicinity to a two-dimensional magnetic material provides a simple and effective way to break the valley degeneracy of transition-metal dichalcogenides because of the magnetic proximity effect. Based on first-principles calculations, we study the band structure of a MoS₂/CrI₃van der Waals heterostructure and its manipulation by vertical electric fields. A huge valley splitting of about 19.60 meV, equivalent to an external magnetic fields of about 89.0 T can be generated by an electric field of 0.115 V Å^-1. The electric field causes discontinuous changes in the valley splitting. The electric field drives the bands of MoS₂across those of CrI₃. At the critical electric fields, the interlayer orbital hybridization leads to the energy level repulsion and an abrupt exchange of the band index. We also study the effect of interlayer distance on the valley splitting and observe a more significant electric field modulation. This work deepens our understanding on the interfacial magnetic proximity effect as a result of the orbital hybridization across the van der Waals gap.

Spontaneous Valley Polarization of Itinerant Electrons

Memory or transistor devices based on an electron's spin rather than its charge degree of freedom offer certain distinct advantages and comprise a cornerstone of spintronics. Recent years have witnessed the emergence of a new field, valleytronics, which seeks to exploit an electron's valley index rather than its spin. An important component in this quest would be the ability to control the valley index in a convenient fashion. Here we show that the valley polarization can be switched from zero to 1 by a small reduction in density, simply tuned by a gate bias, in a two-dimensional electron system. This phenomenon, which is akin to Bloch spin ferromagnetism, arises fundamentally as a result of electron-electron interaction in an itinerant, dilute electron system. Essentially, the kinetic energy favors an equal distribution of electrons over the available valleys, whereas the interaction between electrons prefers single-valley occupancy below a critical density. The gate-bias-tuned transition we observe is accompanied by a sudden, twofold change in sample resistance, making the phenomenon of interest for potential valleytronic transistor device applications. Our observation constitutes a quintessential demonstration of valleytronics in a very simple experiment.

Tunable valley polarization in Janus WSSe by magnetic proximity coupling to a CrI3 layer

We investigate the electronic properties and valley physics of Janus monolayer WSSe on a CrI₃ substrate layer based on first-principles calculations. It is shown that the K and K' valley degeneracy can be lifted which leads to valley polarization (VP) in the WSSe due to the magnetic proximity coupling to a magnetic substrate. The magnitude of VP is highly sensitive to the interfacial electronic properties and can be tuned by varying the stacking configurations of the heterostructure. Interestingly, the direction of VP can be altered by manipulating the layer alignment without reversing the magnetism orientation of the magnetic substrate CrI₃. We suggest that the hybridization between the bands of WSSe and the substrate plays an important role. Meanwhile, the charge distributions have been mapped out to uncover the microscopic origin of the direction variable VP. In addition, large VP can be achieved by adjusting the interlayer spacing. Our investigations may have potential applications in the design of valleytronic devices.

Theoretical evidence of the spin-valley coupling and valley polarization in two-dimensional MoSi2X4 (X = N, P, and As)

Very recently, the centimeter-scale MoSi2N4 monolayer was synthesized experimentally and exhibited a semiconducting nature with high mobility (Hong et al., Science, 2020, 369, 670-674). Here, we show that MoSi2N4 and its analogues, MoSi2P4 and MoSi2As4, are potential two-dimensional (2D) materials for valleytronics based on first-principles calculations. We demonstrate that the intrinsic inversion symmetry breaking and strong spin-orbital coupling lead to the remarkable spin-valley coupling in the inequivalent valleys at K and K' points, which result in not only the valley-contrasting transport properties, but also the spin and valley coupled optical selection rules. Moreover, the in-plane strain can tune the bandgaps and spin splitting or even induce an indirect-to-direct bandgap transition for promising application in the strain-tunable valleytronics. We find that the valley polarization can be generated by doping magnetic element. Our findings offer theoretical insight into the exotic physical properties of novel MoSi2N4-family materials beyond transition metal dichalcogenides.

Valley polarization caused by crystalline symmetry breaking

In two-dimensional (2D) hexagonal lattices with inversion asymmetry, time-reversal (T) connected valleys are at the center of current valleytronic research. In order to trigger valley polarization, dynamical processes and/or magnetism have been considered. In this work, we propose a new mechanism, valley-contrasting sublattice polarization (VCSP), to polarize valleys by reducing the crystalline symmetry that connects the valleys. In our mechanism, significant valley polarization could be readily generated without magnetism, an electric field, or an optical process. Based on tight-binding model analysis and first-principle calculations, the control of valley polarization via crystalline symmetry can be successfully realized in concrete LaOBiS₂ polytypes with Peierls-like structure distortion. Our results provide an unprecedented possibility for exploring valley-contrasting physics.

A Valleytronic Diamond Transistor: Electrostatic Control of Valley Currents and Charge-State Manipulation of NV Centers

The valley degree of freedom in many-valley semiconductors provides a new paradigm for storing and processing information in valleytronic and quantum-computing applications. Achieving practical devices requires all-electric control of long-lived valley-polarized states, without the use of strong external magnetic fields. Because of the extreme strength of the carbon-carbon bond, diamond possesses exceptionally stable valley states that provide a useful platform for valleytronic devices. Using ultrapure single-crystalline diamond, we demonstrate electrostatic control of valley currents in a dual-gate field-effect transistor, where the electrons are generated with a short ultraviolet pulse. The charge current and the valley current measured at the receiving electrodes are controlled separately by varying the gate voltages. We propose a model to interpret experimental data, based on drift-diffusion equations coupled through rate terms, with the rates computed by microscopic Monte Carlo simulations. As an application, we demonstrate valley-current charge-state modulation of nitrogen-vacancy centers.

Valley interference and spin exchange at the atomic scale in silicon

Tunneling is a fundamental quantum process with no classical equivalent, which can compete with Coulomb interactions to give rise to complex phenomena. Phosphorus dopants in silicon can be placed with atomic precision to address the different regimes arising from this competition. However, they exploit wavefunctions relying on crystal band symmetries, which tunneling interactions are inherently sensitive to. Here we directly image lattice-aperiodic valley interference between coupled atoms in silicon using scanning tunneling microscopy. Our atomistic analysis unveils the role of envelope anisotropy, valley interference and dopant placement on the Heisenberg spin exchange interaction. We find that the exchange can become immune to valley interference by engineering in-plane dopant placement along specific crystallographic directions. A vacuum-like behaviour is recovered, where the exchange is maximised to the overlap between the donor orbitals, and pair-to-pair variations limited to a factor of less than 10 considering the accuracy in dopant positioning. This robustness remains over a large range of distances, from the strongly Coulomb interacting regime relevant for high-fidelity quantum computation to strongly coupled donor arrays of interest for quantum simulation in silicon.

Coupled donor wavefunctions in silicon are spatially resolved to evidence valley interference processes. An atomic-scale understanding of the interplay between interference, envelope anisotropy and crystal symmetries unveils a placement strategy compatible with existing technology where the exchange is insensitive to interference.

Spontaneous Valley Polarization of Interacting Carriers in a Monolayer Semiconductor

We report magnetoabsorption spectroscopy of gated WSe_{2} monolayers in high magnetic fields up to 60 T. When doped with a 2D Fermi sea of mobile holes, well-resolved sequences of optical transitions are observed in both σ^{±} circular polarizations, which unambiguously and separately indicate the number of filled Landau levels (LLs) in both K and K^{'} valleys. This reveals the interaction-enhanced valley Zeeman energy, which is found to be highly tunable with hole density p. We exploit this tunability to align the LLs in K and K^{'}, and find that the 2D hole gas becomes unstable against small changes in LL filling and can spontaneously valley polarize. These results cannot be understood within a single-particle picture, highlighting the importance of exchange interactions in determining the ground state of 2D carriers in monolayer semiconductors.

Electrically Tunable Valley Dynamics in Twisted WSe_{2}/WSe_{2} Bilayers

The twist degree of freedom provides a powerful new tool for engineering the electrical and optical properties of van der Waals heterostructures. Here, we show that the twist angle can be used to control the spin-valley properties of transition metal dichalcogenide bilayers by changing the momentum alignment of the valleys in the two layers. Specifically, we observe that the interlayer excitons in twisted WSe_{2}/WSe_{2} bilayers exhibit a high (>60%) degree of circular polarization (DOCP) and long valley lifetimes (>40  ns) at zero electric and magnetic fields. The valley lifetime can be tuned by more than 3 orders of magnitude via electrostatic doping, enabling switching of the DOCP from ∼80% in the n-doped regime to <5% in the p-doped regime. These results open up new avenues for tunable chiral light-matter interactions, enabling novel device schemes that exploit the valley degree of freedom.

Valley-Layer Coupling: A New Design Principle for Valleytronics

The current valleytronics research is based on the paradigm of time-reversal-connected valleys in two-dimensional (2D) hexagonal materials, which forbids the fully electric generation of valley polarization by a gate field. Here, we go beyond the existing paradigm to explore 2D systems with a novel valley-layer coupling (VLC) mechanism, where the electronic states in the emergent valleys have a valley-contrasted layer polarization. The VLC enables a direct coupling between a valley and a gate electric field. We analyze the symmetry requirements for a system to host VLC, demonstrate our idea via first-principles calculations and model analysis of a concrete 2D material example, and show that an electric, continuous, wide-range, and switchable control of valley polarization can be achieved by VLC. Furthermore, we find that systems with VLC can exhibit other interesting physics, such as valley-contrasting linear dichroism and optical selection of the valley and the electric polarization of interlayer excitons. Our finding opens a new direction for valleytronics and 2D materials research.

Asymmetric valley polarization and photoluminescence in MoS2/MoO3 heterostructure

We investigate circularly polarized photoluminescence (PL) in the MoS₂/MoO₃ heterostructure, which was fabricated by transferring MoS₂ monolayer to cover the MoO₃ few layers on the SiO₂/Si substrate. It is shown that the PL with the same helicity as the excitation light is dominant due to the inherent chiral optical selectivity, which allows exciting one of the valleys in MoS₂ monolayer. The degree of polarization (DP), which characterizes the intensity difference of two chiral components of PL, is unequal for the right-handed and left-handed circularly polarized excitations in the MoS₂/MoO₃ heterostructure. This effect is different from the one in pristine MoS₂. Our Raman spectra results together with ab initio calculations indicate the p-doped features of the MoS₂ when it covers the MoO₃ layers. Thus the possible explanation of the unequal DP is that the p-doping process generates a built-in voltage and therefore brings the difference of electron-hole overlaps between K and K' valleys. Namely the asymmetric valley polarization may be obtained in the MoS₂/MoO₃ heterostructure. Consequently, the circularly polarized PL caused by the electron-hole recombination at K and K' valleys manifests unequal DP for the right-handed and left-handed helix excitations. This asymmetric effect is further enhanced by decreasing the temperature in the MoS₂/MoO₃ heterostructure. Our investigation provides a unique platform for developing novel two-dimensional valleytronic devices.

Resymmetrizing Broken Symmetry with Hydraulic Pressure

Recent progress in condensed matter physics, such as for graphene, topological insulators, and Weyl semimetals, often originate from the specific topological symmetries of their lattice structures. Quantum states with different degrees of freedom, e.g., spin, valley, layer, etc., arise from these symmetries, and the coherent superposition of these states form multiple energy subbands. The pseudospin, a concept analogous to the Dirac spinor matrices, is a successful description of such multisubband systems. When the electron-electron interaction dominates, many-body quantum phases arise. They usually have discrete pseudospin polarizations and exhibit sharp phase transitions at certain universal critical pseudospin energy splittings. In this Letter, we present our discovery of hydrostatic-pressure-induced degeneracy between the two lowest Landau levels. This degeneracy is evidenced by the pseudospin polarization transitions of the fragile correlated quantum liquid phases near the Landau level filling factor ν=3/2. Benefitting from the constant hole concentration and the sensitive nature of these transitions, we study the fine-tuning effect of the hydrostatic pressure at the order of 10  μeV, well beyond the meV-level state-of-the-art resolution of other techniques.

Electrically controlled valley states in bilayer graphene

Valley current, a stable, dissipationless current, originates due to the emergence of Berry curvature in inversion symmetry broken systems. Several theoretical predictions and experimental observations have explored layer symmetry breaking in AB-stacked bilayer graphene due to long-range Coulomb interactions between the electrons. However, none of the experimental studies conducted so far have observed valley current in unbiased bilayer graphene, which makes it vital to study the Berry curvature in unbiased bilayer graphene. In this study, we observed a non-zero Berry curvature with opposite values at K and K' valleys, validating the argumentation of the asymmetry persistent in unbiased bilayer graphene. The magnitude, as well as the polarity of the Berry curvature, is tunable with the application of an out-of-plane electric field. These results are especially important because they can lead to the realization of a valley valve, in which the carriers from the K and K' valleys can be regulated with a gate at the centre of a bilayer graphene nanoribbon.

Tuning spin-orbit coupling in 2D materials for spintronics: a topical review

Atomically-thin 2D materials have opened up new opportunities in the past decade in realizing novel electronic device concepts, owing to their unusual electronic properties. The recent progress made in the aspect of utilizing additional degrees of freedom of the electrons such as spin and valley suggests that 2D materials have a significant potential in replacing current electronic-charge-based semiconductor technology with spintronics and valleytronics. For spintronics, spin-orbit coupling plays a key role in manipulating the electrons' spin degree of freedom to encode and process information, and there are a host of recent studies exploring this facet of 2D materials. We review the recent advances in tuning spin-orbit coupling of 2D materials which are of notable importance to the progression of spintronics.

Detection of thermodynamic "valley noise" in monolayer semiconductors: Access to intrinsic valley relaxation time scales

Together with charge and spin, many novel two-dimensional materials also permit information to be encoded in an electron's valley degree of freedom-that is, in particular momentum states in the material's Brillouin zone. With a view toward valley-based (opto)electronic technologies, the intrinsic time scales of valley scattering are therefore of fundamental interest. Here, we demonstrate an entirely noise-based approach for exploring valley dynamics in monolayer transition-metal dichalcogenide semiconductors. Exploiting their valley-specific optical selection rules, we use optical Faraday rotation to passively detect the thermodynamic fluctuations of valley polarization in a Fermi sea of resident carriers. This spontaneous "valley noise" reveals narrow Lorentzian line shapes and, therefore, long exponentially-decaying intrinsic valley relaxation. Moreover, the noise signatures validate both the relaxation times and the spectral dependence of conventional (perturbative) pump-probe measurements. These results provide a viable route toward quantitative measurements of intrinsic valley dynamics, free from any external perturbation, pumping, or excitation.

Valley polarization and ferroelectricity in a two-dimensional GaAsC6 monolayer

Valley polarization and ferroelectricity are the two basic concepts in electronic device applications. However, the coexistence of these two scenarios in one material has not been reported. Here, using first-principles calculations, we demonstrated that the two-dimensional GaAsC6 monolayer which is a hybrid structure of GaAs and graphene has a pair of inequivalent valleys with opposite Berry curvatures and an intrinsic out-of-plane spontaneous electric polarization. It also has a direct band gap of about 1.937 eV and a high carrier mobility of about 1.80 × 105 cm2 V-1 s-1, which are promising for electronic device applications. The integration of valley polarization and ferroelectricity in a single material offers a promising platform for the design of electronic devices.

Intrinsic valley Hall transport in atomically thin MoS2

Electrons hopping in two-dimensional honeycomb lattices possess a valley degree of freedom in addition to charge and spin. In the absence of inversion symmetry, these systems were predicted to exhibit opposite Hall effects for electrons from different valleys. Such valley Hall effects have been achieved only by extrinsic means, such as substrate coupling, dual gating, and light illuminating. Here we report the first observation of intrinsic valley Hall transport without any extrinsic symmetry breaking in the non-centrosymmetric monolayer and trilayer MoS₂, evidenced by considerable nonlocal resistance that scales cubically with local resistance. Such a hallmark survives even at room temperature with a valley diffusion length at micron scale. By contrast, no valley Hall signal is observed in the centrosymmetric bilayer MoS₂. Our work elucidates the topological origin of valley Hall effects and marks a significant step towards the purely electrical control of valley degree of freedom in topological valleytronics.

Electrons hopping in two-dimensional honeycomb lattices possess a valley degree of freedom. Here, the authors observe room-temperature valley Hall transport without any extrinsic symmetry breaking in the non-centrosymmetric monolayer and trilayer MoS₂ by purely electronic means, whereas no valley signal is detected for centrosymmetric bilayer MoS₂.

Polarization switching and electrical control of interlayer excitons in two-dimensional van der Waals heterostructures

Long-lived interlayer excitons in van der Waals heterostructures based on transition metal dichalcogenides, together with unique spin-valley physics, make them promising for next-generation photonic and valleytronic devices. While the emission characteristics of interlayer excitons have been studied, efficient manipulation of their valley-state, a necessary requirement for information encoding, is still lacking. Here, we demonstrate comprehensive electrical control of interlayer excitons in a MoSe₂/WSe₂ heterostructure. Encapsulation of our well-aligned stack with hexagonal boron nitride (h-BN) allows us to resolve two separate narrow interlayer transitions with opposite helicities under circularly polarized excitation, either preserving or reversing the polarization of incoming light. By electrically controlling their relative intensities, we realize a polarization switch with tuneable emission intensity and wavelength. Finally, we demonstrate large Zeeman shifts of these two transitions upon application of an external magnetic field. These results are interpreted within the picture of moiré-induced brightening of forbidden optical transitions. The ability to control the polarization of interlayer excitons is a step forward towards the manipulation of the valley degree-of-freedom in realistic device applications.

Unconventional Anisotropic Even-Denominator Fractional Quantum Hall State in a System with Mass Anisotropy

The fractional quantum Hall state (FQHS) observed at a half-filled Landau level in an interacting two-dimensional electron system (2DES) is among the most exotic states of matter as its quasiparticles are expected to be Majorana excitations with non-Abelian statistics. We demonstrate here the unexpected presence of such a state in a novel 2DES with a strong band-mass anisotropy. The FQHS we observe has unusual characteristics. While its Hall resistance is well quantized at low temperatures, it exhibits highly anisotropic in-plane transport resembling compressible stripe or nematic charge-density-wave phases. More striking, the anisotropy sets in suddenly below a critical temperature, suggesting a finite-temperature phase transition. Our observations highlight how anisotropy modifies the many-body phases of a 2DES, and should further fuel the discussion surrounding the enigmatic even-denominator FQHS.

Long-lived photoluminescence polarization of localized excitons in liquid exfoliated monolayer enriched WS2

Monolayer transition metal dichalcogenides (TMDs) constitute a family of materials, in which coupled spin-valley physics can be explored and which could find applications in novel optoelectronic devices. However, before applications can be designed, a scalable method of monolayer extraction is required. Liquid phase exfoliation is a technique providing large quantities of the monolayer material, but the spin-valley properties of thus obtained TMDs are unknown. In this work, we employ steady-state and time-resolved photoluminescence (PL) to investigate the relaxation dynamics of localized excitons (LXs) in liquid exfoliated WS₂. The results reveal that the circular polarization lifetime of the PL exceeds by at least an order of magnitude the PL lifetime. A rate equations model allows us to reproduce quantitatively the experimental data and to conclude that the observed large and long-lived PL polarization originates from efficient trapping of free excitons at localization sites hindering the intervalley relaxation. Furthermore, our results show that the depolarization process is inefficient for LXs. We discuss various mechanisms leading to this effect such as suppression of intervalley scattering of the LXs or inefficient spin relaxation of the holes.

Magnetoresistance and valley degree of freedom in bulk bismuth

In this paper, we first review fundamental aspects of magnetoresistance in multi-valley systems based on the semiclassical theory. Then we will review experimental evidence and theoretical understanding of magnetoresistance in an archetypal multi-valley system, where the electric conductivity is set by the sum of the contributions of different valleys. Bulk bismuth has three valleys with an extremely anisotropic effective mass. As a consequence the magnetoconductivity in each valley is extremely sensitive to the orientation of the magnetic field. Therefore, a rotating magnetic field plays the role of a valley valve tuning the contribution of each valley to the total conductivity. In addition to this simple semiclassical effect, other phenomena arise in the high-field limit as a consequence of an intricate Landau spectrum. In the vicinity of the quantum limit, the orientation of magnetic field significantly affects the distribution of carriers in each valley, namely, the valley polarization is induced by the magnetic field. Moreover, experiment has found that well beyond the quantum limit, one or two valleys become totally empty. This is the only case in condensed matter physics where a Fermi sea is completely dried up by a magnetic field without a metal-insulator transition. There have been two long-standing problems on bismuth near the quantum limit: the large anisotropic Zeeman splitting of holes, and the extra peaks in quantum oscillations, which cannot be assigned to any known Landau levels. These problems are solved by taking into account the interband effect due to the spin-orbit couplings for the former, and the contributions from the twinned crystal for the latter. Up to here, the whole spectrum can be interpreted within the one-particle theory. Finally, we will discuss transport and thermodynamic signatures of breaking of the valley symmetry in this system. By this term, we refer to the observed spontaneous loss of threefold symmetry at high magnetic field and low temperature. Its theoretical understanding is still missing. We will discuss possible explanations.

Realization of a Valley Superlattice

In a number of widely studied materials, such as Si, AlAs, Bi, graphene, MoS_{2}, and many transition metal dichalcogenide monolayers, electrons acquire an additional, spinlike degree of freedom at the degenerate conduction band minima, also known as "valleys." External symmetry-breaking fields such as mechanical strain, or electric or magnetic fields, can tune the valley polarization of these materials, making them suitable candidates for "valleytronics." Here we study a quantum well of AlAs, where the two-dimensional electrons reside in two energetically degenerate valleys. By fabricating a strain-inducing grating on the sample surface, we engineer a spatial modulation of the electron population in different valleys, i.e., a "valley superlattice" in the quantum well plane. Our results establish a novel manipulation technique of the valley degree of freedom, paving the way to realizing a valley-selective layered structure in multivalley materials, with potential application in valleytronics.

Valley-Selective Response of Nanostructures Coupled to 2D Transition-Metal Dichalcogenides

Monolayer (1L) transition-metal dichalcogenides (TMDCs) are attractive materials for several optoelectronic applications because of their strong excitonic resonances and valley-selective response. Valley excitons in 1L-TMDCs are formed at opposite points of the Brillouin zone boundary, giving rise to a valley degree of freedom that can be treated as a pseudospin, and may be used as a platform for information transport and processing. However, short valley depolarization times and relatively short exciton lifetimes at room temperature prevent using valley pseudospins in on-chip integrated valley devices. Recently, it was demonstrated how coupling these materials to optical nanoantennas and metasurfaces can overcome this obstacle. Here, we review the state-of-the-art advances in valley-selective directional emission and exciton sorting in 1L-TMDC mediated by nanostructures and nanoantennas. We briefly discuss the optical properties of 1L-TMDCs paying special attention to their photoluminescence/absorption spectra, dynamics of valley depolarization, and the valley Hall effect. Then, we review recent works on nanostructures for valley-selective directional emission from 1L-TMDCs.

Evidence for line width and carrier screening effects on excitonic valley relaxation in 2D semiconductors

Monolayers of transition metal dichalcogenides (TMDC) have recently emerged as excellent platforms for exploiting new physics and applications relying on electronic valley degrees of freedom in two-dimensional (2D) systems. Here, we demonstrate that Coulomb screening by 2D carriers plays a critical role in excitonic valley pseudospin relaxation processes in naturally carrier-doped WSe₂ monolayers (1L-WSe₂). The exciton valley relaxation times were examined using polarization- and time-resolved photoluminescence spectroscopy at temperatures ranging from 10 to 160 K. We show that the temperature-dependent exciton valley relaxation times in 1L-WSe₂ under various exciton and carrier densities can be understood using a unified framework of intervalley exciton scattering via momentum-dependent long-range electron-hole exchange interactions screened by 2D carriers that depend on the carrier density and the exciton linewidth. Moreover, the developed framework was successfully applied to engineer the valley polarization of excitons in 1L-WSe₂. These findings may facilitate the development of TMDC-based opto-valleytronic devices.

Valley Physics in Non-Hermitian Artificial Acoustic Boron Nitride

The valley can serve as a new degree of freedom in the manipulation of particles or waves in condensed matter physics, whereas systems containing combinations of gain and loss elements constitute rich building units that can mimic non-Hermitian properties. By introducing gain and loss in artificial acoustic boron nitride, we show that the acoustic valley states and the valley-projected edge states display exotic behaviors in that they sustain either attenuated or amplified wave propagation. Our findings show how non-Hermiticity introduces a mechanism in tuning topological protected valley transports, which may have significance in advanced wave control for sensing and communication applications.

Dielectric function, critical points, and Rydberg exciton series of WSe2 monolayer

The complex dielectric function ([Formula: see text]) of WSe₂ monolayer grown by atomic layer deposition is investigated using spectroscopic ellipsometry. Band structure parameters are obtained by standard line-shape analysis of the second-energy-derivative of [Formula: see text] spectra. The fundamental band gap is observed at 2.26 eV, corresponds to transition between valence band (VB) maximum at the K point and conduction band (CB) minimum at Q point in the Brillouin zone (BZ). Two strong so-called A and B excitonic peaks in [Formula: see text] spectra originate from vertical transitions from spin-orbit split (0.43 eV) VB to CB at K point of the BZ. Binding energies of A and B exactions are 0.71 and 0.28 eV, respectively. Well resolved five excited excitons states has been detected within the spectral region between A and B. Energy profile of the Rydberg series shows significant deviation from the hydrogenic behavior, discussed in connection with the 2D hydrogen model. Results presented here will improve our understanding about the optical response of 2D materials and will help to design better optoelectronic applications and validate theoretical considerations.

Accessing valley degree of freedom in bulk Tin(II) sulfide at room temperature

The field of valleytronics has promised greater control of electronic and spintronic systems with an additional valley degree of freedom. However, conventional and two-dimensional valleytronic systems pose practical challenges in the utilization of this valley degree of freedom. Here we show experimental evidences of the valley effect in a bulk, ambient, and bias-free model system of Tin(II) sulfide. We elucidate the direct access and identification of different sets of valleys, based primarily on the selectivity in absorption and emission of linearly polarized light by optical reflection/transmission and photoluminescence measurements, and demonstrate strong optical dichroic anisotropy of up to 600% and nominal polarization degrees of up to 96% for the two valleys with band-gap values 1.28 and 1.48 eV, respectively; the ease of valley selection further manifested in their non-degenerate nature. Such discovery enables a new platform for better access and control of valley polarization.

Valleytronics leverages the valley degree of freedom to engineer light-matter interaction. Here, the authors demonstrate a room temperature, bias-free valley effect in bulk SnS by means of spectroscopic measurements, previously unattainable using atomically thin transition metal dichalcogenides.

Topological Valley Transport in Two-dimensional Honeycomb Photonic Crystals

Two-dimensional photonic crystals, in analogy to AB/BA stacking bilayer graphene in electronic system, are studied. Inequivalent valleys in the momentum space for photons can be manipulated by simply engineering diameters of cylinders in a honeycomb lattice. The inequivalent valleys in photonic crystal are selectively excited by a designed optical chiral source and bulk valley polarizations are visualized. Unidirectional valley interface states are proved to exist on a domain wall connecting two photonic crystals with different valley Chern numbers. With the similar optical vortex index, interface states can couple with bulk valley polarizations and thus valley filter and valley coupler can be designed. Our simple dielectric PC scheme can help to exploit the valley degree of freedom for future optical devices.

Gate-Controlled Spin-Valley Locking of Resident Carriers in WSe_{2} Monolayers

Using time-resolved Kerr rotation, we measure the spin-valley dynamics of resident electrons and holes in single charge-tunable monolayers of the archetypal transition-metal dichalcogenide (TMD) semiconductor WSe_{2}. In the n-type regime, we observe long (∼130  ns) polarization relaxation of electrons that is sensitive to in-plane magnetic fields B_{y}, indicating spin relaxation. In marked contrast, extraordinarily long (∼2  μs) polarization relaxation of holes is revealed in the p-type regime, which is unaffected by B_{y}, directly confirming long-standing expectations of strong spin-valley locking of holes in the valence band of monolayer TMDs. Supported by continuous-wave Kerr spectroscopy and Hanle measurements, these studies provide a unified picture of carrier polarization dynamics in monolayer TMDs, which can guide design principles for future valleytronic devices.

Realization of Valley and Spin Pumps by Scattering at Nonmagnetic Disorders

The recent success in optical pumping of valley polarization in two-dimensional transition metal dichalcogenides (TMDs) has greatly promoted the concept of valley-based informatics and electronics. However, between the demonstrated valley polarization of transient electron-hole pair excitations and practical valleytronic operations, there exist obvious gaps to fill, among which is the valley pump of long-lived charge carriers. Here we discover that the quested valley pump of electrons or holes can be realized simply by scattering at the ubiquitous nonmagnetic disorders, not relying on any specific material property. The mechanism is rooted in the nature of the valley as a momentum space index: the intervalley backscattering in general has a valley contrasted rate due to the distinct momentum transfers, causing a net transfer of population from one valley to another. As examples, we numerically demonstrate the sizable valley pump effects driven by charge current in nanoribbons of monolayer TMDs, where the spin-orbit scattering by nonmagnetic disorders also realizes a spin pump for the spin-valley locked holes. Our finding points to a new opportunity towards valley spintronics, turning disorders from a deleterious factor to a resource of valley and spin polarization.

Valley- and spin-polarized Landau levels in monolayer WSe2

Electrons in monolayer transition metal dichalcogenides are characterized by valley and spin quantum degrees of freedom, making it possible to explore new physical phenomena and to foresee novel applications in the fields of electronics and optoelectronics. Theoretical proposals further suggest that Berry curvature effects, together with strong spin-orbit interactions, can generate unconventional Landau levels (LLs) under a perpendicular magnetic field. In particular, these would support valley- and spin-polarized chiral edge states in the quantum Hall regime. However, this unique LL structure has not been observed experimentally in transition metal dichalcogenides. Here we report the observation of fully valley- and spin-polarized LLs in high-quality WSe₂ monolayers achieved by exploiting a van der Waals heterostructure device platform. We applied handedness-resolved optical reflection spectroscopy to probe the inter-LL transitions at individual valleys and derived the LL structure in turn. We also measured a sizeable doping-induced mass renormalization driven by the strong Coulomb interactions.

Controlling the spin and valley degeneracy splitting in monolayer MnPSe3 by atom doping

Monolayer manganese chalcogenophosphates MnPSe₃ possess a pair of non-degenerate energy valleys in the vicinities of the vertices of the hexagonal Brillouin zone, which exhibit fascinating optical valley polarization.