Eur. Phys. J. Plus (2017) 132: 17
https://doi.org/10.1140/epjp/i2017-11288-0

Regular Article

Pure gauge spin-orbit couplings

Physics Group, Middle East Technical University Northern Cyprus Campus, via Mersin 10, Güzelyurt, Turkey

^* e-mail: mohammad@metu.edu.tr

Received: 30 October 2016
Accepted: 6 December 2016
Published online: 17 January 2017

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 2×2 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 wave function 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 -dependent potential with the unitary transformation relating the two being again the space-dependent rotation operator characteristic of R+D SOI.