Spin relaxation of two-dimensional electrons with a hierarchy of spin-orbit couplings

TL;DR

This paper uses the density matrix formalism to analyze spin relaxation times in two-dimensional electron systems with various spin-orbit couplings, identifying conditions for infinite spin lifetime and effects of external magnetic fields.

Contribution

It provides a theoretical framework to determine conditions for infinite spin relaxation times in 2D systems with multiple spin-orbit couplings, including the influence of external magnetic fields.

Findings

Spin relaxation time can be infinite under specific coupling conditions.

External magnetic fields can extend spin lifetime when certain relations are met.

Conditions for vanishing Yang-Mills magnetic field lead to infinite spin relaxation times.

Abstract

The density matrix formalism is applied to calculate the spin-relaxation time for two-dimensional systems with a hierarchy of spin-orbit couplings, such as Rashba-type, Dresselhaus-type and so on. It is found that the spin-relaxation time can be infinite if those coupling strengths $\alpha$, $\beta$, $\gamma_1$ and $\gamma_2$ satisfy either condition (i) $\alpha=\beta, \gamma_1=0$ or (ii) $\alpha=-\beta, \gamma_2=0$, which correspond to the vanishing Yang-Mills "magnetic" field. The effect caused by the application of an external magnetic field is also discussed. It is found that the longitudinal and in-plane spin components can possess infinite life time when the spin components, the Larmor precession frequency and the external magnetic field satisfy certain relations.