Experimental observation of the spin-Hall effect in a spin–orbit coupled two-dimensional hole gas

Electrically induced ordering and manipulation of electron spins in semiconductors has a number of practical advantages over the established techniques using circularly polarized light sources, external magnetic fields and spin injection from a ferromagnet. The spin-Hall effect utilizes spin–orbit coupling to induce edge spin accumulation in response to a longitudinal electric field which can be applied locally and lead to low energy consumption devices. We study spin accumulation near the edge of a weakly disordered two-dimensional hole gas (2DHG) in a GaAs/AlGaAs heterostructure where the magnitude of the transverse spin current approaches the intrinsic, disorder independent value, in contrast to the impurity dominated regime observed in 3D electron doped systems. In our experiment, the induced spin polarization is detected by the electroluminescence resulting from two p–n junctions bordering the 2DHG channel. When an electric field is applied across the 2DHG channel, a non-zero out-of-plane component of the spin is optically detected. The sign of the spin depends on the direction of the field and is opposite for the two edges, consistent with theory predictions. We also report and analyze an in-plane spin-polarization effect induced in the device by asymmetric electron–hole recombination.     

Dissipationless spin-Hall current contribution in the extrinsic spin-Hall effect

This paper shows that a substantial amount of dissipationless spin-Hall current contribution may exist in the extrinsic spin-Hall effect, which originates from the spin-orbit coupling induced by the applied external electric field itself that drives the extrinsic spin-Hall effect in a nonmagnetic semiconductor (or metal). By assuming that the impurity density is in a moderate range such that the total scattering potential due to all randomly distributed impurities is a smooth function of the space coordinate, it is shown that this dissipationless contribution shall be of the same orders of magnitude as the usual extrinsic contribution from spin-orbit dependent impurity scatterings (or may even be larger than the latter one). The theoretical results obtained are in good agreement with recent relevant experimental results.     

Intrinsic spin Hall effect in the two-dimensional hole gas

We show that two types of spin-orbit coupling in the 2 dimensional hole gas, with and without inversion symmetry breaking, contribute to the intrinsic spin-Hall effect. Furthermore, the vertex correction due to impurity scattering vanishes in both cases, in sharp contrast to the case of usual Rashba coupling in the electron band. Recently, the spin-Hall effect in a hole doped GaAs semiconductor has been observed experimentally by Wunderlich et al. [ Phys. Rev. Lett. 94, 047204 (2005).]. From the fact that the lifetime broadening is smaller than the spin splitting, and the fact impurity vertex corrections vanish in this system, we argue that the observed spin-Hall effect should be in the intrinsic regime.     

Intrinsic spin-Hall effect: topological transitions in two-dimensional systems

Topological transitions are the discontinuous changes of the Berry phase caused by continuous variation of parameters. These transitions can be detected by investigating the spin-Hall effect in two-dimensional electron and hole systems with a spin-obrit interaction when the density of carriers or the structural asymmetry are varied. The discontinuous behavior and the universality features of the spin-Hall conductivity are determined by the topological properties of the spin-orbit field.     

Effects of spin-orbit interaction on superconductor-ferromagnet heterostructures: Spontaneous electric and spin surface currents

We find proximity-induced spontaneous spin and electric surface currents at all temperatures below the super-conducting T _c in an isotropic s-wave superconductor deposited with a thin ferromagnetic metal layer with spin-orbit interaction. The currents are carried by Andreev surface states and generated as a joint effect of the spin-orbit interaction and the exchange field. The background spin current arises in the thin layer due to different local spin polarizations of electrons and holes, which have almost opposite velocities in each of the surface states. The spontaneous surface electric current in the superconductor originates in the asymmetry of Andreev states with respect to sign reversal of the momentum component parallel to the surface. The conditions for electric and spin currents to show up in the system significantly differ from each other.     

Orbital ac spin-Hall effect in the hopping regime

The Rashba and Dresselhaus spin-orbit interactions are both shown to yield the low temperature spin-Hall effect for strongly localized electrons coupled to phonons. A frequency-dependent electric field E(omega) generates a spin-polarization current, normal to E, due to interference of hopping paths. At zero temperature the corresponding spin-Hall conductivity is real and is proportional to omega2. At nonzero temperatures the coupling to the phonons yields an imaginary term proportional to omega. The interference also yields persistent spin currents at thermal equilibrium, at E=0. The contributions from the Dresselhaus and Rashba interactions to the interference oppose each other.     

Generation of spin currents and spin densities in systems with reduced symmetry

We show that the spin-current response of a semiconductor crystal to an external electric field is considerably more complex than previously assumed. While in systems of high symmetry only the spin-Hall components are allowed, in systems of lower symmetry other non-spin-Hall components may be present. We argue that, when spin-orbit interactions are present only in the band structure, the distinction between intrinsic and extrinsic contributions to the spin current is not useful. We show that the generation of spin currents and that of spin densities in an electric field are closely related, and that our general theory provides a systematic way to distinguish between them in experiment. We discuss also the meaning of vertex corrections in systems with spin-orbit interactions.     

Theory of the vertical Hall effect in a dimensionally quantized system

The transverse redistribution of carriers that occurs in a 2D system under the effect of a tangential electric field and a magnetic field possessing a tangential component is studied. It is shown that the redistribution of carriers gives rise to a Hall voltage across isolated electrodes positioned above and under the quantum film. This voltage is determined by the 2D conductivity tensor and the transverse static electric polarizability of the 2D layer. The additional contribution that appears in the vertical Hall voltage because of the electron spin orientation induced by magnetic field and the spin-orbit interaction of electrons with the quantum well potential is determined.     

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-Hall effect: Back to the beginning at a higher level

The phenomena of the spin-Hall effect, initially proposed over three decades ago in the context of asymmetric Mott skew scattering, was revived recently by the proposal of a possible intrinsic spin-Hall effect originating from a strongly spin-orbit coupled band structures. This new proposal has generated an extensive debate and controversy over the past 2 years. On August 2006 the first workshop on the spin-Hall effect was held at the Asian Pacific Center for Theoretical Physics. Its purpose was to bring together many of the leading groups in this field to resolve such issues and identify future challenges. We offer this short summary to clarify formerly controversial issues now settled and help refocus the research efforts in new and important avenues.     

Spin Hall effect on edge magnetization and electric conductance of a 2D semiconductor strip

The intrinsic spin Hall effect on spin accumulation and electric conductance in a diffusive regime of a 2D electron gas has been studied for a 2D strip of a finite width. It is shown that the spin polarization near the flanks of the strip, as well as the electric current in the longitudinal direction, exhibit damped oscillations as a function of the width and strength of the Dresselhaus spin-orbit interaction. Cubic terms of this interaction are crucial for spin accumulation near the edges. As expected, no effect on the spin accumulation and electric conductance have been found in case of Rashba spin-orbit interaction.     

Spin-orbit coupling and anisotropy of spin splitting in quantum dots

In lateral quantum dots, the combined effect of both Dresselhaus and Bychkov-Rashba spin-orbit coupling is equivalent to an effective magnetic field +/- B(SO) which has the opposite sign for s(z)= +/- 1/2 spin electrons. When the external magnetic field is perpendicular to the planar structure, the field B(SO) generates an additional splitting for electron states as compared to the spin splitting in the in-plane field orientation. The anisotropy of spin splitting has been measured and then analyzed in terms of spin-orbit coupling in several AlGaAs/GaAs quantum dots by means of resonant tunneling spectroscopy. From the measured values and sign of the anisotropy we are able to determine the dominating spin-orbit coupling mechanism.     

Coriolis effect in optics: unified geometric phase and spin-Hall effect

We examine the spin-orbit coupling effects that appear when a wave carrying intrinsic angular momentum interacts with a medium. The Berry phase is shown to be a manifestation of the Coriolis effect in a noninertial reference frame attached to the wave. In the most general case, when both the direction of propagation and the state of the wave are varied, the phase is given by a simple expression that unifies the spin redirection Berry phase and the Pancharatnam-Berry phase. The theory is supported by the experiment demonstrating the spin-orbit coupling of electromagnetic waves via a surface plasmon nanostructure. The measurements verify the unified geometric phase, demonstrated by the observed polarization-dependent shift (spin-Hall effect) of the waves.     

Quantum spin Hall effect and enhanced magnetic response by spin-orbit coupling

We show that the spin-Hall conductivity in insulators is related to a magnetic susceptibility representing the strength of the spin-orbit coupling. We use this relationship as a guiding principle to search real materials showing quantum spin-Hall effect. As a result, we theoretically predict that two-dimensional bismuth will show the quantum spin-Hall effect, both by calculating the helical edge states, and by showing the nontriviality of the Z2 topological number, and propose possible experiments.     

Orbital-angular-momentum based origin of Rashba-type surface band splitting

We propose that the existence of local orbital angular momentum (OAM) on the surfaces of high-Z materials plays a crucial role in the formation of Rashba-type surface band splitting. Local OAM state in a Bloch wave function produces an asymmetric charge distribution (electric dipole). The surface-normal electric field then aligns the electric dipole and results in chiral OAM states and the relevant Rashba-type splitting. Therefore, the band splitting originates from electric dipole interaction, not from the relativistic Zeeman splitting as proposed in the original Rashba picture. The characteristic spin chiral structure of Rashba states is formed through the spin-orbit coupling and thus is a secondary effect to the chiral OAM. Results from first-principles calculations on a single Bi layer under an external electric field verify the key predictions of the new model.     

Universal intrinsic spin Hall effect

We describe a new effect in semiconductor spintronics that leads to dissipationless spin currents in paramagnetic spin-orbit coupled systems. We argue that in a high-mobility two-dimensional electron system with substantial Rashba spin-orbit coupling, a spin current that flows perpendicular to the charge current is intrinsic. In the usual case where both spin-orbit split bands are occupied, the intrinsic spin-Hall conductivity has a universal value for zero quasiparticle spectral broadening.     

Universal quantized spin-Hall conductance fluctuation in graphene

We report theoretical investigations of the quantized spin-Hall conductance fluctuation of graphene in the presence of disorder. Two graphene models that exhibit the quantized spin-Hall effect (QSHE) are analyzed. Model I is with unitary symmetry under an external magnetic field B not = 0 but with a zero spin-orbit interaction, t(SO)=0. Model II is with symplectic symmetry where B=0 but t(SO) not = 0. The two models give exactly the same universal QSHE conductance fluctuation value 0.285+/-0.005e/4pi regardless of symmetry. We also examined a third model that exhibits QSHE but with quadratic dispersion and obtained the same results. Finally, all three models of QSHE have a one-sided log-normal distribution for spin-Hall conductance. Our results strongly suggest that the quantized spin-Hall conductance fluctuation belongs to a new universality class.     

Giant spin-Hall effect induced by the Zeeman interaction in graphene

We propose a new approach to generate and detect spin currents in graphene, based on a large spin-Hall response arising near the neutrality point in the presence of an external magnetic field. Spin currents result from the imbalance of the Hall resistivity for the spin-up and spin-down carriers induced by the Zeeman interaction, and do not involve a spin-orbit interaction. Large values of the spin-Hall response achievable in moderate magnetic fields produced by on-chip sources, and up to room temperature, make the effect viable for spintronics applications.     

Influence of spin-orbit coupling induced by in-plane external electric field on the intrinsic spin-Hall effect in a Rashba two-dimensional electron gas

We study theoretically the influence of spin--orbit coupling induced by in-plane external electric field on the intrinsic spin-Hall effect in a two-dimensional electron gas with Rashba spin--orbit coupling. We show that, after such an influence is taken into account, the static intrinsic spin-Hall effect can be stabilized in a disordered Rashba two-dimensional electron gas, and the static intrinsic spin-Hall conductivity shall exhibit some interesting characteristics as conceived in some original theoretical proposals.     

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.