Graphene is a two-dimensional carbon material with a honeycomb lattice and Dirac-type low-energy spectrum. In a strong magnetic field, where Coulomb interactions dominate against disorder broadening, quantum Hall ferromagnetic states realize at integer fillings. Extending the quantum Hall ferromagnetism to the fractional filling case of massless Dirac fermions, we study the elementally charge excitations which couple with the valley degrees of freedom (so-called valley skyrmions). With the use of the density matrix renomalization group (DMRG) method, the excitation gaps are calculated and extrapolated to the thermodynamic limit. These results exhibit numerical evidences and criterions of the skyrmion excitations in graphene.
We investigate charge, valley, and spin transports in normal/ferromagnetic/normal silicene junc- tion. We show that the charge, valley, and spin conductances in this junction oscillate with the length of the ferromagnetic silicene. It is also found that the current through this junction is valley and spin polarized due to the coupling between valley and spin degrees of freedom, and the valley and spin polarizations can be tuned by local application of a gate voltage. In particular, we find fully valley and spin polarized current by applying the electric field. We also obtain the condition for …
We study intrinsic DC spin and valley Hall conductivity in doped ferromagnetic silicene in the presence of an electric filed applied perpendicular to silicene sheet. By calculating its energy spectrum and wavefunction and by making use of Kubo formalism, we obtain a general relation for the transverse Hall conductivity which can be used to obtain spin- and valley-Hall conductivity. Our results, in the zero limit of the exchange field, reduces to the previous results. Furthermore we discuss electrically tunable spin and valley polarized transport in ferromagnetic silicene and obtain the necessa…
In this Letter, a tunable valley polarization is investigated for honeycomb systems with broken inversion symmetry such as transition-metal dichalcogenide MX2 (M = Mo, W; X = S, Se) monolayers through elliptical pumping. As compared to circular pumping, elliptical pumping is more universal and effective method to create coherent valley polarization. When two valleys of MX2 monolayers are doped or polarized, a novel anomalous valley orbital magnetic moment Hall effect driven by opposite Berry curvatures at different valleys is predicted and can generate orbital magnetic moment current without t…
Bilayer Heisenberg ferromagnetic insulators hold degenerate terahertz Dirac magnon modes associated with two opposite valleys of the hexagonal Brillouin zone. We show that this energy degeneracy can be removed by breaking of the inversion symmetry (I), leading to a topological magnon valley current. We show furthermore that this current leads to valley Seebeck effect for magnons and is thereby detectable. We perform calculations in the specific example of bilayer CrBr3, where I can be broken by electrostatic doping.
We demonstrate a new quantum state of matter---valley-polarized quantum anomalous Hall effect in monolayer silicene. In the presence of extrinsic Rashba spin-orbit coupling and exchange field, monolayer silicene can host a quantum anomalous-Hall state with Chern number C=2. We find that through tuning Rashba spin-orbit coupling, a topological phase transition gives rise to a valley polarized quantum anomalous Hall state, i.e. a quantum state which exhibits electronic properties of both quantum valley-Hall effect (valley Chern number C_V=3) and quantum anomalous Hall effect with C=-1.
For monolayer transition metal chalcogenides (TMDs), electrons and excitons in different valleys can be driven to opposite directions by the Berry curvature, serving as a valley-dependent effective magnetic field. In addition to monolayer TMDs, Van der Waals heterostructures provide an attractive platform for emerging valley physics and devices with superior physics properties. Interlayer excitons in TMD heterostructures have a long valley lifetime as compared to monolayer intralayer excitons. Here we report an interlayer exciton valley polarization and valley Hall effect in MoS2/WSe2 in room …
Electrons hopping in two-dimensional honeycomb lattices possess a valley degree of freedom in addition to charge and spin. In the absence of inversion symmetry, these systems were predicted to exhibit opposite Hall effects for electrons from different valleys. Such valley Hall effects have been achieved only by extrinsic means, such as substrate coupling, dual gating, and light illuminating. Here, we report the first observation of intrinsic valley Hall transport without any extrinsic symmetry breaking in the non-centrosymmetric monolayer and trilayer MoS2, evidenced by considerable nonlocal r…
Gapped graphene has been proposed to be a good platform to observe the valley Hall effect, a transport phenomenon involving the flow of electrons that are characterized by different valley indices. In the present work, we show that this phenomenon is better described as an instance of the orbital Hall effect, where the ambiguous "valley" indices are replaced by a physical quantity, the orbital magnetic moment, which can be defined uniformly over the entire Brillouin zone. This description removes the arbitrariness in the choice of arbitrary cut-off for the valley-restricted integrals in the va…
We study the magnetic and transport properties of epitaxial graphene films in this letter. We predict enhanced signal of magnetic susceptibility and relate it to the intrinsic valley magnetic moments. There is also an anomalous contribution to the ordinary Hall effect, which is due to the valley dependent Berry phase or valley-orbit coupling.
We develop a theory of the valley Hall effect in high-quality graphene samples, in which strain fluctuation-induced random gauge potentials have been suggested as the dominant source of disorder. We find a near-quantized value of valley Hall conductivity in the band transport regime, which originates from an enhanced side jump of a Dirac electron when it scatters off the gauge potential. By assuming a small residue charge density our theory reproduces qualitatively the temperature- and gap-dependence of the observed valley Hall effect at the charge neutral point. Our study suggests that the va…
Electrons in 2-dimensional crystals with a honeycomb lattice structure possess a new valley degree of freedom (DOF) in addition to charge and spin. Each valley is predicted to exhibit a Hall effect in the absence of a magnetic field whose sign depends on the valley index, but to date this effect has not been observed. Here we report the first observation of this new valley Hall effect (VHE). Monolayer MoS2 transistors are illuminated by circularly polarized light which preferentially excites electrons into a specific valley, and a finite anomalous Hall voltage is observed whose sign is control…
The valley degree of freedom of electrons in solids has been proposed as a new type of information carriers beyond the electronic charge and spin. Recent experimental demonstrations of the optical orientation of the valley polarization and generation of the valley current through the valley Hall effect in monolayer MoS2 have shown the potential of two-dimensional semiconductor transition metal dichalcogenides for valley based electronic and optoelectronic applications. The valley Hall conductivity in monolayer MoS2, a non-centrosymmetric crystal, however, cannot be easily tuned, presenting a c…
We point out a practical way to induce a finite charge Hall conductivity in graphene via an off-diagonal strain. Our conclusions are based on a general analysis and supported by numerical examples. The interplay between a substrate-induced gap and the strain is discussed. We show that the substrate-induced gap itself does not break the symmetry that maps one valley onto the other, and hence does not yield a net charge Hall effect. The net charge Hall conductivity is found to be sizable and should be observable in the presence of both the gap and the strain. The sign of the Hall conductivity ca…
We investigate topological phases of bilayer graphene subject to antiferromagnetic exchange field, interlayer bias, and irradiated by light. We discover that at finite bias and light intensity the system transitions into a previously unknown spin-valley polarized quantum anomalous Hall (SVP-QAH) insulator state, for which the subsystem of one spin is a valley Hall topological insulator (TI) and that of the other spin is a QAH insulator. We assess the TI phases occurring in the system by analytically calculating the spin-valley dependent Chern number, and characterize them by considering edge s…
We study spin and valley transports in junctions composed of silicene and topological crystalline insulators. We consider normal/magnetic/normal Dirac metal junctions where a gate electrode is attached to the magnetic region. In normal/antiferromagnetic/normal silicene junction, we show that the current through this junction is valley and spin polarized due to the coupling between valley and spin degrees of freedom, and the valley and spin polarizations can be tuned by local application of a gate voltage. In particular, we find a fully valley and spin polarized current by applying the electric…
The valley dependent optical selection rules in recently discovered monolayer group-VI transition metal dichalcogenides (TMDs) make possible optical control of valley polarization, a crucial step towards valleytronic applications. However, in presence of Landaul level(LL) quantization such selection rules are taken over by selection rules between the LLs, which are not necessarily valley contrasting. Using MoS$_{2}$ as an example we show that the spatial inversion-symmetry breaking results in unusual valley dependent inter-LL selection rules, which directly locks polarization to valley. We fin…
We report on a theoretical study of one-dimensional (1D) states localized at few-layer graphene system ribbon edges, and at interfaces between few-layer graphene systems with different valley Hall conductivities. These 1D states are topologically protected when valley mixing is neglected. We address the influence on their properties of stacking arrangement, interface structure, and external electric field perpendicular to the layers. We find that 1D states are generally absent at multilayer ribbon armchair direction edges, but present irrespective of crystallographic orientation at any interna…
Under more consideration, it seems that bulk valley current mediated nonlocal resistance is inconsistent with Landau-Buttiker formalism. We believe Landau-Buttiker formalism is right and the declared bulk valley current mediated nonlocal resistance is questionable and the experimental signal should be attributed to other origins.
We consider theoretically staggered honeycomb lattices for photons which can be viewed as photonic analogs of transitional metal dichalcogenides (TMD) monolayers. We propose a simple realization of a photonic Quantum Valley Hall effect (QVHE) at the interface between two TMD analogs with opposite staggering on each side. This results in the formation of valley-polarized propagating modes whose existence relies on the difference between the valley Chern numbers, which is a $\mathbb{Z}_2$ topological invariant. We show that the magnitude of the photonic spin-orbit coupling based on the energy sp…
Quantum spin Hall effect was first predicted in graphene. However, the weak spin orbit interaction in graphene meant that the search for quantum spin Hall effect in graphene never fructified. In this work we show how to generate the quantum spin-valley Hall effect in graphene via quantum pumping by adiabatically modulating a magnetic impurity and an electrostatic potential in a monolayer of strained graphene. We see that not only exclusive spin polarized currents can be pumped in the two valleys in exactly opposite directions but one can have pure spin currents flowing in opposite directions i…
We theoretically demonstrate that 100\% valley-polarized transport in monolayers of MoS$_{2}$ and other group-VI dichalcogenides can be obtained using off-resonant circularly polarized light. By tuning the intensity of the off-resonant light the intrinsic band gap in one valley is reduced, while it is enhanced in the other valley, enabling single valley quantum transport. As a consequence, we predict (i) enhancement of the longitudinal electrical conductivity, accompanied by an increase in the spin-polarization of the flowing electrons, (ii) enhancement of the intrinsic spin Hall effect, toget…
We investigate the topological and transport properties of the recently discovered valley-polarized quantum anomalous Hall (VQAH) phase. In single layer, the phase is realized through the competition between two types of spin-orbit coupling, which breaks the symmetry between the two valleys. We show that the topological phase transition from conventional quantum anomalous Hall phase to the VQAH phase is due to the change of topological charges with the generation of additional skyrmions in the real spin texture, when the band gap closes and reopens at one of the valleys. In the presence of sho…
We calculate the dispersion of spinor exciton-polaritons in a planar microcavity with its active region containing a single Transitional Metal Dichalcogenide (TMD) monolayer, taking into account excitonic and photonic spin-orbit coupling. We consider the radial propagation of polaritons in presence of disorder. We show that the reduction of the disorder scattering induced by the formation of polariton states allows to observe an optical Valley Hall effect, namely the coherent precession of the locked valley and polarization pseudospins leading to the formation of spatial valley-polarized domai…
We theoretically investigate gate-defined graphene superlattices with broken inversion symmetry as a platform for realizing tunable valley dependent transport. Our analysis is motivated by recent experiments [C. Forsythe et al., Nat. Nanotechnol. 13, 566 (2018)] wherein gate-tunable superlattice potentials have been induced on graphene by nanostructuring a dielectric in the graphene/patterneddielectric/gate structure. We demonstrate how the electronic tight-binding structure of the superlattice system resembles a gapped Dirac model with associated valley dependent transport using an unfolding …
We investigate the emergence of topological valley Hall and kink states in a two-dimensional topolectrical (TE) model as a result of broken chiral and reflection symmetries. The TE system consists of two segments hosting distinct topological states with opposite signs of the valley Hall index, and separated by a heterojunction. In the practical circuit, the valley Hall index can be flipped between the two segments by modulating the onsite potential on the sublattice nodes of the respective segments. The presence of resistive coupling, which introduces non-Hermiticity in the system, subsequentl…
We predict the emergence and quantization of the valley Hall current of indirect excitons residing in noncentrosymmetric two-dimensional materials in the absence of an external magnetic field. Thus we report on the quantum anomalous valley Hall effect (QAVHE) for bosons. The crucial ingredients of its existence are the finite anomalous group velocity of exciton motion and the presence of the Bose-Einstein condensate, from which the particles are pushed out by external illumination to contribute to the stationary nonequilibrium current, which exhibits a quantized behavior as a function of the f…
We present a theoretical realization of quantum spin and quantum valley Hall effects in silicene. We show that combination of an electric field and intrinsic spin-orbit interaction leads to quantum phase transitions at the charge neutrality point. This phase transition from a two dimensional topological insulator to a trivial insulating state is accompanied by a quenching of the quantum spin Hall effect and the onset of a quantum valley Hall effect, providing a tool to experimentally tune the topological state of silicene. In contrast to graphene and other conventional topological insulators, …
Spin, anomalous, and valley Hall effects in graphene-based hybrid structures are studied theoretically within the Green function formalism and linear response theory. Two different types of hybrid systems are considered in detail: (i) graphene/boron nitride/cobalt(nickel), and (ii) graphene/YIG. The main interest is focused on the proximity-induced exchange interaction between graphene and magnetic substrate and on the proximity-enhanced spin-orbit coupling. The proximity effects are shown to have a significant influence on the electronic and spin transport properties of graphene. To find the …
We report on the emergence of bulk, valley-polarized currents in graphene-based devices, driven by spatially varying regions of broken sublattice symmetry, and revealed by non-local resistance ($R_\mathrm{NL}$) fingerprints. By using a combination of quantum transport formalisms, giving access to bulk properties as well as multi-terminal device responses, the presence of a non-uniform local bandgap is shown to give rise to valley-dependent scattering and a finite Fermi surface contribution to the valley Hall conductivity, related to characteristics of $R_\mathrm{NL}$. These features are robust…
We study the electronic structures and topological properties of $(M+N)$-layer twisted graphene systems. We consider the generic situation that $N$-layer graphene is placed on top of the other $M$-layer graphene, and is twisted with respect to each other by an angle $θ$. In such twisted multilayer graphene (TMG) systems, we find that there exists two low-energy flat bands for each valley emerging from the interface between the $M$ layers and the $N$ layers. These two low-energy bands in the TMG system possess valley Chern numbers that are dependent on both the number of layers and the stacking…
Topologically protected zero-line modes appear at the interface between two regions of the monolayer graphene in quantum anomalous Hall phase with different Chern number. In the presence of staggered sublattice potential, the band gaps of the two valleys become different, and the phase diagram defined by the Chern number has an additional regime of topologically trivial phase. The interface between the topologically trivial and non-trivial regions hosts zero-line mode in only one valley. By tuning the exchange field, three types of interface that host zero-line modes in selected valley(s) are …
Berry curvature hot spots in two-dimensional materials with broken inversion symmetry are responsible for the existence of transverse valley currents, which give rise to giant nonlocal dc voltages. Recent experiments in high-quality gapped graphene have highlighted a saturation of the nonlocal resistance as a function of the longitudinal charge resistivity $ρ_{{\rm c}, xx}$, when the system is driven deep into the insulating phase. The origin of this saturation is, to date, unclear. In this work we show that this behavior is fully compatible with bulk topological transport in the regime of lar…
In addition to spin, electrons in many materials possess an additional pseudo-spin degree of freedom known as 'valley'. In materials where the spin and valley degrees of freedom are weakly coupled, they can be both excited and controlled independently. In this work, we study a model describing the interplay of the spin and valley Hall effects in such two-dimensional materials. We demonstrate the emergence of an additional longitudinal neutral current that is both spin and valley polarized. The additional neutral current allows to control the spin density by tuning the magnitude of the valley H…
The band structure of many semiconducting monolayer transition metal dichalcogenides (TMDs) possesses two degenerate valleys, with equal and opposite Berry curvature. It has been predicted that, when illuminated with circularly polarized light, interband transitions generate an unbalanced non-equilibrium population of electrons and holes in these valleys, resulting in a finite Hall voltage at zero magnetic field when a current flows through the system. This is the so-called valley Hall effect that has recently been observed experimentally. Here, we show that this effect is mediated by photo-ge…
The valley-polarized quantum anomalous Hall (VQAH) state, which forwards a strategy for combining valleytronics and spintronics with nontrivial topology, attracts intensive interest in condensed-matter physics. So far, the explored VQAH states have still been limited to magnetic systems. Here, using the low-energy effective model and Floquet theorem, we propose a different mechanism to realize the Floquet VQAH state in nonmagnetic heterobilayers under light irradiation. We then realize this proposal via first-principles calculations in transition metal dichalcogenide heterobilayers, which init…
We present a microscopic theory for collective excitations of quantum anomalous Hall ferromagnets (QAHF) in twisted bilayer graphene. We calculate the spin magnon and valley magnon spectra by solving Bethe-Salpeter equations, and verify the stability of QAHF. We extract the spin stiffness from the gapless spin wave dispersion, and estimate the energy cost of a skyrmion-antiskyrmion pair, which is found to be comparable in energy with the Hartree-Fock gap. The valley wave mode is gapped, implying that the valley polarized state is more favorable compared to the valley coherent state. Using a no…
In graphene superlattices, bulk topological currents can lead to long-range charge-neutral flow and non-local resistance near Dirac points. A ballistic version of these phenomena has never been explored. Here, we report transport properties of ballistic graphene superlattices. This allows us to study and exploit giant non-local resistances with a large valley Hall angle without a magnetic field. In the low-temperature regime, a crossover occurs toward a new state of matter, referred to as a quantum valley Hall state (qVHS), which is an analog of the quantum Hall state without a magnetic field.…
Inversion symmetry breaking and spin-orbit coupling lead to valley and spin Hall effect in MoS2. Because of the large valley separation in momentum space, the valley index is expected to be robust. In this paper, quantum Hall effect in MoS2 originated from Berry curvature is analyzed after review of symmetry structure and spin-orbit coupling Hamiltonian of MoS2. Finally an expression and rough calculation is given for valley and spin Hall effect.
We numerically study the general valley polarization and anomalous Hall effect in van der Waals (vdW) heterostructures based on monolayer jacutingaite family materials Pt$_{2}$AX$_{3}$ (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 Pt$_{2}$AX$_{3}$ 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$_{3}$/…
We report a new "dip" effect in the Hall resistance, R_{xy}, of a Si metal-oxide-semiconductor field-effect transistor in the quantum Hall effect regime. With increasing magnetic field, the Hall resistance moves from the plateau at Landau filling factor ν=6 directly to the plateau at ν=4, skipping the plateau at ν=5. However, when the filling factor approaches ν=5, the Hall resistance sharply "dives" to the value 1/5(h/e^2) characteristic of the ν=5 plateau, and then returns to 1/4(h/e^2). This is interpreted as a manifestation of the oscillating exchange enhancement of the valley splitting wh…
Intrinsic Hall conductivity, emerging when chiral symmetry is broken, is at the heart of future low energy consumption devices because it can generate non-dissipative charge neutral current. A symmetry breaking state is also induced by electronic correlation even for the centro-symmetric crystalline materials. However, generation of non-dissipative charge neutral current by intrinsic Hall conductivity induced by such spontaneous symmetry breaking is experimentally elusive. Here we report intrinsic Hall conductivity and generation of a non-dissipative charge neutral current in a spontaneous ant…
The polymorph of ${\rm 8-Pmmn}$ borophene is an anisotropic Dirac material with tilted Dirac cones at two valleys. The tilting of the Dirac cones at two valleys are in opposite direction, which manifests itself via valley dependent Landau levels in presence of an in-plane electric field (Hall field). The sensitivity of the Landau levels on valley index causes valley polarized magnetotransport properties in presence of a Hall field, which is in contrast to the monolayer graphene with isotropic non-tilted Dirac cones. The longitudinal conductivity and Hall conductivity are evaluated by using lin…
In few-layer (FL) transition metal dichalcogenides (TMDC), the conduction bands along the Gamma-K directions shift downward energetically in the presence of interlayer interactions, forming six Q valleys related by three-fold rotational symmetry and time reversal symmetry. In even-layers the extra inversion symmetry requires all states to be Kramers degenerate, whereas in odd-layers the intrinsic inversion asymmetry dictates the Q valleys to be spin-valley coupled. In this Letter, we report the transport characterization of prominent Shubnikov-de Hass (SdH) oscillations for the Q valley electr…
The topological properties of a material's electronic structure are encoded in its Berry curvature, a quantity which is intimately related to the transverse electrical conductivity. In transition metal dichalcogenides with broken inversion symmetry, the nonzero Berry curvature results in a valley Hall effect. In this paper we identify a previously unrecognized consequence of Berry curvature in these materials: an electric field-induced change in the electrons' charge density orientation. We use first principles calculations to show that measurements of the electric field-induced change in the …
Graphene subject to high levels of shear strain leads to strong pseudo-magnetic fields resulting in the emergence of Landau levels. Here we show that, with modest levels of strain, graphene can also sustain a classical valley hall effect (VHE) that can be detected in nonlocal transport measurements. We provide a theory of the strain-induced VHE starting from the quantum Boltzmann equation. This allows us to show that, averaging over short-range impurity configurations destroys quantum coherence between valleys, leaving the elastic scattering time and inter-valley scattering rate as the only pa…
We calculate the conductance G of a bipolar junction in a graphene nanoribbon, in the high-magnetic field regime where the Hall conductance in the p-doped and n-doped regions is 2e^2/h. In the absence of intervalley scattering, the result G=(e^2/h)(1-cos Phi) depends only on the angle Phi between the valley isospins (= Bloch vectors representing the spinor of the valley polarization) at the two opposite edges. This plateau in the conductance versus Fermi energy is insensitive to electrostatic disorder, while it is destabilized by the dispersionless edge state which may exist at a zigzag bounda…
We systematically study the impact of various electron-acoustic-phonon coupling mechanisms on valley physics in two-dimensional materials. In the static strain limit, we find that Dirac cone tilt and deformation potential have analogous valley Hall response since they fall into the same universality class of pseudospin structure. However, such argument fails for the coupling mechanism with position-dependent Fermi velocity. For the isotropic case, a significant valley Hall effect occurs near charge neutrality similar to the bond-length change, whereas for the anisotropic case, the geometric va…
The intrinsic spin and valley Hall conductivities of silicene, germanene and other similar two dimensional crystals are explored theoretically. Particular attention is given to the effects of the intrinsic spin-orbit coupling, electron doping and the type of insulating phase of the system (i.e., a topological insulator or a band insulator) which can be tuned by a perpendicular electric field. At finite frequency, the transverse edge to which carriers of particular spin and valley label flow can be controlled such that an accumulation of a particular combination of spin and valley index can be …
