Anomalous valley Hall effect in two-dimensional valleytronic materials

The anomalous valley Hall effect(AVHE)can be used to explore and utilize valley degrees of freedom in materials,which has potential applications in fields such as information storage,quantum computing and optoelectronics.AVHE exists in two-dimensional(2D)materials possessing valley polarization(VP),and such 2D materials usually belong to the hexagonal honeycomb lattice.Therefore,it is necessary to achieve valleytronic materials with VP that are more readily to be synthesized and applicated experimentally.In this topical review,we introduce recent developments on realizing VP as well as AVHE through different methods,i.e.,doping transition metal atoms,building ferrovalley heterostructures and searching for ferrovalley materials.Moreover,2D ferrovalley systems under external modulation are also discussed.2D valleytronic materials with AVHE demonstrate excellent performance and potential applications,which offer the possibility of realizing novel low-energy-consuming devices,facilitating further development of device technology,realizing miniaturization and enhancing functionality of them.

Design of sign-reversible Berry phase effect in 2D magneto-valley material

Manipulating sign-reversible Berry phase effects is both fundamentally intriguing and practically appealing for searching for exotic topological quantum states.However,the realization of multiple Berry phases in the magneto-valley lattice is rather challenging due to the complex interactions from spin-orbit coupling(SOC),band topology,and magnetic ordering.Here,taking single-layer spin-valley RuCl_(2)as an example,we find that sign-reversible Berry phase transitions from ferrovalley(FV)to half-valley semimetal(HVS)to quantum anomalous valley Hall effect(QAVHE)can be achieved via tuning electronic correlation effect or biaxial strains.Remarkably,QAVHE phase,which combines both the features of quantum anomalous Hall and anomalous Hall valley effect,is introduced by sign-reversible Berry curvature or band inversion of d_(xy)/d_(x^(2)-y^(2))and d_(z^(2))orbitals at only one of the K/K′valleys of single-layer RuCl_(2).And the boundary of QAVHE phase is the HVS state,which can achieve 100%intrinsically valley polarization.Further,a k·p model unveiled the valleycontrollable sign-reversible Berry phase effects.These discoveries establish RuCl_(2)as a promising candidate to explore exotic quantum states at the confluence of nontrivial topology,electronic correlation,and valley degree of freedom.

Single-layer intrinsic 2H-phase LuX_(2)(X=Cl,Br,I)with large valley polarization and anomalous valley Hall effect

Manipulation of the valley degree of freedom provides a new path for quantum information technology,but the real intrinsic large valley-polarization materials are rarely reported up to date.Here,we perform first-principles calculations to predict a class of 2H-phase single layer(SL)materials LuX_(2)(X=Cl,Br,I)to be ideal candidates.SL-Lu X_(2)are ferrovalley materials with a giant valley-polarization of 55 meV–148 meV as a result of its large spin–orbital coupling(SOC)and intrinsic ferromagnetism(FM).The magnetic transition temperatures of SL-LuI_(2)and SL-LuCl2are estimated to be 89 K–124 K,with a sizable magnetic anisotropy at out-of-plane direction.Remarkably,the anomalous valley Hall effect(AVHE)can be controlled in SL-LuX_(2)when an external electric field is applied.Moreover,the intrinsic valleypolarization of SL-LuI_(2)is highly robust for biaxial strain.These findings provide a promising ferrovalley material system for the experimentation of valleytronics and subsequent applications.

Large valley Nernst effect in twisted multilayer graphene systems

Valley Nernst effect is a newly proposed and experimentally confirmed effect,which could be used to design novel thermoelectric devices.We study the valley Nernst effect in(M+N)-layer twisted multilayer graphene systems by a simple low-energy effective model.It is found that the total valley Nernst coefficient(VNC)is three orders of magnitude larger than that in monolayer group-Ⅵdichalcogenides.The total VNC increases with the increase of layer numbers.It is shown that the total VNC exhibits a structure with three peaks as a function of the Fermi energy.We identify that the central peak is always negative stemming from the flat band.Two shoulder peaks are positively induced by the conduction and valence bands,respectively.These predicted features can be tested experimentally.The present work would shed more light on valley caloritronics.

Gate tunable spatial accumulation of valley-spin in chemical vapor deposition grown 40°-twisted bilayer WS2

The emerging two-dimensional materials,particularly transition metal dichalcogenides(TMDs),are known to exhibit valley degree of freedom with long valley lifetime,which hold great promises in the implementation of valleytronic devices.Especially,light-valley interactions have attracted attentions in these systems,as the electrical generation of valley magnetization can be readily achieved—a rather different route toward magnetoelectric(ME)effect as compared to that from conventional electron spins.However,so far,the moiré patterns constructed with twisted bilayer TMDs remain largely unexplored in regard of their valley spin polarizations,even though the symmetry might be distinct from the AB stacked bilayer TMDs.Here,we study the valley Hall effect(VHE)in 40°-twisted chemical vapor deposition(CVD)grown WS2moiré transistors,using optical Kerr rotation measurements at 20 K.We observe a clear gate tunable spatial distribution of the valley carrier imbalance induced by the VHE when a current is exerted in the system.

Spin and valley half metal induced by staggered potential and magnetization in silicene

We investigate the electron transport in silicene with both staggered electric potential and magnetization; the latter comes from the magnetic proximity effect by depositing silicene on a magnetic insulator. It is shown that the silicene could be a spin and valley half metal under appropriate parameters when the spin–orbit interaction is considered; further, the filtered spin and valley could be controlled by modulating the staggered potential or magnetization. It is also found that in the spin-valve structure of silicene, not only can the antiparallel magnetization configuration significantly reduce the valve-structure conductance, but the reversing staggered electric potential can cause a high-performance magnetoresistance due to the spin and valley blocking effects. Our findings show that the silicene might be an ideal basis for the spin and valley filter analyzer devices.

Spin and valley filter in strain engineered silicene

The realization of a perfect spin or valley filtering effect in two-dimensional graphene-like materials is one of the fundamental objectives in spintronics and valleytronics. For this purpose, we study spin- and valley-dependent transport in a silicene system with spatially alternative strains. It is found that due to the valley-opposite gauge field induced by the strain, the strained silicene with a superlattice structure exhibits an angle-resolved valley and spin filtering effect when the spin–orbit interaction is considered. When the interaction that breaks the time reversal symmetry is introduced, such as the spin or valley dependent staggered magnetization, the system is shown to be a perfect spin and valley half metal in which only one spin and valley species is allowed to transport. Our findings are helpful to design both spintronic and valleytronic devices based on silicene.

Tailoring edge and interface states in topological metastructures exhibiting the acoustic valley Hall effect

In this study, we investigate the acoustic topological insulator or topological metastructure, where an acoustic wave can exist only in an edge or interface state instead of propagating in bulk. Breaking the structural symmetry enables the opening of the Dirac cone in the band structure and the generation of a new band gap, wherein a topological edge or interface state emerges.Further, we systematically analyze two types of topological states that stem from the acoustic valley Hall effect mechanism;one type is confined to the boundary, whereas the other type can be observed at the interface between two topologically different structures. Results denote that the selection of different boundaries along with appropriately designed interfaces provides the acoustic waves in the band gap range with abilities of one-way propagation, dual-channel propagation, immunity from backscattering at sharp corners, and/or transition between propagation at interfaces and boundaries. Furthermore, we show that the acoustic wave propagation paths can be tailored in diverse and arbitrary ways by combing the two aforementioned types of topological states.

Intrinsic valley polarization and anomalous valley hall effect in single-layer 2H-FeCl_(2)

Valley,as a new degree of freedom for electrons,has drawn considerable attention due to its significant potential for encoding and storing information.Lifting the energy degeneracy to achieve valley polarization is necessary for realizing valleytronic devices.Here,on the basis of first-principles calculations,we show that single-layer FeCl_(2)exhibits a large spontaneous valley polarization(∼101 meV)arising from the broken time-reversal symmetry and spin-orbital coupling,which can be continuously tuned by varying the direction of magnetic crystalline.By employing the perturbation theory,the underlying physical mechanism is unveiled.Moreover,the coupling between valley degree of freedom and ferromagnetic order could generate a spin-and valley-polarized anomalous Hall current in the presence of the in-plane electric field,facilitating its experimental exploration and practical applications.

Nonlinear harmonic generation of terahertz waves in a topological valley polaritonic microcavity

Compact terahertz(THz)devices,especially for nonlinear THz components,have received more and more attention due to their potential applications in THz nonlinearity-based sensing,communications,and computing devices.However,effective means to enhance,control,and confine the nonlinear harmonics of THz waves remain a great challenge for micro-scale THz nonlinear devices.In this work,we have established a technique for nonlinear harmonic generation of THz waves based on phonon polariton-enhanced giant THz nonlinearity in a 2D-topologically protected valley photonic microcavity.Effective THz harmonic generation has been observed in both noncentrosymmetric and centrosymmetric nonlinear materials.These results can provide a valuable reference for the generation and control of THz high-harmonics,thus developing new nonlinear devices in the THz regime.

Experimental observation of coupled valley and spin Hall effect in p-doped WSe2 devices

It is generally accepted that perpendicular magnetic anisotropy(PMA)magnets are preferred over in-plane magnetic anisotropy(IMA)magnets in data storage applications owing to their large thermal stability even at ultra-scaled dimensions.To efficiently and deterministically switch a PMA,out-of-plan spin current is required.However,conventional giant spin Hall effect(GSHE)materials only produce spin currents with in-plane polarization.Our work,on the other hand,demonstrated for the first time that out-of-plane spin currents can indeed be generated by applying electric filed to monolayer WSe2 at room temperature and the spin information was detected by a graphene channel.Supported by theoretical calculations,we found that the interfacial polarization between graphene and WSe2 to be^38%assuming the ferromagnetic detector's polarization efficiency to be^4%.Moreover,the spin polarization is determined by the polarity of the applied electric field.

Interlayer exciton dynamics of transition metal dichalcogenide heterostructures under electric fields

Stacking single layers of atoms on top of each other provides a fundamental way to achieve novel material systems and engineer their physical properties,which offers opportunities for exploring fundamental physics and realizing next-generation optoelectronic devices.Among the two-dimensional(2D)-stacked systems,transition metal dichalcogenide(TMDC)heterostructures are particularly attractive because they host tightly-bonded interlayer excitons which possess various novel and appealing properties.These interlayer excitons have drawn significant research attention and hold high potential for the application in unique optoelectronic devices,such as polarization-and wavelength-tunable single photon emitters,valley Hall transistors,and possible high-temperature superconductors.The development of these devices requires a comprehensive understanding of the fundamental properties of these interlayer excitons and the impact of electric fields on their behaviors.In this review,we summarize the recent advances on the understanding of interlayer exciton dynamics under electric fields in TMDC heterostructures.We put emphasis on the electrical modulation of interlayer excitons’emission,the valley Hall transport of charge carriers after the separation of interlayer excitons by an electric field,and the correlation physics of interlayer excitons and charges under electrical doping and tuning.Challenges and perspectives are finally discussed for the application of TMDC heterostructures in future optoelectronics.

Valleytronics in transition metal dichalcogenides materials

Valley degree of freedom in the first Brillouin zone of Bloch electrons offers an innovative approach to information storage and quantum computation.Broken inversion symmetry together with the presence of time-reversal symmetry endows Bloch electrons non-zero Berry curvature and orbital magnetic moment,which contribute to the valley Hall effect and optical selection rules in valleytronics.Furthermore,the emerging transition metal dichalcogenides(TMDs)materials naturally become the ideal candidates for valleytronics research attributable to their novel structural,photonic and electronic properties,especially the direct bandgap and broken inversion symmetry in the monolayer.However,the mechanism of inter-valley relaxation remains ambiguous and the complicated manipulation of valley predominantly incumbers the realization of valleytronic devices.In this review,we systematically demonstrate the fundamental properties and tuning strategies(optical,electrical,magnetic and mechanical tuning)of valley degree of freedom,summarize the recent progress of TMD-based valleytronic devices.We also highlight the conclusion of present challenges as well as the perspective on the further investigations in valleytronics.

Vector valley Hall edge solitons in the photonic lattice with type-Ⅱ Dirac cones

Topological edge solitons represent a significant research topic in the nonlinear topological photonics.They maintain their profiles during propagation,due to the joint action of lattice potential and nonlinearity,and at the same time are immune to defects or disorders,thanks to the topological protection.In the past few years topological edge solitons were reported in systems composed of helical waveguide arrays,in which the time-reversal symmetry is effectively broken.Very recently,topological valley Hall edge solitons have been demonstrated in straight waveguide arrays with the time-reversal symmetry preserved.However,these were scalar solitary structures.Here,for the first time,we report vector valley Hall edge solitons in straight waveguide arrays arranged according to the photonic lattice with innate type-II Dirac cones,which is different from the traditional photonic lattices with type-I Dirac cones such as honeycomb lattice.This comes about because the valley Hall edge state can possess both negative and positive dispersions,which allows the mixing of two different edge states into a vector soliton.Our results not only provide a novel avenue for manipulating topological edge states in the nonlinear regime,but also enlighten relevant research based on the lattices with type-II Dirac cones.

Large valley-polarized state in single-layer NbX2 (X=S,Se):Theoretical prediction

Exploring two-dimensional valleytronic crystals with large valley-polarized state is of considerable importance due to the promising applications in next-generation information related devices.Here,we show first-principles evidence that single-layer NbX_(2)(X=S,Se)is potentially the long-sought two-dimensional valleytronic crystal.Specifically,the valley-polarized state is found to occur spontaneously in single-layer NbX_(2),without needing any external tuning,which arises from their intrinsic magnetic exchange interaction and inversion asymmetry.Moreover,the strong spin-orbit coupling strength within Nb-d orbitals renders their valley-polarized states being of remarkably large(NbS_(2)∼156 meV/NbSe_(2)∼219 meV),enabling practical utilization of their valley physics accessible.In additional,it is predicted that the valley physics(i.e.,anomalous valley Hall effect)in single-layer NbX_(2) is switchable via applying moderate strain.These findings make single-layer NbX_(2) tantalizing candidates for realizing high-performance and controllable valleytronic devices.