Finite-size Effects in a Two-Dimensional Electron Gas with Rashba Spin-Orbit Interaction

TL;DR

This paper investigates how finite system size and disorder influence the spin-Hall conductivity in a two-dimensional electron gas with Rashba spin-orbit interaction, revealing the dominant role of the spin-precession length.

Contribution

It introduces a numerical method to analyze finite-size effects on spin-Hall conductivity and identifies the spin-precession length as a key scale affecting conductivity reduction.

Findings

Spin-precession length critically reduces spin-Hall conductivity in finite systems.

Disorder strength has a minor effect compared to system size.

Numerical algorithm based on time-dependent Schrödinger equation integration.

Abstract

Within the Kubo formalism, we estimate the spin-Hall conductivity in a two-dimensional electron gas with Rashba spin-orbit interaction and study its variation as a function of disorder strength and system size. The numerical algorithm employed in the calculation is based on the direct numerical integration of the time-dependent Schrodinger equation in a spin-dependent variant of the particle source method. We find that the spin-precession length, L_s controlled by the strength of the Rashba coupling, establishes the critical lengthscale that marks the significant reduction of the spin-Hall conductivity in bulk systems. In contrast, the electron mean free path, inversely proportional to the strength of disorder, appears to have only a minor effect.