Ultrafast field-driven valley polarization of transition metal dichalcogenide quantum dots

We study theoretically the electron dynamics of transition metal dichalcogenide (TMDC) quantum dots (QDs) in the field of an ultrashort and ultrafast circularly polarized optical pulse. The QDs have the shape of a disk and their electron systems are described within an effective model with infinite mass boundary conditions. Similar to TMDC monolayers, a circularly polarized pulse generates ultrafast valley polarization of such QDs. The dependence of the valley polarization on the size of the dot is sensitive to the dot material and, for different materials, show both monotonic increase with the dot radius and nonmonotonic behavior with a local maximum at a finite dot radius.

Transition Metal Dichalcogenides: Making Atomic-Level Magnetism Tunable with Light at Room Temperature

The capacity to manipulate magnetization in 2D dilute magnetic semiconductors (2D-DMSs) using light, specifically in magnetically doped transition metal dichalcogenide (TMD) monolayers (M-doped TX2 , where M = V, Fe, and Cr; T = W, Mo; X = S, Se, and Te), may lead to innovative applications in spintronics, spin-caloritronics, valleytronics, and quantum computation. This Perspective paper explores the mediation of magnetization by light under ambient conditions in 2D-TMD DMSs and heterostructures. By combining magneto-LC resonance (MLCR) experiments with density functional theory (DFT) calculations, we show that the magnetization can be enhanced using light in V-doped TMD monolayers (e.g., V-WS2 , V-WSe2 ). This phenomenon is attributed to excess holes in the conduction and valence bands, and carriers trapped in magnetic doping states, mediating the magnetization of the semiconducting layer. In 2D-TMD heterostructures (VSe2 /WS2 , VSe2 /MoS2 ), the significance of proximity, charge-transfer, and confinement effects in amplifying light-mediated magnetism is demonstrated. We attributed this to photon absorption at the TMD layer that generates electron-hole pairs mediating the magnetization of the heterostructure. These findings will encourage further research in the field of 2D magnetism and establish a novel design of 2D-TMDs and heterostructures with optically tunable magnetic functionalities, paving the way for next-generation magneto-optic nanodevices.

Coexisting Phases in Transition Metal Dichalcogenides: Overview, Synthesis, Applications, and Prospects

Over the past decade, significant advancements have been made in phase engineering of two-dimensional transition metal dichalcogenides (TMDCs), thereby allowing controlled synthesis of various phases of TMDCs and facile conversion between them. Recently, there has been emerging interest in TMDC coexisting phases, which contain multiple phases within one nanostructured TMDC. By taking advantage of the merits from the component phases, the coexisting phases offer enhanced performance in many aspects compared with single-phase TMDCs. Herein, this review article thoroughly expounds the latest progress and ongoing efforts on the syntheses, properties, and applications of TMDC coexisting phases. The introduction section overviews the main phases of TMDCs (2H, 3R, 1T, 1T', 1Td), along with the advantages of phase coexistence. The subsequent section focuses on the synthesis methods for coexisting phases of TMDCs, with particular attention to local patterning and random formations. Furthermore, on the basis of the versatile properties of TMDC coexisting phases, their applications in magnetism, valleytronics, field-effect transistors, memristors, and catalysis are discussed. Lastly, a perspective is presented on the future development, challenges, and potential opportunities of TMDC coexisting phases. This review aims to provide insights into the phase engineering of 2D materials for both scientific and engineering communities and contribute to further advancements in this emerging field.

Light-Shaping of Valley States

The established paradigm to create valley states, excitations at local band extrema ("valleys"), is through selective occupation of specific valleys via circularly polarized laser pulses. Here we show a second way exists to create valley states, not by valley population imbalance but by "light-shaping" in momentum space, i.e. controlling the shape of the distribution of excited charge at each valley. While noncontrasting in valley charge, such valley states are instead characterized by a valley current, identically zero at one valley and finite and large at the other. We demonstrate that these (i) are robust to quantum decoherence, (ii) allow lossless toggling of the valley state with successive femtosecond laser pulses, and (iii) permit valley contrasting excitation both with and without a gap. Our findings open a route to robust ultrafast and switchable valleytronics in a wide scope of 2d materials, bringing closer the promise of valley-based electronics.

Valley filters using graphene blister defects from first principles

Valleytronics, which makes use of the two valleys in graphenes, attracts considerable attention and a valley filter is expected to be the central component in valleytronics. We propose the application of the graphene valley filter using blister defects to the investigation of the valley-dependent transport properties of the Stone-Wales and blister defects of graphenes by density functional theory calculations. It is found that the intervalley transition from theKvalley to theK'valleys is completely suppressed in some defects. Using a large bipartite honeycomb cell (BHC) including several carbon atoms in a cell and replacing atomic orbitals with molecular orbitals in the tight-binding model, we demonstrate analytically and numerically that the symmetry between the A and B sites of the BHC contributes to the suppression of the intervalley transition. In addition, the universal rule for the atomic structures of the blisters suppressing the intervalley transition is derived. Furthermore, by introducing additional carbon atoms to graphenes to form blister defects, we can split the energies of the states at which resonant scattering occurs on theKandK'channel electrons. Because of this split, the fully valley-polarized current will be achieved by the local application of a gate voltage.

Giant and Controllable Valley Currents in Graphene by Double Pumped THz Light

The field of valleytronics considers the creation and manipulation of "valley states", charge excitations characterized by a particular value of the crystal momentum in the Brillouin zone. Here we show, using the example of minimally gapped (≤40 meV) graphene, that there exist lightforms that create almost perfect valley contrasting current states (up to ∼80% valley purity) in the absence of a valley contrasting charge excitation. These "momentum streaked" THz waveforms act by deforming the excited state population in momentum space such that current flows at one valley yet is blocked at the conjugate valley. This approach both unlocks the potential of graphene as a materials platform for valleytronics, as gaps of 10-40 meV are robustly found in useful experimental contexts such as graphene/hBN systems, while simultaneously providing a tool toward ultrafast light control of valley currents in diverse minimally gapped matter, including many topological insulator systems.

On the electronic and spin-valley coupling of vanadium doped MoS2(1-x)Se2xmonolayers

Monolayers of MoS2with tunable bandgap and valley positions are highly demanding for their applications in opto-spintronics. Herein, selenium (Se) and vanadium (V) co-doped MoS2monolayers (vanadium doped MoS2(1-x)Se2x(V-MoSSe)) are developed and showed their variations in the electronic and optical properties with dopant content. Vanadium gets substitutionally (in place of Mo) doped within the MoS2lattice while selenium doped in place of sulfur, as shown by a detailed microstructure and spectroscopy analyses. The bandgap tunability with selenium doping can be achieved while valley shift is occurred due to the doping of vanadium. Chemical vapor deposition assisted grown MoS2(also selenium doped MoS2as shown here) is known for its n-type transport behavior while vanadium doping is found to be changing its nature to p-doping. Chirality dependent photoexcitation studies indicate a room temperature valley splitting in V-MoSSe (∼8 meV), where such a valley splitting is verified using density functional theory based calculations.

Switching the Moiré Lattice Models in the Twisted Bilayer WSe2 by Strain or Pressure

Moiré superlattices of twisted van der Waals heterostructures provide a promising and tunable platform for simulating correlated two-dimensional physical models. In twisted bilayer transition-metal dichalcogenides with twist angles close to 0°, the Γ and K valley moiré bands are described by the honeycomb and the triangular effective lattice models, respectively, with distinct physics. Using large-scale first-principles calculations, we show that in-plane biaxial strain and out-of-plane pressure provide effective knobs for switching the moiré lattice models that emerged at the band edges in twisted bilayer WSe2 by shifting the energy positions of the Γ and K valley minibands. The shifting mechanism originates from the differences in the orbital characters of the Γ and K valley states and their responses to strain and pressure. The critical strain and pressure for switching the Γ/K valleys are 2.11% and 2.175 GPa, respectively.

Nonlinear All-Optical Coherent Generation and Read-Out of Valleys in Atomically Thin Semiconductors

With conventional electronics reaching performance and size boundaries, all-optical processes have emerged as ideal building blocks for high speed and low power consumption devices. A promising approach in this direction is provided by valleytronics in atomically thin semiconductors, where light-matter interaction allows to write, store, and read binary information into the two energetically degenerate but non-equivalent valleys. Here, nonlinear valleytronics in monolayer WSe2 is investigated and show that an individual ultrashort pulse with a photon energy tuned to half of the optical band-gap can be used to simultaneously excite (by coherent optical Stark shift) and detect (by a rotation in the polarization of the emitted second harmonic) the valley population.

Band Nonlinearity-Enabled Manipulation of Dirac Nodes, Weyl Cones, and Valleytronics with Intense Linearly Polarized Light

We study low-frequency linearly polarized laser-dressing in materials with valley (graphene and hexagonal-Boron-Nitride) and topological (Dirac- and Weyl-semimetals) properties. In Dirac-like linearly dispersing bands, the laser substantially moves the Dirac nodes away from their original position, and the movement direction can be fully controlled by rotating the laser polarization. We prove that this effect originates from band nonlinearities away from the Dirac nodes. We further demonstrate that this physical mechanism is widely applicable and can move the positions of the valley minima in hexagonal materials to tune valley selectivity, split and move Weyl cones in higher-order Weyl semimetals, and merge Dirac nodes in three-dimensional Dirac semimetals. The model results are validated with ab initio calculations. Our results directly affect efforts for exploring light-dressed electronic structure, suggesting that one can benefit from band nonlinearity for tailoring material properties, and highlight the importance of the full band structure in nonlinear optical phenomena in solids.

Tunable valley splitting in two-dimensional CrBr3/VSe2van der Waals heterostructure under strains and electric fields

Valleytronics opens up fascinating opportunities for using the valley degree of freedom in information storage and quantum computation. Here, based on the first-principles calculations, we investigate the effects of biaxial strains and electric fields on the magnetic, electronic, and valleytronic properties of two-dimensional CrBr3/VSe2van der Waals (vdW) heterostructure consisting of two ferromagnetic monolayers. An interlayer magnetic phase transition from parallel to antiparallel is found when a compressive strain exceeds-2%or a tensile strain exceeds 4% is applied, while the interlayer magnetic configuration remains parallel under perpendicular electric fields. The valley splitting in the conduction bands is significantly enhanced by a compressive strain or an electric field pointing from the VSe2to the CrBr3layer. Specifically, a large valley splitting about 30.8 meV is obtained in the system with antiparallel interlayer magnetic configurations under a compressive strain of-4%, which is more than three times that of pristine CrBr3/VSe2heterostructure. Our findings provide new insights into the future valleytronic applications for two-dimensional magnetic vdW heterostructures.

Controlling Valley-Specific Light Emission from Monolayer MoS2 with Achiral Dielectric Metasurfaces

Excitons in two-dimensional transition metal dichalcogenides have a valley degree of freedom that can be optically manipulated for quantum information processing. Here, we integrate MoS₂ monolayers with achiral silicon disk array metasurfaces to enhance and control valley-specific absorption and emission. Through the coupling to the metasurface electric and magnetic Mie modes, the intensity and lifetime of the emission of neutral excitons, trions, and defect bound excitons can be enhanced and shortened, respectively, while the spectral shape can be modified. Additionally, the degree of polarization (DOP) of exciton and trion emission from the valley can be symmetrically enhanced at 100 K. The DOP increase is attributed to both the metasurface-enhanced chiral absorption of light and the metasurface-enhanced exciton emission from the Purcell effect. Combining Si-compatible photonic design with large-scale 2D materials integration, our work makes an important step toward on-chip valleytronic applications approaching room-temperature operation.

Dielectrics for Two-Dimensional Transition-Metal Dichalcogenide Applications

Despite over a decade of intense research efforts, the full potential of two-dimensional transition-metal dichalcogenides continues to be limited by major challenges. The lack of compatible and scalable dielectric materials and integration techniques restrict device performances and their commercial applications. Conventional dielectric integration techniques for bulk semiconductors are difficult to adapt for atomically thin two-dimensional materials. This review provides a brief introduction into various common and emerging dielectric synthesis and integration techniques and discusses their applicability for 2D transition metal dichalcogenides. Dielectric integration for various applications is reviewed in subsequent sections including nanoelectronics, optoelectronics, flexible electronics, valleytronics, biosensing, quantum information processing, and quantum sensing. For each application, we introduce basic device working principles, discuss the specific dielectric requirements, review current progress, present key challenges, and offer insights into future prospects and opportunities.

Valley-polarized and enhanced transmission in graphene with a smooth strain profile

We explore the influence of strain on the valley-polarized transmission of graphene by employing the wave-function matching and the non-equilibrium Green's function technique. When the transmission is along the armchair direction, we show that the valley polarization and transmission can be improved by increasing the width of the strained region and increasing (decreasing) the extensional strain in the armchair (zigzag) direction. It is noted that the shear strain does not affect transmission and valley polarization. Furthermore, when we consider the smooth strain barrier, the valley-polarized transmission can be enhanced by increasing the smoothness of the strain barrier. We hope that our finding can shed new light on constructing graphene-based valleytronic and quantum computing devices by solely employing strain.

Floquet Engineering of Nonequilibrium Valley-Polarized Quantum Anomalous Hall Effect with Tunable Chern Number

Here, we propose that Floquet engineering offers a strategy to realize the nonequilibrium quantum anomalous Hall effect (QAHE) with tunable Chern number. Using first-principles calculations and Floquet theorem, we unveil that QAHE related to valley polarization (VP-QAHE) is formed from the hybridization of Floquet sidebands in the two-dimensional family MSi₂Z₄ (M = Mo, W, V; Z = N, P, As) by irradiating circularly polarized light (CPL). Through the tuning of frequency, intensity, and handedness of CPL, the Chern number of VP-QAHE is highly tunable and up to C = ±4, which attributes to light-induced trigonal warping and multiple-band inversion at different valleys. The chiral edge states and quantized plateau of Hall conductance are visible inside the global band gap, thereby facilitating the experimental measurement. Our work not only establishes Floquet engineering of nonequilibrium VP-QAHE with tunable Chern number in realistic materials but also provides an avenue to explore emergent topological phases under light irradiation.

Negative Valley Polarization of the Intralayer Exciton via One-Step Growth of H-Type Heterobilayer WS2/MoS2

Vertical type II van der Waals heterobilayers of transition metal dichalcogenides (TMDs) have attracted wide attention due to their distinctive features mostly arising from the emergence of intriguing electronic structures that include moiré-related phenomena. Owing to strong spin-orbit coupling under a noncentrosymmetric environment, TMD heterobilayers host nonequivalent +K and -K valleys of contrasting Berry curvatures, which can be optically controlled by the helicity of optical excitation. The corresponding valley selection rules are well established by not only intralayer excitons but also interlayer excitons. Quite intriguingly, here, we experimentally demonstrate that unusual valley switching can be achieved using the lowest-lying intralayer excitons in H-type heterobilayer WS₂/MoS₂ prepared by one-step growth. This TMD combination provides an ideal case for interlayer coupling with an almost perfect lattice match, thereby also in the momentum space between +K and -K valleys in the H-type heterostructure. The underlying valley-switching mechanism can be understood by bright-to-dark conversion of initially created electrons in the valley of WS₂, followed by interlayer charge transfer to the opposite valley in MoS₂. Our suggested model is also confirmed by the absence of valley switching when the lowest-lying excitons in MoS₂ are directly generated in the heterobilayer. In contrast to the H-type case, we show that no valley switching is observed from R-type heterobilayers prepared by the same method, where interlayer charge transfer does not occur between the opposite valleys. We compare the case with the series of valley polarization data from other heterobilayer combinations obtained under different excitation energies and temperatures. Our valley switching mechanism can be utilized for valley manipulation by controlling the excitation photon energy together with the photon helicity in valleytronic devices derived from H-type TMD heterobilayers.

Robust Second-Order Topological Insulators with Giant Valley Polarization in Two-Dimensional Honeycomb Ferromagnets

Magnetic topological states have attracted great attention that provide exciting platforms for exploring prominent physical phenomena and applications of topological spintronics. Here, using a tight-binding model and first-principles calculations, we put forward that, in contrast to previously reported magnetic second-order topological insulators (SOTIs), robust SOTIs can emerge in two-dimensional ferromagnets regardless of magnetization directions. Remarkably, we identify intrinsic ferromagnetic 2H-RuCl₂ and Janus VSSe monolayers as experimentally feasible candidates of predicted robust SOTIs with the emergence of nontrivial corner states along different magnetization directions. Moreover, under out-of-plane magnetization, we unexpectedly point out that the valley polarization of SOTIs can be huge and much larger than that of the known ferrovalley materials, opening up a technological avenue to bridge the valleytronics and higher-order topology with high possibility of innovative applications in topological spintronics and valleytronics.

2D Ladder Polyborane: An Ideal Dirac Semimetal with a Multi-Field-Tunable Band Gap

Hydrogen, a simple and magic element, has attracted increasing attention for its effective incorporation within solids and powerful manipulation of electronic states. Here, we show that hydrogenation tackles common problems in two-dimensional borophene, e.g., stability and applicability. As a prominent example, a ladder-like boron hydride sheet, named as 2D ladder polyborane, achieves the desired outcome, enjoying the cleanest scenario with an anisotropic and tilted Dirac cone, that can be fully depicted by a minimal two-band tight-binding model. Introducing external fields, such as an electric field or a circularly polarized light field, can effectively induce distinctive massive Dirac fermions, whereupon four types of multi-field-driven topological domain walls hosting tunable chirality and valley indexes are further established. Moreover, the 2D ladder polyborane is thermodynamically stable at room temperature and supports highly switchable Dirac fermions, providing an ideal platform for realizing and exploring the various multi-field-tunable electronic states.

Direct Observation of Self-Hybridized Exciton-Polaritons and Their Valley Polarizations in a Bare WS2 Layer

The strong excitonic properties of transition metal dichalcogenides (TMD) have led to the successful demonstration of exciton-polaritons (EPs) in various optical cavity structures. Recently, self-hybridized EPs have been discovered in a bare TMD layer, but experimental investigation is still lacking because of their nonradiative nature. Herein, the direct observation of self-hybridized EPs in a bare multilayer WS₂ via the evanescent field coupling technique is reported. Because of the thickness-dependent Rabi splitting energy, the dispersion curves of the EPs change sensitively with sample thickness. Moreover, continuous tuning of EP dispersion curves is demonstrated by controlling the excitation laser power. Lastly, it is observed that guided EPs retain valley polarization up to 0.2 at room temperature, representing a valley-preserved strong coupling regime. It is believed that the high tunability and valley polarization properties of the guided EPs in bare TMD layers can facilitate new nanophotonic and valleytronic applications.

Symmetric domain segmentation in WS2flakes: correlating spatially resolved photoluminescence, conductance with valley polarization

The incidence of intra-flake heterogeneity of spectroscopic and electrical properties in chemical vapour deposited (CVD) WS₂flakes is explored in a multi-physics investigation via spatially resolved spectroscopic maps correlated with electrical, electronic and mechanical properties. The investigation demonstrates that the three-fold symmetric segregation of spectroscopic response, in topographically uniform WS₂flakes are accompanied by commensurate segmentation of electronic properties e.g. local carrier density and the differences in the mechanics of tip-sample interactions, evidenced via scanning probe microscopy phase maps. Overall, the differences are understood to originate from point defects, namely sulfur vacancies within the flake along with a dominant role played by the substrate. While evolution of the multi-physics maps upon sulfur annealing elucidates the role played by sulfur vacancy, substrate-induced effects are investigated by contrasting data from WS₂flake on Si and Au surfaces. Local charge depletion induced by the nature of the sample-substrate junction in case of WS₂on Au is seen to invert the electrical response with comprehensible effects on their spectroscopic properties. Finally, the role of these optoelectronic properties in preserving valley polarization that affects valleytronic applications in WS₂flakes, is investigated via circular polarization discriminated photoluminescence experiments. The study provides a thorough understanding of spatial heterogeneity in optoelectronic properties of WS₂and other transition metal chalcogenides, which are critical for device fabrication and potential applications.

A Steady-State Approach for Studying Valley Relaxation Using an Optical Vortex Beam

Spin-valley coupling in monolayer transition-metal dichalcogenides gives rise to valley polarization and coherence effect, limited by intervalley scattering caused by exciton-phonon, exciton-impurity, and electron-hole exchange interactions (EHEIs). We explore an approach to tune the EHEI by controlling the exciton center of mass momentum (COM) utilizing the photon distribution of higher-order optical vortex beams. By virtue of this, we have observed exciton-COM-dependent valley depolarization and decoherence, which gives us the ability to probe the valley relaxation time scale in a steady-state measurement. Our steady-state technique to probe the valley dynamics can open up a new paradigm to explore the physics of excitons in two-dimensional systems.

Ab initiocalculations of spin-nonconserving exciton-phonon scattering in monolayer transition metal dichalcogenides

We investigate the spin-nonconserving relaxation channel of excitons by their couplings with phonons in two-dimensional transition metal dichalcogenides usingab initioapproaches. Combining GW-Bethe-Salpeter equation method and density functional perturbation theory, we calculate the electron-phonon and exciton-phonon coupling matrix elements for the spin-flip scattering in monolayer WSe₂, and further analyze the microscopic mechanisms influencing these scattering strengths. We find that phonons could produce effective in-plane magnetic fields which flip spin of excitons, giving rise to relaxation channels complimentary to the spin-conserving relaxation. Finally, we calculate temperature-dependent spin-flip exciton-phonon relaxation times. Our method and analysis can be generalized to study other two-dimensional materials and would stimulate experimental measurements of spin-flip exciton relaxation dynamics.

Quantum-Engineered Devices Based on 2D Materials for Next-Generation Information Processing and Storage

As an approximation to the quantum state of solids, the band theory, developed nearly seven decades ago, fostered the advance of modern integrated solid-state electronics, one of the most successful technologies in the history of human civilization. Nonetheless, their rapidly growing energy consumption and accompanied environmental issues call for more energy-efficient electronics and optoelectronics, which necessitate the exploration of more advanced quantum mechanical effects, such as band-to-band tunneling, spin-orbit coupling, spin-valley locking, and quantum entanglement. The emerging 2D layered materials, featured by their exotic electrical, magnetic, optical, and structural properties, provide a revolutionary low-dimensional and manufacture-friendly platform (and many more opportunities) to implement these quantum-engineered devices, compared to the traditional electronic materials system. Here, the progress in quantum-engineered devices is reviewed and the opportunities/challenges of exploiting 2D materials are analyzed to highlight their unique quantum properties that enable novel energy-efficient devices, and useful insights to quantum device engineers and 2D-material scientists are provided.

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.

Valleytronics in two-dimensional materials with line defect

The concept of valley originates from two degenerate but nonequivalent energy bands at the local minimum in the conduction band or local maximum in the valence band. Manipulating the valley states for information storage and processing develops a brand-new electronics-valleytronics. Broken inversion symmetry is a necessary condition to produce pure valley currents. The polycrystalline two-dimensional materials (graphene, silicene, monolayer group-VI transition metal dichalcogenides, etc) with pristine grains stitched together by disordered grain boundaries (GBs) are the natural inversion-symmetry-broken systems and the candidates in the field of valleytronics. Different from their pristine forms, the Dirac valleys on both sides of GBs are mismatched in the momentum space and induce peculiar valley transport properties across the GBs. In this review, we systematically demonstrate the fundamental properties of valley degree of freedom across mostly studied and experimentally feasible polycrystalline structure-the line defect, and the manipulation strategies with electrical, magnetic and mechanical methods to realize the valley polarization. We also introduce an effective numerical method, the non-equilibrium Green's function technique, to tackle the valley transport issues in the line defect systems. The present challenges and the perspective on the further investigations of the line defect in valleytronics are also summarized.

Enhanced Valley Polarization in WS2 /LaMnO3 Heterostructure

Monolayer transition metal dichalcogenides have attracted great attention for potential applications in valleytronics. However, the valley polarization degree is usually not high because of the intervalley scattering. Here, a largely enhanced valley polarization up to 80% in monolayer WS₂ under nonresonant excitation at 4.2 K is demonstrated using WS₂ /LaMnO₃ thin film heterostructure, which is much higher than that for monolayer WS₂ on SiO₂ /Si substrate with a valley polarization of 15%. Furthermore, the greatly enhanced valley polarization can be maintained to a high temperature of about 160 K with a valley polarization of 53%. The temperature dependence of valley polarization is strongly correlated with the thermomagnetic curve of LaMnO₃ , indicating an exciton-magnon coupling between WS₂ and LaMnO₃ . A simple model is introduced to illustrate the underlying mechanisms. The coupling of WS₂ and LaMnO₃ is further confirmed with an observation of two interlayer excitons with opposite valley polarizations in the heterostructure, resulting from the spin-orbit coupling induced splitting of the conduction bands in monolayer transition metal dichalcogenides. The results provide a pathway to control the valleytronic properties of transition metal dichalcogenides by means of ferromagnetic van der Waals engineering, paving a way to practical valleytronic applications.

Laser-Patterned Submicrometer Bi2Se3-WS2 Pixels with Tunable Circular Polarization at Room Temperature

Characterizing and manipulating the circular polarization of light is central to numerous emerging technologies, including spintronics and quantum computing. Separately, monolayer tungsten disulfide (WS₂) is a versatile material that has demonstrated promise in a variety of applications, including single photon emitters and valleytronics. Here, we demonstrate a method to tune the photoluminescence (PL) intensity (factor of ×161), peak position (38.4 meV range), circular polarization (39.4% range), and valley polarization of a Bi₂Se₃-WS₂ 2D heterostructure using a low-power laser (0.762 μW) in ambient conditions. Changes are spatially confined to the laser spot, enabling submicrometer (814 nm) features, and are long-term stable (>334 days). PL and valley polarization changes can be controllably reversed through laser exposure in a vacuum, allowing the material to be erased and reused. Atmospheric experiments and first-principles calculations indicate oxygen diffusion modulates the exciton radiative vs nonradiative recombination pathways, where oxygen absorption leads to brightening and desorption to darkening.

Realizing Quantum Technologies in Nanomaterials and Nanoscience

A brief overview of quantum materials and their prospects for applications, in the near, mid, and far-term in the areas of quantum information science, spintronics, valleytronics, and twistronics and those involving topology are covered in this perspective. The material and processing challenges that will modulate the realism of the applications will be discussed as well.

Electrically Tunable and Dramatically Enhanced Valley-Polarized Emission of Monolayer WS2 at Room Temperature with Plasmonic Archimedes Spiral Nanostructures

Monolayer transition metal dichalcogenides (TMDs) have intrinsic valley degrees of freedom, making them appealing for exploiting valleytronic applications in information storage and processing. WS₂ monolayer possesses two inequivalent valleys in the Brillouin zone, each valley coupling selectively with a circular polarization of light. The degree of valley polarization (DVP) under the excitation of circularly polarized light (CPL) is a parameter that determines the purity of valley polarized photoluminescence (PL) of monolayer WS₂ . Here efficient tailoring of valley-polarized PL from monolayer WS₂ at room temperature (RT) through surface plasmon-exciton interactions with plasmonic Archimedes spiral (PAS) nanostructures is reported. The DVP of WS₂ at RT can be enhanced from <5% to 40% and 50% by using 2 turns (2T) and 4 turns (4T) of PAS, respectively. Further enhancement and control of excitonic valley polarization is demonstrated by electrostatically doping monolayer WS₂ . For CPL on WS₂ -2TPAS heterostructures, the 40% valley polarization is enhanced to 70% by modulating the carrier doping via a backgate, which may be attributed to the screening of momentum-dependent long-range electron-hole exchange interactions. The manifestation of electrically tunable valley-polarized emission from WS₂ -PAS heterostructures presents a new strategy toward harnessing valley excitons for application in ultrathin valleytronic devices.

Selective Growth and Robust Valley Polarization of Bilayer 3R-MoS2

Noncentrosymmetric transition-metal dichalcogenides, particularly their 3R polymorphs, provide a robust setting for valleytronics. Here, we report on the selective growth of monolayers and bilayers of MoS₂, which were acquired from two closely but differently oriented substrates in a chemical vapor deposition reactor. It turns out that as-grown bilayers are predominantly 3R-type, not more common 2H-type, as verified by microscopic and spectroscopic characterization. As expected, the 3R bilayer showed a significantly higher valley polarization compared with the centrosymmetric 2H bilayer, which undergoes efficient interlayer scattering across contrasting valleys because of their vertical alignment of the K and K' points in momentum space. Interestingly, the 3R bilayer showed even higher valley polarization compared with the monolayer counterpart. Moreover, the 3R bilayer reasonably maintained its valley efficiency over a very wide range of excitation power density from ∼0.16 kW/cm² to ∼0.16 MW/cm² at both low and room temperatures. These observations are rather surprising because valley dephasing could be more efficient in the bilayer via both interlayer and intralayer scatterings, whereas only intralayer scattering is allowed in the monolayer. The improved valley polarization of the 3R bilayer can be attributed to its indirect-gap nature, where valley-polarized excitons can relax into the valley-insensitive band edge, which otherwise scatter into the contrasting valley to effectively cancel out the initial valley polarization. Our results provide a facile route for the growth of 3R-MoS₂ bilayers that could be utilized as a platform for advancing valleytronics.

Large valley polarization in a novel two-dimensional semiconductor H-ZrX2(XCl, Br, I)

Inspired by the new progress in the research field of two-dimensional valleytronics materials, we propose a new class of transition metal halides, i.e. H-ZrX₂(X = Cl, Br, I), and investigated their valleytronics properties under the first-principles calculations. It harbors the spin-valley coupling at K and K' points in the top of valence band, in which the valley spin splitting of ZrI₂can reach up to 115 meV. By carrying out the strain engineering, the valley spin splitting and Berry curvature can be effectively tuned. The long-sought valley polarization reaches up to 108 meV by doping Cr atom, which corresponds to the large Zeeman magnetic field of 778 T. Furthermore, the valley polarization in ZrX₂can be lineally adjusted or flipped by manipulating the magnetization orientation of the doped magnetic atoms. All the results demonstrate the well-founded application prospects of single-layer ZrX₂, which can be considered as great candidate for the development of valleytronics and spintronics.

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.

Valley-Polarized Plasmonic Edge Mode Visualized in the Near-Infrared Spectral Range

Valley polarization has recently been adopted in optics, offering robust waveguiding and angular momentum sorting. The success of valley systems in photonic crystals suggests a plasmonic counterpart that can merge topological photonics and topological condensed matter systems, for instance, two-dimensional materials with the enhanced light-matter interaction. However, a valley plasmonic waveguide with a sufficient propagation distance in the near-infrared (NIR) or visible spectral range has so far not been realized due to ohmic loss inside the metal. Here, we employ gap surface plasmons for high index contrasting and realize a wide-bandgap valley plasmonic crystal, allowing waveguiding in the NIR-visible range. The edge mode with a propagation distance of 5.3 μm in the range of 1.31-1.36 eV is experimentally confirmed by visualizing the field distributions with a scanning transmission electron microscope cathodoluminescence technique, suggesting a practical platform for transferring angular momentum between photons and carriers in mesoscopic active devices.

Topological kink states in graphene

Due to the unique band structure, graphene exhibits a number of exotic electronic properties that have not been observed in other materials. Among them, it has been demonstrated that there exist the one-dimensional valley-polarized topological kink states localized in the vicinity of the domain wall of graphene systems, where a bulk energy gap opens due to the inversion symmetry breaking. Notably, the valley-momentum locking nature makes the topological kink states attractive to the property manipulation in valleytronics. This paper systematically reviews both the theoretical research and experimental progress on topological kink states in monolayer graphene, bilayer graphene and graphene-like classical wave systems. Besides, various applications of topological kink states, including the valley filter, current partition, current manipulation, Majorana zero modes and etc, are also introduced.

Sub-10 fs Intervalley Exciton Coupling in Monolayer MoS2 Revealed by Helicity-Resolved Two-Dimensional Electronic Spectroscopy

The valley pseudospin at the K and K' high-symmetry points in monolayer transition metal dichalcogenides (TMDs) has potential as an optically addressable degree of freedom in next-generation optoelectronics. However, intervalley scattering and relaxation of charge carriers leads to valley depolarization and limits practical applications. In addition, enhanced Coulomb interactions lead to pronounced excitonic effects that dominate the optical response and initial valley depolarization dynamics but complicate the interpretation of ultrafast spectroscopic experiments at short time delays. Employing broadband helicity-resolved two-dimensional electronic spectroscopy (2DES), we observe ultrafast (∼10 fs) intervalley coupling between all A and B valley exciton states that results in a complete breakdown of the valley index in large-area monolayer MoS₂ films. These couplings and subsequent dynamics exhibit minimal excitation fluence or temperature dependence and are robust toward changes in sample grain size and inherent strain. Our observations strongly suggest that this direct intervalley coupling on the time scale of optical excitation is an inherent property of large-area MoS₂ distinct from dynamic carrier or exciton scattering, phonon-driven processes, and multiexciton effects. This ultrafast intervalley coupling poses a fundamental challenge for exciton-based valleytronics in monolayer TMDs and must be overcome to fully realize large-area valleytronic devices.

Enhanced Valley Splitting in Monolayer WSe2 by Phase Engineering

Lifting the valley degeneracy in two-dimensional transition metal dichalcogenides could promote their applications in information processing. Various external regulations, including magnetic substrate, magnetic doping, electric field, and carrier doping, have been implemented to enhance the valley splitting under the magnetic field. Here, a phase engineering strategy, through modifying the intrinsic lattice structure, is proposed to enhance the valley splitting in monolayer WSe₂. The valley splitting in hybrid H and T phase WSe₂ is tunable by the concentration of the T phase. An obvious valley splitting of ∼4.1 meV is obtained with the T phase concentration of 31% under ±5 T magnetic fields, which corresponds to an effective Landé g_eff factor of -14, about 3.5-fold of that in pure H-WSe₂. Comparing the temperature and magnetic field dependent polarized photoluminescence and also combining the theoretical simulations reveal the enhanced valley splitting is dominantly attributed to exchange interaction of H phase WSe₂ with the local magnetic moments induced by the T phase. This finding provides a convenient solution for lifting the valley degeneracy of two-dimensional materials.

Strong valley splitting ind0two-dimensional SnO induced by magnetic proximity effect

Strong magnetic interfacial coupling in van der Waals heterostructures is important for designing novel electronic devices. Besides the most studied transition metal dichalcogenides (TMDCs) materials, we demonstrate that the valley splitting can be activated in two-dimensional tetragonald⁰metal oxide, SnO, via the magnetic proximity effect by EuBrO. In SnO/EuBrO, the valley splitting of SnO can reach ∼46 meV, which is comparable to many TMDCs and equivalent to an external magnetic field of 800 T. In addition, the valley splitting can be further enhanced by adjusting interlayer distance and applying uniaxial strains. A design principle of new spintronic device based on this unique electronic structure of SnO/EuBrO has been proposed. Our findings indicate that SnO is a promising material for future valleytronics applications.

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.

Kondo effects in small-bandgap carbon nanotube quantum dots

We study the magnetoconductance of small-bandgap carbon nanotube quantum dots in the presence of spin-orbit coupling in the strong-correlations regime. A finite-U slave-boson mean-field approach is used to study many-body effects. Different degeneracies are restored in a magnetic field and Kondo effects of different symmetries arise, including SU(3) effects of different types. Full spin-orbital degeneracy might be recovered at zero field and, correspondingly, the SU(4) Kondo effect sets in. We point out the possibility of the occurrence of electron-hole Kondo effects in slanting magnetic fields, which we predict to occur in magnetic fields with an orientation close to perpendicular. When the field approaches a transverse orientation a crossover from SU(2) or SU(3) symmetry into SU(4) is observed.

Exciton Fine Structure in Lead Chalcogenide Quantum Dots: Valley Mixing and Crucial Role of Intervalley Electron-Hole Exchange

We study the exciton fine structure in quantum dots of multivalley lead chalcogenides. We demonstrate that intervalley electron-hole exchange interaction, ignored in previous studies, dramatically modifies the exciton fine structure and leads to appearance of the ultrabright valley-symmetric spin-triplet exciton state dominating interband optical absorption. Valley mixing leads to brightening of other symmetry-allowed spin-triplet states which dominate low-temperature photoluminescence.

Perovskite-Derivative Valleytronics

Halide perovskites are revolutionizing the renewable energy sector owing to their high photovoltaic efficiency, low manufacturing cost, and flexibility. Their remarkable mobility and long carrier lifetime are also valuable for information technology, but fundamental challenges like poor stability under an electric field prevent realistic applications of halide perovskites in electronics. Here, it is discovered that valleytronics is a promising route to leverage the advantages of halide perovskites and derivatives for information storage and processing. The synthesized all-inorganic lead-free perovskite derivative, Cs₃ Bi₂ I₉ , exhibits strong light-matter interaction and parity-dependent optically addressable valley degree of freedom. Robust optical helicity in all odd-layer-number crystals with inversion symmetry breaking is observed, indicating excitonic coherence extending well beyond 11 layers. The excellent optical and valley properties of Cs₃ Bi₂ I₉ arise from the unique parallel bands, according to first principles calculations. This discovery points to new materials design principles for scalable valleytronic devices and demonstrates the promise of perovskite derivatives beyond energy applications.

Lateral Heterostructures of Multilayer GeS and SnS van der Waals Crystals

Engineered heterostructures derive distinct properties from materials integration and interface formation. Two-dimensional crystals have been combined to form vertical stacks and lateral heterostuctures with covalent line interfaces. While thicker vertical stacks have been realized, lateral heterostructures from multilayer van der Waals crystals, which could bring the benefits of high-quality interfaces to bulk-like layered materials, have remained much less explored. Here, we demonstrate the integration of anisotropic layered Sn and Ge monosulfides into complex heterostructures with seamless lateral interfaces and tunable vertical design using a two-step growth process. The anisotropic lattice mismatch at the lateral interfaces between GeS and SnS is relaxed via dislocations and interfacial alloying. Nanoscale optoelectronic measurements by cathodoluminescence spectroscopy show the characteristic light emission of joined high-quality van der Waals crystals. Spectroscopy across the lateral interface indicates valley-selective luminescence in the bulk SnS component that arises due to anisotropic electron transfer across the interface. The results demonstrate the ability to realize high-quality lateral heterostructures of multilayer van der Waals crystals for diverse applications, e.g., in optoelectronics or valleytronics.

Nanoscale Optical Addressing of Valley Pseudospins through Transverse Optical Spin

Valley pseudospin has emerged as a good quantum number to encode information, analogous to spin in spintronics. Two-dimensional transition metal dichalcogenides (2D TMDCs) recently attracted enormous attention for their easy access to the valley pseudospin through valley-dependent optical transitions. Different ways have been reported to read out the valley pseudospin state. For practical applications, on-chip access to and manipulation of valley pseudospins is paramount, not only to read out but especially to initiate the valley pseudospin state. Here, we experimentally demonstrate the selective on-chip, optical near-field initiation of valley pseudospins at room temperature. We exploit a nanowire optical waveguide, such that the local transverse optical spin of its guided modes selectively excites a specific valley pseudospin. Furthermore, spin-momentum locking of the transverse optical spin enables us to flip valley pseudospins with the opposite propagation direction. Thus, we open up ways to realize integrated hybrid opto-valleytronic devices.

Continuous Wave Sum Frequency Generation and Imaging of Monolayer and Heterobilayer Two-Dimensional Semiconductors

We report continuous-wave second harmonic and sum frequency generation from two-dimensional transition metal dichalcogenide monolayers and their heterostructures with pump irradiances several orders of magnitude lower than those of conventional pulsed experiments. The high nonlinear efficiency originates from above-gap excitons in the band nesting regions, as revealed by wavelength-dependent second order optical susceptibilities quantified in four common monolayer transition metal dichalcogenides. Using sum frequency excitation spectroscopy and imaging, we identify and distinguish one- and two-photon resonances in both monolayers and heterobilayers. Data for heterostructures reveal responses from constituent layers accompanied by nonlinear signal correlated with interlayer transitions. We demonstrate spatial mapping of heterogeneous interlayer coupling by sum frequency and second harmonic confocal microscopy on heterobilayer MoSe₂/WSe₂.

Machine-Learning Analysis to Predict the Exciton Valley Polarization Landscape of 2D Semiconductors

We demonstrate the applicability of employing machine-learning-based analysis to predict the low-temperature exciton valley polarization landscape of monolayer tungsten diselenide (1L-WSe₂) using position-dependent information extracted from its photoluminescence (PL) spectra at room temperature. We performed low- and room-temperature polarization-resolved PL mapping and used the obtained experimental data to create regression models for the prediction using the Random Forest machine-learning algorithm. The local information extracted from the room-temperature PL spectra and the low-temperature exciton valley polarization was used as the input and output data for the machine-learning process, respectively. The spatial distribution of the exciton valley polarization in a 1L-WSe₂ sample that was not used for the learning of the decision trees was successfully predicted. Furthermore, we numerically obtained the degree of importance for each input variable and demonstrated that this parameter provides helpful information for examining the physics that shape the spatially heterogeneous valley polarization landscape of 1L-WSe₂.

Ultrafast Unbalanced Electron Distributions in Quasicrystalline 30° Twisted Bilayer Graphene

Ultrafast carrier dynamics in a graphene system are very important in terms of optoelectronic devices. Recently, a twisted bilayer graphene has been discovered that possesses interesting electronic properties owing to strong modifications in interlayer couplings. Thus, a better understanding of ultrafast carrier dynamics in a twisted bilayer graphene is highly desired. Here, we reveal the unbalanced electron distributions in a quasicrystalline 30° twisted bilayer graphene (QCTBG), using time- and angle-resolved photoemission spectroscopy on the femtosecond time scale. We distinguish time-dependent electronic behavior between the upper- and lower-layer Dirac cones and gain insight into the dynamical properties of replica bands, which show characteristic signatures due to Umklapp scatterings. The experimental results are reproduced by solving a set of rate equations among the graphene layers and substrate. We find that the substrate buffer layer plays a key role in initial carrier injections to the upper and lower layers. Our results demonstrate that QCTBG can be a promising element for future devices.

Triferroic Material and Electrical Control of Valley Degree of Freedom

The generation and manipulation of valley polarization in controllable ways are important for the valley-related physics and devices. In analogy to multiferroic materials with more than one ferromagnetic, ferroelectric, and ferroelastic orders, a new triferroic system with ferromagnetism, ferroelectricity, and ferrovalley is proposed, namely, the monolayer AgBiP₂Se₆/CrI₃ van der Waals heterostructure. Using density functional theory, we further predict that the electrical control on the valley degree of freedom could be realized in this triferroic system. The mechanism of electrically controlled valley is elucidated as an intermediate coupling between lattice and ferroelectricity. The coupling of three ferroic orders in triferroic material paves the way for electrically controlled valleytronic devices.

Spatial Separation of Carrier Spin by the Valley Hall Effect in Monolayer WSe2 Transistors

We investigate the valley Hall effect (VHE) in monolayer WSe₂ field-effect transistors using optical Kerr rotation measurements at 20 K. While studies of the VHE have so far focused on n -doped MoS₂, we observe the VHE in WSe₂ in both the n - and p -doping regimes. Hole doping enables access to the large spin-splitting of the valence band of this material. The Kerr rotation measurements probe the spatial distribution of the valley carrier imbalance induced by the VHE. Under current flow, we observe distinct spin-valley polarization along the edges of the transistor channel. From analysis of the magnitude of the Kerr rotation, we infer a spin-valley density of 44 spins/μm, integrated over the edge region in the p -doped regime. Assuming a spin diffusion length less than 0.1 μm, this corresponds to a spin-valley polarization of the holes exceeding 1%.

Edge-Limited Valley-Preserved Transport in Quasi-1D Constriction of Bilayer Graphene

We investigated the quantization of the conductance of quasi-one-dimensional (quasi-1D) constrictions in high-mobility bilayer graphene (BLG) with different geometrical aspect ratios. Ultrashort (a few tens of nanometers long) constrictions were fabricated by applying an under-cut etching technique. Conductance was quantized in steps of ∼4 e²/ h (∼2 e²/ h) in devices with aspect ratios smaller (larger) than 1. We argue that scattering at the edges of a quasi-1D BLG constriction limits the intervalley scattering length, which causes valley-preserved (valley-broken) quantum transport in devices with aspect ratios smaller (larger) than 1. The subband energy levels, analyzed in terms of the bias-voltage and temperature dependences of the quantized conductance, indicated that they corresponded well to the effective channel width of a physically defined conducting channel with a hard-wall confining potential. Our study in ultrashort high-mobility BLG nano constrictions with physically tailored edges clearly confirms that physical edges are the major source of intervalley scattering in graphene in the ballistic limit.

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.