Subband anticrossing and the spin Hall effect in quantum wires

We report on numerical simulations of the intrinsic spin Hall effect in semiconductor quantum wires as a function of the Rashba spin-orbit coupling strength, the electron density, and the width of the wire. We find that the strength of the spin Hall effect does not depend monotonically on these parameters, but instead exhibits a local maximum. This behavior is explained by considering the dispersion relation of the electrons in the wire, which is characterized by the anticrossing of adjacent subbands. These results lead to a simple estimate of the optimal wire width for spin Hall transport experiments, and simulations indicate that this optimal width is independent of disorder. The anticrossing of adjacent subbands is related to a quantum phase transition in momentum space, and is accompanied by an enhancement of the Berry curvature and subsequently in the magnitude of the spin Hall effect.

Anisotropic intrinsic spin Hall effect in quantum wires

We use numerical simulations to investigate the spin Hall effect in quantum wires in the presence of both Rashba and Dresselhaus spin-orbit coupling. We find that the intrinsic spin Hall effect is highly anisotropic with respect to the orientation of the wire, and that the nature of this anisotropy depends strongly on the electron density and the relative strengths of the Rashba and Dresselhaus spin-orbit coupling. In particular, at low densities when only one subband of the quantum wire is occupied, the spin Hall effect is strongest for electron momentum along the $[bar{1}10]$ axis, which is opposite than what is expected for the purely 2D case. In addition, when more than one subband is occupied, the strength and anisotropy of the spin Hall effect can vary greatly over relatively small changes in electron density, which makes it difficult to predict which wire orientation will maximize the strength of the spin Hall effect. These results help to illuminate the role of quantum confinement in spin-orbit-coupled systems, and can serve as a guide for future experimental work on the use of quantum wires for spin-Hall-based spintronic applications.