Dimensional Control of Antilocalisation and Spin Relaxation in Quantum Wires

TL;DR

This paper analytically investigates how the spin relaxation rate in disordered quantum wires with spin-orbit coupling varies with wire width, revealing a transition from weak anti-localization to weak localization as the wire narrows.

Contribution

It provides an analytical derivation of the spin relaxation rate dependence on wire width, highlighting the suppression of relaxation in narrow wires and the resulting change in quantum conductivity correction.

Findings

Spin relaxation rate decreases as wire width W becomes smaller than L_SO.

Weak anti-localization transitions to weak localization in narrow wires.

Cubic Dresselhaus coupling contributes a small residual relaxation rate.

Abstract

The spin relaxation rate $1/\tau_s (W)$ in disordered quantum wires with Rashba and Dresselhaus spin-orbit coupling is derived analytically as a function of wire width $W$. It is found to be diminished when $W$ is smaller than the bulk spin-orbit length $L_{\rm SO}$. Only a small spin relaxation rate due to cubic Dresselhaus coupling $\gamma$ is found to remain in this limit. As a result, when reducing the wire width $W$ the quantum conductivity correction changes from weak anti- to weak localization and from negative to positive magnetoconductivity.