Spin-Hall effect in two-dimensional electron systems with Rashba spin-orbit coupling and disorder

Spin-Hall conductivity and Hall angle in a two-dimensional system with impurities in the presence of spin–orbit interactions

We investigate the spin-torque-dependent Spin Hall phenomenon in a two-dimensional tight-binding system in the presence of Rashba and Dresselhaus spin–orbit interactions and random static impurities. We employ the Matsubara Green function techniques to calculate the relaxation time caused by the scattering of electrons by impurities. The longitudinal and transverse conductivities are next calculated with the help of the Kubo formalism. We have also calculated the spin Hall angle for the present model and studied its dependence on spin–orbit interactions and impurity strength. Finally, we explore the effect of interplay between the Rashba and Dresselhaus interactions on the spin-Hall effect.

Anderson Transition of Cold Atoms with Synthetic Spin-Orbit Coupling in Two-Dimensional Speckle Potentials

We investigate the metal-insulator transition occurring in two-dimensional (2D) systems of noninteracting atoms in the presence of artificial spin-orbit interactions and a spatially correlated disorder generated by laser speckles. Based on a high order discretization scheme, we calculate the precise position of the mobility edge and verify that the transition belongs to the symplectic universality class. We show that the mobility edge depends strongly on the mixing angle between Rashba and Dresselhaus spin-orbit couplings. For equal couplings a non-power-law divergence is found, signaling the crossing to the orthogonal class, where such a 2D transition is forbidden.

Spin Hall Effect and Origins of Nonlocal Resistance in Adatom-Decorated Graphene

Recent experiments reporting an unexpectedly large spin Hall effect (SHE) in graphene decorated with adatoms have raised a fierce controversy. We apply numerically exact Kubo and Landauer-Büttiker formulas to realistic models of gold-decorated disordered graphene (including adatom clustering) to obtain the spin Hall conductivity and spin Hall angle, as well as the nonlocal resistance as a quantity accessible to experiments. Large spin Hall angles of ∼0.1 are obtained at zero temperature, but their dependence on adatom clustering differs from the predictions of semiclassical transport theories. Furthermore, we find multiple background contributions to the nonlocal resistance, some of which are unrelated to the SHE or any other spin-dependent origin, as well as a strong suppression of the SHE at room temperature. This motivates us to design a multiterminal graphene geometry which suppresses these background contributions and could, therefore, quantify the upper limit for spin-current generation in two-dimensional materials.

Maximum intrinsic spin-Hall conductivity in two-dimensional systems with k-linear spin-orbit interaction

We analytically calculate the intrinsic spin-Hall conductivities (ISHCs) (σ(z)(xy) and σ(z)(yx)) in a clean, two-dimensional system with generic k-linear spin-orbit interaction. The coefficients of the product of the momentum and spin components form a spin-orbit matrix β̃. We find that the determinant of the spin-orbit matrix detβ̃ describes the effective coupling of the spin sz and orbital motion Lz. The decoupling of spin and orbital motion results in a sign change of the ISHC and the band-overlapping phenomenon. Furthermore, we show that the ISHC is in general unsymmetrical (σ(z)(xy) ≠ -σ(z)(yx)), and it is governed by the asymmetric response function Δβ̃, which is the difference in band-splitting along two directions: those of the applied electric field and the spin-Hall current. The obtained non-vanishing asymmetric response function also implies that the ISHC can be larger than e/8π, but has an upper bound value of e/4π. We will show that the unsymmetrical properties of the ISHC can also be deduced from the manifestation of the Berry curvature in the nearly degenerate area. On the other hand, by investigating the equilibrium spin current, we find that detβ̃ determines the field strength of the SU(2) non-Abelian gauge field.

Predicted signatures of the intrinsic spin Hall effect in closed systems

We study a two-dimensional electron system in the presence of spin-orbit interaction. It is shown analytically that the spin-orbit interaction acts as a transversal effective electric field, whose orientation depends on the sign of the z-axis spin projection. This effect does not require any driving electrical field and is inherent to the spin-orbit interactions present in semiconductor materials. Therefore, it should manifest in both closed and open systems. An experiment is proposed to observe the intrinsic spin Hall effect in the far infrared absorption of an asymmetric semiconductor nanostructure.

Spin filtering and quantum phase transition in double quantum dots attached to spin-polarized leads

We study the spin filtering and quantum phase transition (QPT) in double quantum dots attached to spin-polarized leads. For spin-independent leads, we observe a Kosterlitz-Thouless transition between the local triplet and doublet. For spin-polarized leads, the above QPT becomes first order, and Kondo splitting, gate-controlled spin reversal and a perfect spin filtering are observed. The breaking of spin-rotation SU(2) symmetry and the interdot transport mediated by the conduction electron are responsible for the fully spin-polarized conductance. Because spin-polarized leads suppress the Kondo effect, in order to obtain a large conductance with perfect spin filtering, one should choose leads with small spin polarization, such as Rashba spin-orbital coupling leads.

Observation of intrinsic inverse spin Hall effect

We report observation of intrinsic inverse spin Hall effect in undoped GaAs multiple quantum wells with a sample temperature of 10 K. A transient ballistic pure spin current is injected by a pair of laser pulses through quantum interference. By time resolving the dynamics of the pure spin current, the momentum relaxation time is deduced, which sets the lower limit of the scattering time between electrons and holes. The transverse charge current generated by the pure spin current via the inverse spin Hall effect is simultaneously resolved. We find that the charge current is generated well before the first electron-hole scattering event. Generation of the transverse current in the scattering-free ballistic transport regime provides unambiguous evidence for the intrinsic inverse spin Hall effect.

Generation and detection of spin current in the three-terminal quantum dot

We propose a novel device composed of a quantum dot tunneling coupled to ferromagnetic, superconducting, and normal-metal leads. This device can generate, manipulate, and detect pure spin current through the interplay between the spin-polarized quantum transport and the Andreev reflection. The spin current in this device is a well-defined conserved current since there is no need for any spin-orbit coupling. The proposed device is realizable using present nanotechnology.

Intrinsic spin hall effect induced by quantum phase transition in HgCdTe quantum wells

The spin Hall effect can be induced by both extrinsic impurity scattering and intrinsic spin-orbit coupling in the electronic structure. The HgTe/CdTe quantum well has a quantum phase transition where the electronic structure changes from normal to inverted. We show that the intrinsic spin Hall effect of the conduction band vanishes on the normal side, while it is finite on the inverted side. By tuning the Cd content, the well width, or the bias electric field across the quantum well, the intrinsic spin Hall effect can be switched on or off and tuned into resonance under experimentally accessible conditions.

Mesoscopic spin Hall effect

We investigate the spin Hall effect in ballistic chaotic quantum dots with spin-orbit coupling. We show that a longitudinal charge current can generate a pure transverse spin current. While this transverse spin current is generically nonzero for a fixed sample, we show that when the spin-orbit coupling time is short compared to the mean dwell time inside the dot, it fluctuates universally from sample to sample or upon variation of the chemical potential with a vanishing average.

Low-field phase diagram of the spin Hall effect in the mesoscopic regime

When a mesoscopic two dimensional four-terminal Hall cross bar with spin-orbit interaction (SOI) is subjected to a perpendicular uniform magnetic field B, both integer quantum Hall effect (IQHE) and mesoscopic spin Hall effect (MSHE) may exist when disorder strength W in the sample is weak. We have calculated the low field "phase diagram" of MSHE in the (B,W) plane for disordered samples in the IQHE regime. For weak disorder, MSHE conductance G(sH) and its fluctuations rms(G(sH)) vanish identically on even numbered IQHE plateaus, they have finite values on those odd numbered plateaus induced by SOI, and they have values G(sH)=1/2 and rms(G(sH))=0 on those odd numbered plateaus induced by Zeeman energy. At larger disorders, the system crosses over into a regime where both G(sH) and rms(G(sH)) are finite, a chaotic regime, and finally a localized regime.

Universal spin-Hall conductance fluctuations in two dimensions

We report a theoretical investigation on spin-Hall conductance fluctuation of disordered four-terminal devices in the presence of Rashba or/and Dresselhaus spin-orbital interactions in two dimensions. As a function of disorder, the spin-Hall conductance GsH shows ballistic, diffusive, and insulating transport regimes. For given spin-orbit interactions, a universal spin-Hall conductance fluctuation (USCF) is found in the diffusive regime. The value of the USCF depends on the spin-orbit coupling tso but is independent of other system parameters. It is also independent of whether Rashba or Dresselhaus or both spin-orbital interactions are present. When tso is comparable to the hopping energy t, the USCF is a universal number approximately 0.18e/4pi. The distribution of GsH crosses over from a Gaussian distribution in the metallic regime to a non-Gaussian distribution in the insulating regime as the disorder strength is increased.

Spin accumulation on a one-dimensional mesoscopic Rashba ring

The nonequilibrium spin accumulation on a one-dimensional (1D) mesoscopic Rashba ring is investigated with unpolarized current injected through ideal leads. Due to the Rashba spin-orbit (SO) coupling and back-scattering at the interfaces between the leads and the ring, a beating pattern is formed in the fast oscillation of spin accumulation. If every beating period is complete, a plateau is formed, where the variation of spin accumulation with the external voltage is slow, but if new incomplete periods emerge in the envelope function, a transitional region appears. This plateau structure and the beating pattern are related to the tunnelling through spin-dependent resonant states. Because of the Aharonov-Casher (AC) effect, the average spin accumulation oscillates quasi-periodically with the Rashba SO coupling and has a series of zeros. In some situations, the direction of the average spin accumulation can be reversed by the external voltage in this 1D Rashba ring.

Resonant intrinsic spin hall effect in p-type GaAs quantum well structure

We study intrinsic spin Hall effect in p-type GaAs quantum well structure described by Luttinger Hamiltonian and a Rashba spin-orbit coupling arising from the structural inversion symmetry breaking. The Rashba term induces an energy level crossing in the lowest heavy hole subband, which gives rise to a resonant spin Hall conductance. The resonance may be used to identify the intrinsic spin Hall effect in experiments.

Consistency in formulation of spin current and torque associated with a variance of angular momentum

Based on the Noether's theorem, we develop systematically and rigorously the spin-dependent formulation of the conservation laws. The effect of the electronic polarization due to the spin-orbit coupling is included in the Maxwell equations. The polarization is related to the antisymmetric components of spin current, and it provides a possibility to measure the spin current directly. The variances of spin and orbit angular momentum currents imply a torque on the "electric dipole" associated with the moving electron. The dependencies of the torque on the polarization and the force on the motions of spin-polarized electrons in a two-dimensional electron gas with the Rashba spin-orbit coupling are discussed.

Sign changes of intrinsic spin Hall effect in semiconductors and simple metals: first-principles calculations

First-principles calculations are applied to study spin Hall effect in semiconductors and simple metals. We found that intrinsic spin Hall conductivity (ISHC) in realistic materials shows rich sign changes, which may be used to distinguish the effect from the extrinsic one. The calculated ISHC in n-doped GaAs can be well compared with experiment, and it differs from the sign obtained from the extrinsic effect. On the other hand, the ISHC in W and Au, which shows opposite sign, respectively, is robust and not sensitive to the disorder.

Nondissipative spin Hall effect via quantized edge transport

The spin Hall effect in a two-dimensional electron system on honeycomb lattice with both intrinsic and Rashba spin-orbit couplings is studied numerically. Integer quantized spin Hall conductance is obtained at the zero Rashba coupling limit when electron Fermi energy lies in the energy gap created by the intrinsic spin-orbit coupling, in agreement with recent theoretical prediction. While nonzero Rashba coupling destroys electron spin conservation, the spin Hall conductance is found to remain near the quantized value, being insensitive to disorder scattering, until the energy gap collapses with increasing the Rashba coupling. We further show that the charge transport through counterpropagating spin-polarized edge channels is well quantized, which is associated with a topological invariant of the system.

Numerical study of the spin-Hall conductance in the Luttinger model

We present the first numerical studies of the disorder effect on the recently proposed intrinsic spin-Hall conductance in a three dimensional lattice Luttinger model. The results show that the spin-Hall conductance remains finite in a wide range of disorder strength, with large fluctuations. The disorder-configuration-averaged spin-Hall conductance monotonically decreases with the increase of disorder strength and vanishes before the Anderson localization takes place. The finite-size effect is also discussed.

Nonequilibrium spin Hall accumulation in ballistic semiconductor nanostructures

We demonstrate that the flow of a longitudinal unpolarized current through a ballistic two-dimensional electron gas with Rashba spin-orbit coupling will induce a nonequilibrium spin accumulation which has opposite signs for the two lateral edges and is, therefore, the principal observable signature of the spin Hall effect in two-probe semiconductor nanostructures. The magnitude of its out-of-plane component is gradually diminished by static disorder, while it can be enhanced by an in-plane transverse magnetic field. Moreover, our prediction of the longitudinal component of the spin Hall accumulation, which is insensitive to the reversal of the bias voltage, offers direct evidence to differentiate experimentally between the extrinsic, intrinsic, and mesoscopic spin Hall mechanisms.

Spin Hall current driven by quantum interferences in mesoscopic Rashba rings

We propose an all-electrical nanostructure where pure spin current is induced in the transverse voltage probes attached to a quantum-coherent ballistic one-dimensional ring when unpolarized charge current is injected through its longitudinal leads. Tuning of the Rashba spin-orbit coupling in a semiconductor heterostructure hosting the ring generates quasiperiodic oscillations of the predicted spin-Hall current due to spin-sensitive quantum-interference effects caused by the difference in the Aharonov-Casher phase accumulated by opposite spin states. Its amplitude is comparable to that of the spin-Hall current predicted for finite-size (simply connected) two-dimensional electron gases, while it gets reduced gradually in wide two-dimensional rings or due to spin-independent disorder.

Experimental observation of the spin-Hall effect in a two-dimensional spin-orbit coupled semiconductor system

We report the experimental observation of the spin-Hall effect in a 2D hole system with spin-orbit coupling. The 2D hole layer is a part of a p-n junction light-emitting diode with a specially designed coplanar geometry which allows an angle-resolved polarization detection at opposite edges of the 2D hole system. In equilibrium the angular momenta of the spin-orbit split heavy-hole states lie in the plane of the 2D layer. When an electric field is applied across the hole channel, a nonzero out-of-plane component of the angular momentum is detected whose sign depends on the sign of the electric field and is opposite for the two edges. Microscopic quantum transport calculations show only a weak effect of disorder, suggesting that the clean limit spin-Hall conductance description (intrinsic spin-Hall effect) might apply to our system.