Pure Gauge Spin-Orbit Couplings

TL;DR

This paper uses non-Abelian gauge theory to analyze planar systems with linear spin-orbit interactions, revealing special Abelian cases like equal-strength Rashba-Dresselhaus SOI and their implications for phenomena such as the Persistent Spin Helix.

Contribution

It introduces a gauge-theoretic formalism for spin-orbit couplings, identifying Abelian gauge fields within the non-Abelian framework and applying this to the R+D SOI case and ring geometries.

Findings

Equal-strength R+D SOI corresponds to an Abelian gauge field.

The formalism explains the Persistent Spin Helix phenomenon.

Hamiltonians with R+D SOI are unitarily equivalent to simpler potentials.

Abstract

Planar systems with a general linear spin-orbit interaction (SOI) that can be cast in the form of a non-Abelian pure gauge field are investigated using the language of non-Abelian gauge field theory. A special class of these fields that, though a $2\times2$ matrix, are Abelian are seen to emerge and their general form is given. It is shown that the unitary transformation that gauges away these fields induces at the same time a rotation on the wavefunction about a fixed axis but with a space-dependent angle, both of which being characteristics of the SOI involved.The experimentally important case of equal-strength Rashba and Dresselhaus SOI (R+D SOI) is shown to fall within this special class of Abelian gauge fields, and the phenomenon of Persistent Spin Helix (PSH) that emerges in the presence of this latter SOI in a plane is shown to fit naturally within the general formalism developed. The general formalism is also extended to the case of a particle confined to a ring. It is shown that the Hamiltonian on a ring in the presence of equal-strength R+D SOI is unitarily equivalent to that of a particle subject to only a spin-independent but $\theta$-dependent potential with the unitary transformation relating the two being again the space-dependent rotation operator characteristic of R+D SOI.