Recent progress on valley polarization and valley-polarized topological states in two-dimensional materials

Valleytronics, using valley degree of freedom to encode, process, and store information, may find practical applications in low-power-consumption devices. Recent theoretical and experimental studies have demonstrated that twodimensional(2D) honeycomb lattice systems with inversion symmetry breaking, such as transition-metal dichalcogenides(TMDs), are ideal candidates for realizing valley polarization. In addition to the optical field, lifting the valley degeneracy of TMDs by introducing magnetism is an efficient way to manipulate the valley degree of freedom. In this paper, we first review the recent progress on valley polarization in various TMD-based systems, including magnetically doped TMDs,intrinsic TMDs with both inversion and time-reversal symmetry broken, and magnetic TMD heterostructures. When topologically nontrivial bands are empowered into valley-polarized systems, valley-polarized topological states, namely valleypolarized quantum anomalous Hall effect can be realized. Therefore, we have also reviewed the theoretical proposals for realizing valley-polarized topological states in 2D honeycomb lattices. Our paper can help readers quickly grasp the latest research developments in this field.

Valley polarization in transition metal dichalcogenide layered semiconductors:Generation,relaxation,manipulation and transport

In recent years,valleytronics researches based on 2D semiconducting transition metal dichalcogenides have attracted considerable attention.On the one hand,strong spin–orbit interaction allows the presence of spin–valley coupling in this system,which provides spin addressable valley degrees of freedom for information storage and processing.On the other hand,large exciton binding energy up to hundreds of me V enables excitons to be stable carriers of valley information.Valley polarization,marked by an imbalanced exciton population in two inequivalent valleys(+K and-K),is the core of valleytronics as it can be utilized to store binary information.Motivated by the potential applications,we present a thorough overview of the recent advancements in the generation,relaxation,manipulation,and transport of the valley polarization in nonmagnetic transition metal dichalcogenide layered semiconductors.We also discuss the development of valleytronic devices and future challenges in this field.

Enhancement of subgap conductance in a graphene superconductor junction by valley polarization

We theoretically study the differential conductance of a graphene/graphene superconductor junction, where the valley polarization of Dirac electrons is considered in the nonsuperconducting region. It is shown that the subgap conductance will increase monotonically with the valley-polarization strength when the chemical potential μ is near the Dirac point μ≤ 3？（？ is the superconducting gap）, whereas it will decrease monotonically when μ is far away from the Dirac point, μ≥ 5？.The former case is induced by the specular Andreev reflection while the retro-reflection accounts for the later result. Our findings may shed light on the control of conductance of a graphene superconductor junction by valley polarization.

Enhanced valley polarization in WSe_(2)/YIG heterostructures via interfacial magnetic exchange effect

Exploiting the valley degrees of freedom as information carriers provides new opportunities for the development of valleytronics.Monolayer transition metal dichalcogenides(TMDs)with broken space-inversion symmetry exhibit emerging valley pseudospins,making them ideal platforms for studying valley electronics.However,intervalley scattering of different energy valleys limits the achievable degree of valley polarization.Here,we constructed WSe_(2)/yttrium iron garnet(YIG)heterostructures and demonstrated that the interfacial magnetic exchange effect on the YIG magnetic substrate can enhance valley polarization by up to 63%,significantly higher than that of a monolayer WSe_(2)on SiO_(2)/Si(11%).Additionally,multiple sharp exciton peaks appear in the WSe_(2)/YIG heterostructures due to the strong magnetic proximity effect at the magnetic-substrate interface that enhances exciton emission efficiency.Moreover,under the effect of external magnetic field,the magnetic direction of the magnetic substrate enhances valley polarization,further demonstrating that the magnetic proximity effect regulates valley polarization.Our results provide a new way to regulate valley polarization and demonstrate the promising application of magnetic heterojunctions in magneto-optoelectronics.

Valleytronic topological filters in silicene-like inner-edge systems

Inner edge state with spin and valley degrees of freedom is a promising candidate for designing a dissipationless device due to the topological protection. The central challenge for the application of the inner edge state is to generate and modulate the polarized currents. In this work, we discover a new mechanism to generate fully valley-and spin–valley-polarized current caused by the Bloch wavevector mismatch(BWM). Based on this mechanism, we design some serial-typed inner-edge filters. By using once of the BWM, the coincident states could be divided into transmitted and reflected modes, which can serve as a valley or spin–valley filter. In particular, while with twice of the BWM, the incident current is absolutely reflected to support an off state with a specified valley and spin, which is different from the gap effect.These findings give rise to a new platform for designing valleytronics and spin-valleytronics.

Progress on two-dimensional ferrovalley materials

The electron's charge and spin degrees of freedom are at the core of modern electronic devices. With the in-depth investigation of two-dimensional materials, another degree of freedom, valley, has also attracted tremendous research interest. The intrinsic spontaneous valley polarization in two-dimensional magnetic systems, ferrovalley material, provides convenience for detecting and modulating the valley. In this review, we first introduce the development of valleytronics.Then, the valley polarization forms by the p-, d-, and f-orbit that are discussed. Following, we discuss the investigation progress of modulating the valley polarization of two-dimensional ferrovalley materials by multiple physical fields, such as electric, stacking mode, strain, and interface. Finally, we look forward to the future developments of valleytronics.

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.

Fully spin-polarized, valley-polarized and spin-valley-polarized electron beam splitters utilizing zero-line modes in a three-terminal device

Topological zero-line modes(ZLMs) with spin and valley degrees of freedom give rise to spin, valley and spinvalley transport, which support a platform for exploring quantum transport physics and potential applications in spintronic/valleytronic devices. In this work, we investigate the beam-splitting behaviors of the charge current due to the ZLMs in a three-terminal system. We show that with certain combinations of ZLMs, the incident charge current along the interface between different topological phases can be divided into different polarized currents with unit transmittance in two outgoing terminals. As a result, fully spin-polarized, valley-polarized and spin-valley-polarized electron beam splitters are generated. The mechanism of these splitters is attributed to the cooperative effects of the distribution of the ZLMs and the intervalley and intravalley scatterings that are modulated by the wave-vector mismatch and group velocity mismatch. Interestingly, half-quantized transmittance of these scatterings is found in a fully spin-valley-polarized electron beam splitter.Furthermore, the results indicate that these splitters can be applicable to graphene, silicene, germanene and stanene due to their robustness against the spin–orbit coupling. Our findings offer a new way to understand the transport mechanism and investigate the promising applications of ZLMs.

Valley polarization in stacked MoS2 induced by circularly polarized light

Manipulation of valley pseudospins is crucial for future valleytronics. lhe emerging transition metal dichalcogenides （TMDs） provide new possibilities for exploring the interplay among the quantum degrees of freedom, including real spin, valley pseudospin, and layer pseudospin. For example, spin-valley coupling results in valley-dependent circular dichroism in which electrons with particular spin （up or down） can be selectively excited by chiral optical pumping in monolayer TMDs, whereas in few-layer TMDs, the interlayer hopping further affects the spin-valley coupling. In addition to valley and layer pseudospins, here we propose a new degree of freedom--stacking pseudospin--and demonstrate new phenomena correlated to this new stacking freedom that otherwise require the application of external electrical or magnetic field. We investigated all possible stacking configurations of chemical-vapor-deposition-grown trilayer MoS2 （AAA, ABB, AAB, ABA, and 3R）. Although the AAA, ABA, 3R stackings possess a sole peak with lower degree of valley polarization than that in monolayer samples, the AAB （ABB） stackings exhibit two distinct peaks, one similar to that observed in monolayer MoS2 and findings provide a more future valleytronics. an additional unpolarized complete understanding of peak at lower energy. Our valley quantum control for

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.

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.

Tunable valley filter efficiency by spin-orbit coupling in silicene nanoconstrictions

Valley filter is a promising device for producing valley polarized current in graphene-like two-dimensional honeycomb lattice materials.The relatively large spin-orbit coupling in silicene contributes to remarkable quantum spin Hall effect,which leads to distinctive valley-dependent transport properties compared with intrinsic graphene.In this paper,quantized conductance and valley polarization in silicene nanoconstrictions are theoretically investigated in quantum spin-Hall insulator phase.Nearly perfect valley filter effect is found by aligning the gate voltage in the central constriction region.However,the valley polarization plateaus are shifted with the increase of spin-orbit coupling strength,accompanied by smooth variation of polarization reversal.Our findings provide new strategies to control the valley polarization in valleytronic devices.

Valley-polarized pumping current in zigzag graphene nanoribbons with different spatial symmetries

We numerically investigate the valley-polarized current in symmetric and asymmetric zigzag graphene nanoribbons(ZGNRs) by the adiabatic pump, and the effect of spatial symmetry is considered by introducing different pumping regions. It is found that pumping potentials with the symmetry Vp(x,y) = Vp(-x,y)can generate the largest valleypolarized current. The valley-polarized currents I13~L with the pumping potential symmetry Vp(x,y) =Vp(x,-y,) and I14~L with Vp(x,y) = Vp(-x,-y) of symmetric ZGNRs are much smaller than those of asymmetric ZGNRs. We also find I13~L and I14~L of symmetric ZGNRs decrease and increase with the increasing pumping amplitude, respectively. Moreover, the dephasing effect from the electron-phonon coupling within the Buttiker dephasing scheme is introduced. The valley-polarized current of the symmetric ZGNRs with Vp(x,y)= Vp(x,-y) increases with the increase of the dephasing strength while that with Vp(x,y) = Vp(-x,-y) decreases as the dephasing strength increases.

Valley dynamics of different excitonic states in monolayer WSe_(2)grown by molecular beam epitaxy

Monolayer transition-metal dichalcogenides possess rich excitonic physics and unique valley-contrasting optical selection rule,and offer a great platform for long spin/valley lifetime engineering and the associated spin/valleytronics exploration.Using two-color time-resolved Kerr rotation and time-resolved reflectivity spectroscopy,we investigate the spin/valley dynamics of different excitonic states in monolayer WSe_(2)grown by molecular beam epitaxy.With fine tuning of the photon energy of both pump and probe beams,the valley relaxation process for the neutral excitons and trions is found to be remarkably different-their characteristic spin/valley lifetimes vary from picoseconds to nanoseconds,respectively.The observed long trion spin lifetime of>2.0 ns is discussed to be associated with the dark trion states,which is evidenced by the photon-energy dependent valley polarization relaxation.Our results also reveal that valley depolarization for these different excitonic states is intimately connected with the strong Coulomb interaction when the optical excitation energy is above the exciton resonance.

Recent advances of defect-induced spin and valley polarized states in graphene

Electrons in graphene have fourfold spin and valley degeneracies owing to the unique bipartite honeycomb lattice and an extremely weak spin-orbit coupling,which can support a series of broken symmetry states.Atomic-scale defects in graphene are expected to lift these degenerate degrees of freedom at the nanoscale,and hence,lead to rich quantum states,highlighting promising directions for spintronics and valleytronics.In this article,we mainly review the recent scanning tunneling microscopy(STM)advances on the spin and/or valley polarized states induced by an individual atomicscale defect in graphene,including a single-carbon vacancy,a nitrogen-atom dopant,and a hydrogen-atom chemisorption.Lastly,we give a perspective in this field.

Janus VXY monolayers with tunable large Berry curvature

The Rashba effect and valley polarization provide a novel paradigm in quantum information technology. However,practical materials are scarce. Here, we found a new class of Janus monolayers VXY(X = Cl, Br, I;Y = Se, Te) with excellent valley polarization effect. In particular, Janus VBrSe shows Zeeman type spin splitting of 14 meV, large Berry curvature of 182.73 bohr2,and, at the same time, a large Rashba parameter of 176.89 meV·?. We use the k·p theory to analyze the relationship between the lattice constant and the curvature of the Berry. The Berry curvature can be adjusted by changing the lattice parameter,which will greatly improve the transverse velocities of carriers and promote the efficiency of the valley Hall device. By applying biaxial strain onto VBrSe, we can see that there is a correlation between Berry curvature and lattice constant, which further validates the above theory. All these results provide tantalizing opportunities for efficient spintronics and valleytronics.

Valley-polarized quantum anomalous Hall effect in van der Waals heterostructures based on monolayer jacutingaite family materials

We numerically study the general valley polarization and anomalous Hall effect in van der Waals(vdW)heterostructures based on monolayer jacutingaite family materials Pt2AX3(A=Hg,Cd,Zn;X=S,Se,Te).We perform a systematic study on the atomic,electronic,and topological properties of vdW heterostructures composed of monolayer Pt2AX3 and two-dimensional ferromagnetic insulators.We show that four kinds of vdW heterostructures exhibit valley-polarized quantum anomalous Hall phase,i.e.,Pt_(2)HgS_(3)/NiBr_(2),Pt_(2)HgSe_(3)/CoBr_(2),Pt_(2)HgSe_(3)/NiBr_(2),and Pt_(2)ZnS_(3)/CoBr_(2),with a maximum valley splitting of 134.2 meV in Pt_(2)HgSe_(3)/NiBr_(2) and sizable global band gap of 58.8 meV in Pt_(2)HgS_(3)/NiBr_(2).Our findings demonstrate an ideal platform to implement applications on topological valleytronics.

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.

Valley-resolved transport in zigzag graphene nanoribbon junctions

Applying the transfer matrix and Green’s function methods,we study the valley-resolved transport properties of zigzag graphene nanoribbon(ZGN_(R))junctions.The width of the left and right ZGN_(R)s are N_(L)and N_(R),and N_(L)≥N_(R).The step/dip positions of the conductance G,the intravalley transmission coefficients(TKKand TK’K’),and the valley polarization efficiency PK’K correspond to the subband edges of the right/left ZGN_(R)that are controlled by N_(R)/N_(L).The intervalley transmission coefficients(TKK and TK’K)exhibit peaks at most of the subband edge of the left and right ZGN_(R)s.In the bulk gap of the right ZGN_(R),TKK’=TK’K=0,and PKK’=±1,the valley polarization is well preserved.As N_(R)increases,the energy region for PK’K=±1 decreases.When N_(L)is fixed and N_(R)decreases,G,TKK,TK’K’and PKK’exhibit more and more dips,and the peaks of TKK’(TK’K)become more and more high,especially when(N_(L)-N_(R))/2 is odd.These characters are quite useful for manipulating the valley dependent transport properties of carriers in ZGN_(R)junctions by modulating N_(L)or N_(R),and our results are helpful to the design of valleytronics based on ZGN_(R)junctions.

Imaging field-tuned quantum Hall broken-symmetry orders and the quantum Hall conducting channel in a charge-neutral graphene/WSe_(2) heterostructure

The zeroth Landau level(0LL)in graphene has emerged as a flat band platform in which distinct many-body phases can be explored with unprecedented control by simply tuning the strength and/or direction of the magnetic field.A rich set of quantum Hall ferromagnetic phases with different lattice-scale symmetry-breaking orders are predicted to be realized in high magnetic fields when the 0LL in graphene is half-filled.Here we report on a field-tuned continuous phase transition of different valley orderings in a quantum Hall ferromagnetic phase of charge-neutral graphene on insulating tungsten diselenide(WSe_(2)).The phase transition is clearly revealed by an anomalous field-dependent energy gap in the half-filled 0LL.Using atomic resolution imaging of electronic wavefunctions during the phase transition,we unexpectedly observe the microscopic signatures of fieldtuned continuous-varied valley polarization and valley inversion,which are beyond current theoretical predictions.Moreover,the quantum Hall conducting channel of the graphene is directly imaged when the substrate(WSe_(2))introduces band bending of the 0LL.