Out-of-plane equilibrium spin current in a quasi-two-dimensional electron gas under in-plane magnetic field

TL;DR

This paper calculates the out-of-plane equilibrium spin current in a quasi-2D electron gas under an in-plane magnetic field, revealing how magnetic fields and spin-orbit interactions influence spin currents.

Contribution

It introduces a model accounting for finite thickness and magnetic effects, showing the emergence of out-of-plane spin currents and symmetry breaking in spin-orbit interactions.

Findings

Out-of-plane spin current appears with magnetic field and multiple filled levels.

Magnetic field breaks symmetry, leading to finite spin current when Rashba and Dresselhaus coefficients are equal.

Magnetic field modifies in-plane spin currents and introduces linear terms in spin-orbit constants.

Abstract

Equilibrium spin-current is calculated in a quasi-two-dimensional electron gas with finite thickness under in-plane magnetic field and in the presence of Rashba- and Dresselhaus spin-orbit interactions. The transverse confinement is modeled by means of a parabolic potential. An orbital effect of the in-plane magnetic field is shown to mix a transverse quantized spin-up state with nearest-neighboring spin-down states. The out-off-plane component of the equilibrium spin current appears to be not zero in the presence of an in-plane magnetic field, provided at least two transverse-quantized levels are filled. In the absence of the magnetic field the obtained results coincide with the well-known results, yielding cubic dependence of the equilibrium spin current on the spin-orbit coupling constants. The persistent spin-current vanishes in the absence of the magnetic field if Rashba- and Dresselhaus spin-orbit coefficients,{\alpha} and {\beta}, are equal each other. In-plane magnetic field destroys this symmetry, and accumulates a finite spin-current as {\alpha} \rightarrow {\beta}. Magnetic field is shown to change strongly the equilibrium current of the in-plane spin components, and gives new contributions to the cubic-dependent on spin-orbit constants terms. These new terms depend linearly on the spin-orbit constants.