Spin Transport in Two Dimensional Hopping Systems

TL;DR

This paper models spin transport in a two-dimensional hopping system with Rashba spin-orbit interaction, deriving rate equations and identifying conditions for spin-charge coupling and spin accumulation.

Contribution

It derives rate equations for charge and spin evolution in 2D hopping systems, revealing the role of multi-site hopping in spin-charge coupling and spin Hall effects.

Findings

Decoupled charge and spin evolution with two-site hopping.

Critical electric field induces oscillations in spin polarization.

Three-site hopping couples charge density and spin, leading to spin Hall effects.

Abstract

A two dimensional hopping system with Rashba spin-orbit interaction is considered. Our main interest is concerned with the evolution of the spin degree of freedom of the electrons. We derive the rate equations governing the evolution of the charge density and spin polarization of this system in the Markovian limit in one-particle approximation. If only two-site hopping events are taken into account, the evolution of the charge density and of the spin polarization is found to be decoupled. A critical electric field is found, above which oscillations are superimposed on the temporal decay of the total polarization. A coupling between charge density and spin polarization occurs on the level of three-site hopping events. The coupling terms are identified as the anomalous Hall effect and the recently proposed spin Hall effect. Thus, an unpolarized charge current through a sheet of finite width leads to a transversal spin accumulation in our model system.