Recent experiments have studied the temperature and gate voltage dependence of nonlocal transport in bilayer graphene, identifying features thought to be associated with the two-dimensional semiconductor's bulk intrinsic valley Hall effect. Here, we use both simple microscopic tight-binding ribbon models and phenomenological bulk transport equations to emphasize the impact of sample edges on the nonlocal voltage signals. We show that the nonlocal valley Hall response is sensitive to electronic structure details at the sample edges, and that it is enhanced when the local longitudinal conductivity is larger near the sample edges than in the bulk. We discuss recent experiments in light of these findings and also discuss the close analogy between electron pumping between valleys near two-dimensional sample edges in the valley Hall effect, and bulk pumping between valleys due to the chiral anomaly in three-dimensional topological semimetals.
We investigate with polarized microphotoluminescence the optical pumping of the valley degree of freedom in charge-tunable MoS2 monolayers encapsulated with hexagonal boron nitride at cryogenic temperatures. We report a large steady state valley polarization of the different excitonic complexes following circularly-polarized laser excitation 25 meV above the neutral exciton transition. For the first time in this material we reveal efficient valley pumping of positively-charged trions, which were so far elusive in non-encapsulated monolayers due to defect and laser-induced large electron doping…
Monolayers of transition metal dichalcogenides are ideal materials to control both spin and valley degrees of freedom either electrically or optically. Nevertheless, optical excitation mostly generates excitons species with inherently short lifetime and spin/valley relaxation time. Here we demonstrate a very efficient spin/valley optical pumping of resident electrons in n-doped WSe2 and WS2 monolayers. We observe that, using a continuous wave laser and appropriate doping and excitation densities, negative trion doublet lines exhibit circular polarization of opposite sign and the photoluminesce…
We propose an experimental scheme to realize adiabatic topological spin and valley pumping by using silicene subject to an in-plane $ac$ electric field with amplitude $E_{y}$ and a vertical electric field consisting of an electrostatic component and an $ac$ component with amplitudes $E_{z}^{0}$ and $E_{z}^{1}$. By tuning $E_{z}^{0}$ and $E_{z}^{1}$, topological valley pumping or spin-valley pumping can be achieved. The noisefree valley and spin currents generated could be useful in valleytronic and spintronic applications. This work demonstrates that bulk topological spin or valley pumping is …
We report experimental evidences on selective occupation of the degenerate valleys in MoS2 monolayers by circularly polarized optical pumping. Over 30% valley polarization has been observed at K and K' valley via the polarization resolved luminescence spectra on pristine MoS2 monolayers. It demonstrates one viable way to generate and detect valley polarization towards the conceptual valleytronics applications with information carried by the valley index.
The low-energy theory of the surface of the topological crystalline insulator (TCI) is characterized by four Dirac cones anisotropic into the $x$ and $y$ directions. Recent experiments have shown that the band gap can be introduced in these Dirac cones by crystal distortion by applying strain to the crystal structure. The TCI surface provides us with a new way to valleytronics when gaps are given to Dirac cones. Indeed the system has the Chern number and three valley-Chern numbers. We investigate the optical absorption on the TCI surface. It shows a strong elliptic dichroism though the four Di…
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…
Based on the Keldysh Green's function method, we report an unconventional two-parameter quantum pumping in graphene with a line defect. It is found that different from the conventional sinusoidal relation, the pumped current in this device is cosinusoid dependence on the phase difference between the two pumping potentials, which adopts its positive/nagative maximum value at while tends to zero at . This phenomenon is related to the peculiar valley tunneling characteristics across the line defects and the exchange of valley indices on both sides of the line defect. Moreover, the pumped currents…
We study an adiabatic quantum pump effect in a two terminal graphene device with two oscillating square electric barriers and a stationary magnetic barrier using the scattering matrix approach. The model employs the low-energy Dirac approximation and incorporates the possible existence of a finite band gap in graphene spectrum. We show that in this case valley-polarized and pure valley currents can be pumped due to the valley symmetry breaking. For a δ-function magnetic barrier we present analytical expressions for bilinear total and valley pumping responses. These results are compared to nume…
Chiral anomaly, a non-conservation of chiral charge pumped by the topological nontrivial gauge fields, has been predicted to exist in Weyl semimetals. However, until now, the experimental signature of this effect exclusively relies on the observation of negative longitudinal magnetoresistance at low temperatures. Here, we report the field-modulated chiral charge pumping process and valley diffusion in Cd3As2. Apart from the conventional negative magnetoresistance, we observe an unusual nonlocal response with negative field dependence up to room temperature, originating from the diffusion of va…
We consider a nonadiabatic quantum pumping phenomena in a ballistic narrow constriction. The pumping is induced by a potential that has both spatial and temporal periodicity characterized by $K$ and $Ω$. In the zero frequency ($Ω=0$) limit, the transmission through narrow constriction exhibits valley structures due to the opening up of energy gaps in the pumping region -- a consequence of the $K$ periodicity. These valley structures remain robust in the regime of finite $Ω$, while their energies of occurrence are shifted by about $\hbarΩ/2$. The direction of these energy shifts depend on the d…
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…
Monolayer $MoS_2$ is a typical valleytronic material with valley-spin locked valence bands. We numerically investigate the valley-spin polarized current in monolayer $\rm MoS_2$ via adiabatic electron pumping. By introducing an exchange field to break the energy degeneracy of monolayer $MoS_2$, the top of its valence bands is valley-spin polarized and tunable by the exchange field. A device with spin-up polarized left lead, spin-down polarized right lead, and untuned central region is constructed through applying different exchange fields in the corresponding regions. Then, equal amount of pum…
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…
Using a spatially-resolved optical pump-probe experiment, we measure the lateral transport of spin/valley polarized electrons over very long distances (tens of micrometers) in a single WSe2 monolayer. By locally pumping the Fermi sea of 2D electrons to a high degree of spin/valley polarization (up to 75%) using circularly-polarized light, the lateral diffusion of the electron polarization can be mapped out via the photoluminescence induced by a spatially-separated and linearly-polarized probe laser. Up to 25% spin-valley polarization is observed at pump-probe separations up to 20 microns. Char…
We provide a critical discussion concerning the claim of topological valley currents, driven by a global Berry curvature and valley Hall effect proposed in recent literature. After pointing out a major inconsistency of the theoretical scenario proposed to interpret giant nonlocal resistance, we discuss various possible alternative explanations and open directions of research to solve the mystery of nonlocal transport in graphene superlattices.
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.
A pure spin current injector is proposed based on adiabatic pumping and crossed normal/Andreev reflection. The device consists of a three-terminal ferromagnet-superconductor-semiconductor system in which the injection of a pure spin current is into the semiconductor which is coupled to the superconductor within a coherence length away from the ferromagnet enabling the phenomena of crossed normal /Andreev reflection to operate. Quantum pumping is induced by adiabatically modulating two independent parameters of the ferromagnetic lead, namely the magnetization strength and the strength of coupli…
The Hall effect can be extended by inducing a temperature gradient in lieu of electric field that is known as the Nernst (-Ettingshausen) effect. The recently discovered spin Nernst effect in heavy metals continues to enrich the picture of Nernst effect-related phenomena. However, the collection would not be complete without mentioning the valley degree of freedom benchmarked by the observation of the valley Hall effect. Here we show the experimental evidence of its missing counterpart, the valley Nernst effect. Using millimeter-sized WSe$_{2}$ mono-multi-layers and the ferromagnetic resonance…
Electronic and spintronic devices rely on the fact that free charge carriers in solids carry electric charge and spin, respectively. There are, however, other properties of charge carriers that might be exploited in new families of devices. In particular, if there are two or more conduction (or valence) band extrema in momentum space, then confining charge carriers in one of these valleys allows the possibility of valleytronic devices. Such valley polarization has been demonstrated by using strain and magnetic fields, but neither of these approaches allow for dynamic control. Recently, optical…
The recent observation [R. V. Gorbachev et al., Science {\bf 346}, 448 (2014)] of nonlocal resistance $R_\mathrm{NL}$ near the Dirac point (DP) of multiterminal graphene on aligned hexagonal boron nitride (G/hBN) has been interpreted as the consequence of topological valley Hall currents carried by the Fermi sea states just beneath the bulk gap $E_g$ induced by the inversion symmetry breaking. However, the valley Hall conductivity $σ^v_{xy}$, quantized inside $E_g$, is not directly measurable. Conversely, the Landauer-Büttiker formula, as numerically exact approach to observable nonlocal trans…
We calculate the Hall viscosity and the nonlocal (i.e., dependent on wave vector $\bm q$) Hall conductivity of "gapped graphene" (a non-topological insulator with two valleys) in the presence of a strong perpendicular magnetic field. Using the linear-response theory at zero temperature within the Dirac approximation for the Landau levels, we present analytical expressions for both valley and total Hall viscosity and conductivity up to $\bm q^2$ at all frequencies. Although the final formulas for total Hall viscosity and conductivity are similar to the ones previously obtained for gapless graph…
2D materials based superlattices have emerged as a promising platform to modulate band structure and its symmetries. In particular, moiré periodicity in twisted graphene systems produces flat Chern bands. The recent observation of anomalous Hall effect (AHE) and orbital magnetism in twisted bilayer graphene has been associated with spontaneous symmetry breaking of such Chern bands. However, the valley Hall state as a precursor of AHE state, when time-reversal symmetry is still protected, has not been observed. Our work probes this precursor state using the valley Hall effect. We show that brok…
The observation of large nonlocal resistances near the Dirac point in graphene has been related to a variety of intrinsic Hall effects, where the spin or valley degrees of freedom are controlled by symmetry breaking mechanisms. Engineering strong spin or valley Hall signals on scalable graphene devices could stimulate further practical developments of spin- and valleytronics. Here we report on scale-invariant nonlocal transport in large-scale chemical vapour deposition graphene under an applied external magnetic field. Contrary to previously reported Zeeman spin Hall effect, our results are ex…
We not only reproduce burst of short-wavelength spin waves (SWs) observed in recent experiment [S. Woo et al., Nat. Phys. 13, 448 (2017)] on magnetic-field-driven annihilation of two magnetic domain walls (DWs) but, furthermore, we predict that this setup additionally generates highly unusual} pumping of electronic spin currents in the absence of any bias voltage. Prior to the instant of annihilation, their power spectrum is ultrabroadband, so they can be converted into rapidly changing in time charge currents, via the inverse spin Hall effect, as a source of THz radiation of bandwidth $\simeq…
The generation of valley current is a fundamental goal in graphene valleytronics but no practical ways of its realization are known yet. We propose a workable scheme for the generation of bulk valley current in a graphene mechanical resonator through adiabatic cyclic deformations of the strains and chemical potential in the suspended region. The accompanied strain gauge fields can break the spatial mirror symmetry of the problem within each of the two inequivalent valleys, leading to a fnite valley current due to quantum pumping. An all-electrical measurement configuration is designed to detec…
Graphene on hexagonal boron nitride (hBN) can exhibit a topological phase via mutual crystallographic alignment. Recent measurements of nonlocal resistance ($R_{nl}$) near the secondary Dirac point (SDP) in ballistic graphene/hBN superlattices have been interpreted as arising due to the quantum valley Hall state. We report hBN/graphene/hBN superlattices in which $R_{nl}$ at SDP is negligible, but below 60 K approaches the value of $h/2e^{2}$ in zero magnetic field at the primary Dirac point with a characteristic decay length of 2 $μ$m. Furthermore, nonlocal transport transmission probabilities…
We study theoretically nonlinear valley polarization dynamics of excitons in atom-thin semiconductors. The presence of significant polarization slows down valley relaxation due to an effective magnetic field resulting from exciton-exciton interactions. We address temporal dynamics of valley polarized excitons and study the steady states of the polarized exciton gas. We demonstrate bistability of the valley polarization where two steady states with low and high valley polarization are formed. We study the effects of fluctuations and noise in such system. We evaluate valley polarization autocorr…
Graphene superlattices have recently been attracting growing interest as an emergent class of quantum metamaterials. In this paper, we report the observation of nonlocal transport in bilayer graphene (BLG) superlattices encapsulated between two hexagonal boron nitride (hBN) layers, which formed hBN/BLG/hBN moiré superlattices. We then employed these superlattices to detect a long-range charge-neutral valley current using an all-electrical method. The moiré superlattice with broken inversion symmetry leads to a hot spot with Berry curvature accumulating at the charge neutral point (CNP), and it…
Valley pseudospin, the quantum degree of freedom characterizing the degenerate valleys in energy bands, is a distinct feature of two-dimensional Dirac materials. Similar to spin, the valley pseudospin is spanned by a time reversal pair of states, though the two valley pseudospin states transform to each other under spatial inversion. The breaking of inversion symmetry induces various valley-contrasted physical properties; for instance, valley-dependent topological transport is of both scientific and technological interests. Bilayer graphene (BLG) is a unique system whose intrinsic inversion sy…
In monolayers of transition metal dichalcogenides the nonlocal nature of the effective dielectric screening leads to large binding energies of excitons. Additional lateral confinement gives rise to exciton localization in quantum dots. By assuming parabolic confinement for both the electron and the hole, we derive model wave functions for the relative and the center-of-mass motions of electron-hole pairs, and investigate theoretically resonant energy transfer among excitons localized in two neighboring quantum dots. We quantify the probability of energy transfer for a direct-gap transition by …
Manipulating spin polarization of electrons in nonmagnetic semiconductors by means of electric fields or optical fields is an essential theme of the conceptual nonmagnetic semiconductor-based spintronics. Here we experimentally demonstrate a method of generating spin polarization in monolayer transition metal dichalcogenides (TMD) by the circularly polarized optical pumping. The fully spin-polarized photocurrent is achieved through the valley dependent optical selection rules and the spin-valley locking in monolayer WS2, and electrically detected by a lateral spin-valve structure with ferromag…
Together with charge and spin degrees of freedom, many new 2D materials also permit information to be encoded in an electron's valley degree of freedom - that is, in particular momentum states in the material's Brillouin zone. With a view towards future generations of valley-based (opto)electronic technologies, the intrinsic timescales of scattering and relaxation between valleys therefore represent fundamental parameters of interest. Here we introduce and demonstrate an entirely passive, noise-based approach for exploring intrinsic valley dynamics in atomically-thin transition-metal dichalcog…
Van der Waals heterostructures formed by two different monolayer semiconductors have emerged as a promising platform for new optoelectronic and spin/valleytronic applications. In addition to its atomically thin nature, a two-dimensional semiconductor heterostructure is distinct from its three-dimensional counterparts due to the unique coupled spin-valley physics of its constituent monolayers. Here, we report the direct observation that an optically generated spin-valley polarization in one monolayer can be transferred between layers of a two-dimensional MoSe2-WSe2 heterostructure. Using nondeg…
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…
Weyl semimetals are three-dimensional crystalline systems where pairs of bands touch at points in momentum space, termed Weyl nodes, that are characterized by a definite topological charge: the chirality. Consequently, they exhibit the Adler-Bell-Jackiw anomaly, which in this condensed matter realization implies that application of parallel electric ($\mathbf{E}$) and magnetic ($\mathbf{B}$) fields pumps electrons between nodes of opposite chirality at a rate proportional to $\mathbf{E}\cdot\mathbf{B}$. We argue that this pumping is measurable via nonlocal transport experiments, in the limit o…
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…
Two dimensional heterostructures are likely to provide new avenues for the manipulation of magnetization that is crucial for spintronics or magnetoelectronics. Here, we demonstrate that optical spin pumping can generate a large effective magnetic field in two dimensional MoSe2/WSe2 heterostructures. We determine the strength of the generated field by polarization-resolved measurement of the interlayer exciton photoluminescence spectrum: the measured splitting exceeding 10 milli-electron volts (meV) between the emission originating from the two valleys corresponds to an effective magnetic field…
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…
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…
A recent scientific debate has arisen: Which processes underlie the actual ground of the valley Hall effect (VHE) in two-dimensional materials? The original VHE emerges in samples with ballistic transport of electrons due to the anomalous velocity terms resulting from the Berry phase effect. In disordered samples though, alternative mechanisms associated with electron scattering off impurities have been suggested: (i) asymmetric electron scattering, called skew scattering, and (ii) a shift of the electron wave packet in real space, called a side jump. It has been claimed that the side jump not…
We study the photogalvanic effect caused by a simultaneous action of circular-polarized interband and linearly-polarized intraband illuminations. It is found that, in such conditions, the steady photocurrent appears. The effect originates from the valley-selective pumping by the circular light, the trigonal asymmetry of the valleys together with the even asymmetry of the linearly-polarized light, that produces a polar in-plane asymmetry of the electron and hole distribution functions, leading to the photocurrent. The approach is based on the solution of the classical kinetic equation for carri…
We evidenced unconventionnal Anomalous Hall Effects (AHE) in 3d/5d (Co0.2nm/Ni0.6nm)N multilayers grown on a thin Pt layer or thin Au:W alloy. The inversion observed on AHE originates from the opposite sign of the spin-orbit coupling of Pt compared to Ni. Via advanced simulations methods for the description of the spin-current profiles based on the spin-dependent Boltzmann formalism, we extracted the spin Hall angle (SHA) of Pt and (Co/Ni) as well as the relevant transport parameters. The extracted SHA for Pt, +20%, is opposite to the one of (Co/Ni), giving rise to an effective AHE inversion f…
Near a magic twist angle, the lowest energy conduction and valence bands of bilayer graphene moiré superlattices become extremely narrow. The band dispersion that remains is sensitive to the moiré's strain pattern, nonlocal tunneling between layers, and filling-factor dependent Hartree and exchange band renormalizations. In this article we analyze the influence of these band-structure details on the pattern of flavor-symmetry-breaking observed in this narrow band system, and on the associated pattern of Fermi surface reconstructions revealed by weak-field-Hall and Schubnikov-de Haas magneto-tr…
We develop a microscopic theory of an unconventional photogalvanic effect in two-dimensional materials with the Dirac energy spectrum of the carriers of charge under strong driving. As a test bed, we consider a layer of a transition metal dichalcogenide, exposed to two different electromagnetic fields. The first pumping field is circularly-polarized, and its frequency exceeds the material bandgap. It creates an extremely nonequilibrium distribution of electrons and holes in one valley (K) and opens dynamical gaps, whereas the other valley (K') remains empty due to the valley-dependent interban…
We discuss the universal spin dynamics in quasi one-dimensional systems including the real spin in narrow-gap semiconductors like InAs and InSb, the valley pseudospin in staggered single-layer graphene, and the combination of real spin and valley pseudospin characterizing single-layer transition metal dichalcogenides (TMDCs) such as MoS$_2$, WS$_2$, MoSe$_2$, and WSe$_2$. All these systems can be described by the same Dirac-like Hamiltonian. Spin-dependent observable effects in one of these systems thus have counterparts in each of the other systems. Effects discussed in more detail include eq…
Two complementary effects modify the GHz magnetization dynamics of nanoscale heterostructures of ferromagnetic and normal materials relative to those of the isolated magnetic constituents: On the one hand, a time-dependent ferromagnetic magnetization pumps a spin angular-momentum flow into adjacent materials and, on the other hand, spin angular momentum is transferred between ferromagnets by an applied bias, causing mutual torques on the magnetizations. These phenomena are manifestly nonlocal: they are governed by the entire spin-coherent region that is limited in size by spin-flip relaxation …
Topological materials may exhibit Hall-like currents flowing transversely to the applied electric field even in the absence of a magnetic field. In graphene superlattices, which have broken inversion symmetry, topological currents originating from graphene's two valleys are predicted to flow in opposite directions and combine to produce long-range charge neutral flow. We observe this effect as a nonlocal voltage at zero magnetic field in a narrow energy range near Dirac points at distances as large as several microns away from the nominal current path. Locally, topological currents are compara…
