Coupled Spin and Valley Physics in Monolayers ofMoS2and Other Group-VI Dichalcogenides

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 charge density or local density of states in MoS2 can be used to measure its energy-dependent valley and orbital Hall conductivity.

Anomaly cancelation has been shown to occur in time-reversal symmetry-broken Weyl metals, which explains the existence of a Fermi arc. We extend this result in the case of inversion symmetry-broken Weyl metals. Constructing a minimal model that takes a double pair of Weyl points, we demonstrate the anomaly cancelation explicitly. This demonstration explains why a chiral pair of Fermi arcs appear in inversion symmetry-broken Weyl metals. In particular, we find that this pair of Fermi arcs gives rise to either "quantized" spin Hall or valley Hall effects, which corresponds to the "quantized" version of the charge Hall effect in time-reversal symmetry-broken Weyl metals.

The spin and valley physics in 2-dimensional van der Waals materials provides a unique platform for novel applications in spintronics and valleytronics. 2H phase transition metal dichalcogenides (TMD) monolayers possesses broken inversion symmetry and strong spin-orbit coupling, leading to a coupled spin and valley physics that makes them better candidates for these applications. For practical device applications, spin and valley Hall effect (SVHE) is a good way of charge to spin and charge to valley conversion, making the electrical generation of spin and valley polarization possible. While SVHE has been observed via optical measurements at cryotemperatures below 30 K, the behavior at elevated temperatures and thorough understanding of the data are still lacking. In this work we conduct spatial Kerr rotation (KR) measurements on monolayer tungsten diselenide (WSe₂) field effect transistors and study the electrical control and temperature dependence of SVHE. We image the distribution of the spin and valley polarization directly and find clear evidence of the spin and valley accumulation at the edges. We show that the SVHE can be electrically modulated by the gate and drain bias, and the polarization persists at elevated temperatures. We then conduct four-port electrical test reflection spectra measurement and use a drift-diffusion model to interpret the data and extract key parameters. A lower-bound spin/valley lifetime is predicted of 40 ns and a mean free path of 240 nm below 90 K. The spin/valley polarization on the edge is calculated to be ~4% at 45 K. WSe₂-on-hBN samples are prepared as well, and the KR measurements on these samples are discussed.

We predict the coexistence of tunneling spin and valley Hall effects when electrons in graphene coherently transmit through a barrier with the broken inversion symmetry and proximity-induced spin-orbit coupling. Due to the rotation of the pseudospin in the tunneling process, the transmitted electrons acquire a finite spin- and valley-dependent backreflection geometric phase when the two interfaces of the barrier are asymmetric. This results in a spin- and valley-dependent skew coherent tunneling, which is responsible for the transverse spin and valley Hall currents. We further demonstrate that the coherent-tunneling assisted charge-spin and charge-valley conversions are highly efficient with large Hall angles. Our work provides a new route for the generation of efficient spin and valley Hall effects, suggesting potential applications for spintronic and valleytronic devices.

We provide deeper insights into the nonlinear transports in strained monolayer graphene and find that both nonlinear valley and nonlinear charge Hall effects can be interpreted with the orbital magnetic moment (OMM). Since strain induced anisotropic velocities and band-warping terms break the inversion and rotation symmetry, the nonlinear valley and charge Hall effect emerges. We demonstrate that the intrinsic OMM, originating from Berry curvature linearly corrected by electric field, is valley-contrasting which contributes to the nonlinear valley Hall current, and the shift OMM, originating from Fermi distribution function linearly corrected by electric field, is valley-independent which contributes to the nonlinear Berry-curvature-dipole (BCD) Hall current. Thus, we reveal that the nonlinear BCD Hall current and nonlinear valley current essentially have the same physics and the dependence of valley index of the orbital magnetic moment determines which nonlinear Hall effect emerges. Physically, we give an interpretation of two-step process: One electric field Ex induces an orbital magnetization and then the other electric field Ex generates the anomalous Hall effect under the orbital magnetization. These results establish a microscopic connection between orbital magnetization and nonlinear Hall responses. Furthermore, the strong dependence of OMM on strain provides a route to strain-engineered control of the nonlinear Hall transports.

Engineering pseudo-spin and valley degrees of freedom using quantum spin Hall and valley Hall effects has opened up remarkable possibilities for highly efficient and robust signal transport in time-reversal invariant photonic systems. Here we present a spin-valley locked photonic crystal that has distinct signs of chirality of sublattices in a honeycomb unit cell. We show that the photonic crystal has an insulating bulk dispersion and sublattice-dependent spin-valley coupled gapless edge states by exploiting a coupled dipole method and demonstrate valley-selective propagation by controlling spin state of an external dipole source. The interplay between spin, valley and sublattice shows a judicious way for one-way photon transport by using multiple degrees of freedom.

The exploration of valley-contrasting physics in two-dimensional materials with strong spin-orbit coupling is of great significance for both fundamental physics and advanced information technology. Here, using first-principles calculations, we report the identification of promising valley-contrasting physics in single-layer CrSi2N4 and CrSi2P4. Single-layer CrSi2N4 and CrSi2P4 are semiconductors with a direct band gap locating at the K/K' point, which forms a pair of degenerate but nonequivalent valleys in both the conduction and valence bands. These valleys display the intriguing valley spin splitting when considering spin-orbit coupling. Particularly for the valence bands, the valley spin splitting can reach up to 0.13/0.17 eV, giving rise to the robust spin-valley coupling and thus the coexistence of spin and valley Hall effects. The underlying physics are uncovered in detail. Moreover, strain is demonstrated to be an effective way for manipulating their coupled spin and valley physics.

Monolayer transition metal dichalcogenides have strong spin–orbit coupling and broken space inversion symmetry, which enable them to be the key building blocks in realizing spin and valley-related effects. Here, we report the spin and valley Hall conductivities of monolayer transition metal dichalcogenides in the presence of the magnetic proximity effect, which is introduced by a ferromagnetic substrate. It is found that the profile and magnitude of the spin and valley Hall conductivities in monolayer transition metal dichalcogenides are different with and without magnetic exchange interactions. This difference can be attributed to the asymmetrical band structure of monolayer transition metal dichalcogenides and chemical potential-dependent interband transitions. The former comes from the fact that the magnetic proximity effect can effectively break the time reversal symmetry and thus lead to the asymmetry of the band structures between K+ and K− valleys, which causes the final changes in the spin and valley Hall conductivities. Our findings demonstrate that the magnetic proximity effect can affect the spin as well as valley Hall behaviors in monolayer transition metal dichalcogenides, and this strategy is applicable for other two-dimensional layered materials, which is promising for spintronic and valleytronic devices.

Valleytronic materials, characterized by local extrema (valleys) in their bands, and topological insulators have separately attracted great interest recently. However, the interplay between valleytronic and topological properties in one single system, likely to enable important unexplored phenomena and applications, has been largely overlooked so far. Here, by combining a tight-binding model with first-principles calculations, we find the large-band-gap quantum spin Hall effects (QSHEs) and valley Hall effects appear simultaneously in the bismuth monolayers decorated with hydrogen/halogen elements, denoted as Bi2XY (X, Y = H, F, Cl, Br, or I). A staggered exchange field is introduced into the Bi2XY monolayers by transition-metal atom (Cr, Mo, or W) doping or LaFeO3 magnetic substrates, which together with the strong spin-orbit coupling of bismuth atoms generates a time-reversal-symmetry-broken QSHE and a huge valley splitting (up to 513 meV) in the system. With gate control, QSHE and anomalous charge, spin, valley Hall effects can be observed in the single system. These predicted multiple and exotic Hall effects, associated with various degrees of freedom of electrons, could enable applications of the functionalized bismuth monolayers in electronics, spintronics, and valleytronics.

The discovery of the integer quantum Hall effect in the early eighties of the last century, with highly precise quantization values for the Hall conductance in multiples of e2/h, has been the first fascinating manifestation of the topological state of matter driven by magnetic field and disorder, and related to the formation of non-dissipative current flow. Throughout the 2000’s, several new phenomena such as the spin Hall effect and the quantum spin Hall effect were confirmed experimentally for systems with strong spin-orbit coupling effects and in the absence of external magnetic field. More recently, the Zeeman spin Hall effect and the formation of valley Hall topological currents have been introduced for graphene-based systems, under time-reversal or inversion symmetry-breaking conditions, respectively. This review presents a comprehensive coverage of all these Hall effects in disordered graphene from the perspective of numerical simulations of quantum transport in two-dimensional bulk systems (by means of the Kubo formalism) and multiterminal nanostructures (by means of the Landauer-Buttiker scattering and non-equilibrium Green’s function approaches). In contrast to usual two-dimensional electron gases in semiconductor heterostructures, the presence of defects in graphene generates more complex electronic features such as electron-hole asymmetry, defect-induced resonances in the electron density of states or percolation effect between localized impurity states, which, together with extra degrees of freedom (sublattice pseudospin and valley isospin), bring a higher degree of complexity and enlarge the transport phase diagram.

Monolayer transition metal dichalcogenide (TMD) materials have exciting potential for applications in spintronics. Due to the monolayer geometry and strong spin-orbit coupling, they are predicted to have a coupled spin and valley Hall effect (SVHE), where valley-polarized conduction carriers have opposite spin [1, 2, 3]. This could provide a valley-preserved spin Hall effect for switching future magnetic memories. WSe2 is an attractive 2D material in this context because of its large valence band spin splitting. Lifetimes of spin and valley polarized carriers in monolayer WSe 2 have been measured from 0.7 ns to 1 μs at 10 K [4, 5, 6]. Such long lifetimes combined with reasonable mobilities lead to spin-valley accumulation that can be imaged via the magneto-optical Kerr effect (MOKE). For use in applications, it is necessary to electrically control the SVHE and push it towards room temperature.

The new-type monolayer semiconductor material molybdenum disulfide (MoS2) is direct band gap semiconductor with a similar geometrical structure to graphene, and as it owns superior physical features such as spin/valley Hall effect, it should be more excellent than graphene from the viewpoint of device design and applications. The manipulation of the spin and valley transport in MoS2-based device has been an interesting subject in both experimental and theoretical researches. Experimentally, the photoninduced quantum spin and valley Hall effects may result in high on-off speed spin and/or valley switching based on MoS2. Theoretically, the off-resonant electromagnetic field induced Floquet effective energy should modulate effectively the electronic structure, spin/valley Hall conductance as well as the spin/valley polarization of the MoS2, through the virtual photon absorption and/or emission processes. Utilizing the low energy effective Hamilton model from the tight-binding approximation and Kubo linear response theorem, we theoretically investigate the electronic structure and spin/valley transport properties of the monolayer MoS2 under the irradiation of the off-resonant circularly polarized light in the present work. The band gaps around the K and K' point of the Brillouin region for monolayer MoS2 proves to increase linearly and decrease firstly and then increase, respectively with the increase of external off-resonant right-circularly polarized light induced effective coupling energy, and decrease firstly and then increase and increase linearly with the increase of left-circularly polarized light induced effective coupling energy, therefore, the interesting transition of semiconducting-semimetallic-semiconducting may be observable in monolayer MoS2. Furthermore, the spin and valley Hall conductance of the monolayer MoS2 for the case without off-resonant circularly polarized light are 0 and 2e2/h, respectively, and they will convert into -2e2/h and 0 when the absolute value of the off-resonant circularly polarized light induced effective coupling energy is in a range of 0.79-0.87 eV. Finally, the spin polarization for monolayer MoS2 increases up to a largest value and changes from positive to negative and/or negative to positive at the vicinity of the effective coupling energy ±0.79 eV of the off-resonant right/left circularly polarized light, while the valley polarization should increase firstly and then decrease with the off-resonant circularly polarized light, and goes up to 100% in the range of 0.79-0.87 eV of the absolute value for effective coupling energy. Therefore, the external off-resonant circularly polarized electromagnetic field should be an effective means in manipulating the electronic structure, spin/valley Hall conductance and spin/valley polarization of the monolayer MoS2, the two-dimensional MoS2 may be tuned into a brand bandgap material with excellent spin/valley and optoelectrical properties.

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/ferromagnetic metal (cobalt or nickel), and (ii) graphene/magnetic insulator (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 spin, anomalous and valley Hall conductivities we employ certain effective Hamiltonians which have been proposed recently for the hybrid systems under considerations. Both anomalous and valley Hall conductivities are shown to have universal values when the Fermi level is inside the energy gap in the electronic spectrum.

In solids, electronic Bloch states are formed by atomic orbitals. While it is natural to expect that orbital composition and information about Bloch states can be manipulated and transported, in analogy to the spin degree of freedom extensively studied in past decades, it has been assumed that orbital quenching by the crystal field prevents significant dynamics of orbital degrees of freedom. However, recent studies reveal that an orbital current, given by the flow of electrons with a finite orbital angular momentum, can be electrically generated and transported in wide classes of materials despite the effect of orbital quenching in the ground state. Orbital currents also play a fundamental role in the mechanisms of other transport phenomena such as spin Hall effect and valley Hall effect. Most importantly, it has been proposed that orbital currents can be used to induce magnetization dynamics, which is one of the most pivotal and explored aspects of magnetism. Here, we give an overview of recent progress and the current status of research on orbital currents. We review proposed physical mechanisms for generating orbital currents and discuss candidate materials where orbital currents are manifest. We review recent experiments on orbital current generation and transport and discuss various experimental methods to quantify this elusive object at the heart of orbitronics —an area which exploits the orbital degree of freedom as an information carrier in solid-state devices.

Silicene takes precedence over graphene due to its buckling type structure and strong spin orbit coupling. Motivated by these properties, we study the silicene bilayer in the presence of applied perpendicular electric field and intrinsic spin orbit coupling to probe as quantum spin/valley Hall effect. Using analytical approach, we calculate the spin Chern-number of bilayer silicene and then compare it with monolayer silicene. We reveal that bilayer silicene hosts double spin Chern-number as compared to single layer silicene and therefore accordingly has twice as many edge states in contrast to single layer silicene. In addition, we investigate the combined effect of intrinsic spin orbit coupling and the external electric field, we find that bilayer silicene, likewise single layer silicene, goes through a phase transitions from a quantum spin Hall state to a quantum valley Hall state when the strength of the applied electric field exceeds the intrinsic spin orbit coupling strength. We believe that the results and outcomes obtained for bilayer silicene are experimentally more accessible as compared to bilayer graphene, because of strong SO coupling in bilayer silicene.