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.

Band engineering of valleytronics WSe_(2)–MoS_(2)heterostructures via stacking form,magnetic moment and thickness

Spin-valley polarization and bandgap regulation are critical in the developing of quantum devices.Here,by employing the density functional theory,we investigate the effects of stacking form,thickness and magnetic moment in the electronic structures of WSe_(2)–MoS_(2)heterostructures.Calculations show that spin-valley polarization maintains in all situations.Increasing thickness of 2H-MoS_(2)not only tunes the bandgap but also changes the degeneracy of the conduction band minimums(CBM)at K/K_(1) points.Gradual increase of micro magnetic moment tunes the bandgap and raises the valence band maximums(VBM)atΓpoint.In addition,the regulation of band gap by the thickness of 2H-MoS_(2)and introduced magnetic moment depends on the stacking type.Results suggest that WSe_(2)–MoS_(2)heterostructure supports an ideal platform for valleytronics applications.Our methods also give new ways of optical absorption regulation in spin-valley devices.

Proposal for valleytronic materials:Ferrovalley metal and valley gapless semiconductor

Valleytronic materials can provide new degrees of freedom to future electronic devices.In this work,the concepts of the ferrovalley metal(FVM)and valley gapless semiconductor(VGS)are proposed,which can be achieved in valleytronic bilayer systems by electric field engineering.In valleytronic bilayer systems,the interaction between out-of-plane ferroelectricity and A-type antiferromagnetism can induce layer-polarized anomalous valley Hall(LP-AVH)effect.The K and−K valleys of FVM are both metallic,and electron and hole carriers simultaneously exist.In the extreme case,the FVM can become VGS by analogizing spin gapless semiconductor(SGS).Moreover,it is proposed that the valley splitting enhancement and valley polarization reversal can be achieved by electric field engineering in valleytronic bilayer systems.Taking the bilayer RuBr_(2)as an example,our proposal is confirmed by the first-principle calculations.The FVM and VGS can be achieved in bilayer RuBr_(2)by applying electric field.With appropriate electric field range,increasing electric field can enhance valley splitting,and the valley polarization can be reversed by flipping electric field direction.To effectively tune valley properties by electric field in bilayer systems,the parent monolayer should possess out-of-plane magnetization,and have large valley splitting.Our results shed light on the possible role of electric field in tuning valleytronic bilayer systems,and provide a way to design the ferrovalley-related material by electric field.

Layer-controlled nonlinear terahertz valleytronics in two-dimensional semimetal and semiconductor PtSe_(2)

Platinum diselenide(PtSe_(2))is a promising two-dimensional(2D)material for the terahertz(THz)range as,unlike other transition metal dichalcogenides(TMDs),its bandgap can be uniquely tuned from a semiconductor in the nearinfrared to a semimetal with the number of atomic layers.This gives the material unique THz photonic properties that can be layer-engineered.Here,we demonstrate that a controlled THz nonlinearity—tuned from monolayer to bulk PtSe_(2)—can be realized in wafer size polycrystalline PtSe_(2)through the generation of ultrafast photocurrents and the engineering of the bandstructure valleys.This is combined with the PtSe_(2)layer interaction with the substrate for a broken material centrosymmetry,permitting a second order nonlinearity.Further,we show layer dependent circular dichroism,where the sign of the ultrafast currents and hence the phase of the emitted THz pulse can be controlled through the excitation of different bandstructure valleys.In particular,we show that a semimetal has a strong dichroism that is absent in the monolayer and few layer semiconducting limit.The microscopic origins of this TMD bandstructure engineering are highlighted through detailed DFT simulations,and shows the circular dichroism can be controlled when PtSe_(2)becomes a semimetal and when the K-valleys can be excited.As well as showing that PtSe_(2)is a promising material for THz generation through layer controlled optical nonlinearities,this work opens up a new class of circular dichroism materials beyond the monolayer limit that has been the case of traditional TMDs,and impacting a range of domains from THz valleytronics,THz spintronics to harmonic generation.

Valley filtering and valley-polarized collective modes in bulk graphene monolayers

The presence of two sublattices in hexagonal graphene brings two energetically degenerate extremes in the conduction and valence bands, which are identified by the valley quantum number. Recently, this valley degree of freedom has been suggested to encode and process information, which develops a new carbon-based electronics named graphene valleytronics. In this topical review, we present and discuss valley-related transport properties in bulk graphene monolayers,which are due to strain-induced pseudomagnetic fields and associated vector potential, sublattice-stagger potential, and the valley-Zeeman effect. These valley-related interactions can be utilized to obtain valley filtering, valley spatial separation, valley-resolved guiding modes, and valley-polarized collective modes such as edge or surface plasmons. The present challenges and the perspectives on graphene valleytronics are also provided in this review.

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.

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.

Switching of K-Q intervalley trions fine structure and their dynamics in n-doped monolayer WS_(2)

Monolayer group VI transition metal dichalcogenides(TMDs)have recently emerged as promising candidates for photonic and opto-valleytronic applications.The optoelectronic properties of these atomically-thin semiconducting crystals are strongly governed by the tightly bound electron-hole pairs such as excitons and trions(charged excitons).The anomalous spin and valley configurations at the conduction band edges in monolayer WS_(2)give rise to even more fascinating valley many-body complexes.Here we find that the indirect Q valley in the first Brillouin zone of monolayer WS_(2)plays a critical role in the formation of a new excitonic state,which has not been well studied.By employing a high-quality h-BN encapsulated WS_(2)field-effect transistor,we are able to switch the electron concentration within K-Q valleys at conduction band edges.Consequently,a distinct emission feature could be excited at the high electron doping region.Such feature has a competing population with the K valley trion,and experiences nonlinear power-law response and lifetime dynamics under doping.Our findings open up a new avenue for the study of valley many-body physics and quantum optics in semiconducting 2D materials,as well as provide a promising way of valley manipulation for next-generation entangled photonic devices.

Perspectives of spin-valley locking devices

Valleytronics is an emerging field of research which utilizes the valley degree of freedom to encode information.However,it is technically nontrivial to produce a stable valley polarization and to achieve efficient control and manipulation of valleys.Spin–valley locking refers to the coupling between spin and valley degrees of freedom in the materials with large spin–orbit coupling(SOC)and enables the manipulation of valleys indirectly through controlling spins.Here,we review the recent advances in spin–valley locking physics and outline possible device implications.In particular,we focus on the spin–valley locking induced by SOC and external electric field in certain two-dimensional materials with inversion symmetry and demonstrate the intriguing switchable valley–spin polarization,which can be utilized to design the promising electronic devices,namely,valley-spin valves and logic gates.

MoiréDirac fermions in transition metal dichalcogenides heterobilayers

Monolayer group-VIB transition metal dichalcogenides(TMDs)feature low-energy massive Dirac fermions,which have valley contrasting Berry curvature.This nontrivial local band topology gives rise to valley Hall transport and optical selection rules for interband transitions that open up new possibilities for valleytronics.However,the large bandgap in TMDs results in relatively small Berry curvature,leading to weak valley contrasting physics in practical experiments.Here,we show that Dirac fermions with tunable large Berry curvature can be engineered in moirésuperlattice of TMD heterobilayers.These moiréDirac fermions are created in a magnified honeycomb lattice with its sublattice degree of freedom formed by two local moirépotential minima.We show that applying an on-site potential can tune the moiréflat bands into helical ones.In short-period moirésuperlattice,we find that the two moirévalleys become asymmetric,which results in a net spin Hall current.More interestingly,a circularly polarized light drives these moiréDirac fermions into quantum anomalous Hall phase with chiral edge states.Our results open a new possibility to design the moiré-scale spin and valley physics using TMD moiréstructures.

Photoinduced valley-dependent equal-spin Andreev reflection in Ising superconductor junction

The Ising spin–orbit coupling could give rise to the spin-triplet Cooper pairs and equal-spin Andreev reflection(AR)in Ising superconductors.Here we theoretically study the valley-dependent equal-spin AR in a ferromagnet/Ising superconductor junction with a circularly polarized light applied to the ferromagnet.Because of the spin-triplet Cooper pairs and the optical irradiation,eight kinds of AR processes appear in the junction,including equal-spin AR and normal AR,the strengths and properties of which strongly depend on the valley degree of freedom.The AR probabilities for the incident electron from the two valleys exhibit certain symmetry with respect to the magnetization angle and the effective energy of light.The equal-spin AR and normal AR present different features and resonant behaviors near the superconducting gap edges.Due to equal-spin-triplet Cooper pairs,not only charge supercurrent but also spin supercurrent can transport in the Ising superconductors.The differential spin conductance for electron injecting from the two valleys can be controlled by the circularly polarized light.

First-principles investigation of the valley and electrical properties of carbon-dopedα-graphyne-like BN sheet

Based on ab initio density functional theory calculations,we demonstrate that two carbon-doped boron nitride analog ofα-graphyne structures,B_(3) C_(2) N_(3)) and BC_(6) N monolayers,are two-dimensional direct wide band gap semiconductors,and there are two inequivalent valleys in the vicinities of the vertices of their hexagonal Brillouin zones.Besides,B_(3)C_(2)N_(3) and BC_(6)N monolayers exhibit relatively high carrier mobilities,and their direct band gap feature is robust against the biaxial strain.More importantly,the energetically most favorable B_(3)C_(2)N_(3) and BC_(6)N bilayers also have direct wide band gaps,and valley polarization could be achieved by optical helicity.Finally,we show that BC_(6) N monolayer might have high efficiency in photo-splitting reactions of water,and a vertical van der Waals heterostructure with a type-Ⅱenergy band alignment could be designed using B_(3)C_(2)N_(3)and BC_(6)N monolayers.All the above-mentioned characteristics make B_(3)C_(2)N_(3) and BC_(6)N monolayers,bilayers,and their heterostructures recommendable candidates for applications in valleytronic devices,metal-free photocatalysts,and photovoltaic cells.

Improvement of valley splitting and valley injection efficiency for graphene/ferromagnet heterostructure

The valley splitting has been realized in the graphene/Ni heterostructure with the splitting value of 14 meV,and the obtained valley injecting efficiency from the heterostructure into graphene was 6.18%[Phys.Rev.B 92115404(2015)].In this paper,we report a way to improve the valley splitting and the valley injecting efficiency of the graphene/Ni heterostructure.By intercalating an Au monolayer between the graphene and the Ni,the split can be increased up to 50 meV.However,the valley injecting efficiency is not improved because the splitted valley area of graphene moves away from the Fermi level.Then,we mend the deviation by covering a monolayer of Cu on the graphene.As a result,the valley injecting efficiency of the Cu/graphene/Au/Ni heterostructure reaches 10%,which is more than 60%improvement compared to the simple graphene/Ni heterostructure.Then we theoretically design a valley-injection device based on the Cu/graphene/Au/Ni heterostructure and demonstrate that the valley injection can be easily switched solely by changing the magnetization direction of Ni,which can be used to generate and control the valley-polarized current.

Ultrafast investigation of room temperature valley polarization in“optical bilayer”WS_(2)

Monolayer transition metal dichalcogenides(TMDCs)have become a promising platform in valleytronics due to possessing the regulatable valley degrees of freedom.While,as a result of the rapid intervalley scattering,it is difficult to measure the PL valley polarization of monolayer TMDCs at room temperature,which limits their application in valleytronics devices.Here,we report a room temperature photoluminescence(PL)valley polarization up to 3.73%in an“optical bilayer”WS_(2)formed by transferring monolayer WS_(2)onto flat Ag film.Furthermore,in the transient absorption(TA)measurements,a remarkably long valley depolarization lifetime is found.Thus,we demonstrate the valley properties of such“optical bilayer”WS_(2)resemble actual bilayer WS_(2),in which the robust valley polarization can be attributed to the phonons depletion effect and the blocked interlayer hopping processes.These peculiar valley features in“optical bilayer”WS_(2)provide a particularly simple method to enhance valley control at room temperature.

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.

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.

摩尔超晶格中电场可调的极化激元拓扑输运

在由不同的单层过渡金属硫族化合物堆叠形成的双层范德瓦尔斯异质结中,两层之间的微小转角可导致摩尔超晶格的出现,其基态光学性质由位于不同层的电子和空穴通过库仑吸引形成的层间激子主导.层间激子携带的静电偶极矩使得它可以通过静电势来操控其定向流动,同时层间激子也具有一定的光学跃迁偶极矩,它的大小和方向随层间激子在摩尔超晶格中的位置而变化.本文指出摩尔超晶格中的层间激子与二维平面光学微腔内光子模的杂化可产生两种具备不同拓扑性质的摩尔极化激元,可导致自旋/谷霍尔效应和偏振霍尔效应.通过调节两层间的电压改变层间激子与光学腔内光子模的失谐量,可选择特定种类的摩尔极化激元,这使得它的拓扑输运现象具备卓越的电场可调性.