Pure gauge spin-orbit couplings

Shikakhwa M. S.

EUROPEAN PHYSICAL JOURNAL PLUS, vol.132, no.1, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 132 Issue: 1
  • Publication Date: 2017
  • Doi Number: 10.1140/epjp/i2017-11288-0
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Middle East Technical University Affiliated: Yes


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 x 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 theta-dependent potential with the unitary transformation relating the two being again the space-dependent rotation operator characteristic of R+D SOI.