Eur. Phys. J. B (2015) 88: 198
https://doi.org/10.1140/epjb/e2015-60257-4

Regular Article

Gauge transformations of spin-orbit interactions in graphene

¹ Groupe de Physique Statistique, Institut Jean Lamour, Université de Lorraine, 54506 Vandoeuvre-les-Nancy, France
² Centro de Física, Instituto Venezolano de Investigaciones Científicas, 21827 Caracas, 1020 A, Venezuela
³ Escuela de Física, Facultad de Ciencias, Universidad Central de Venezuela, 1040 Caracas, Venezuela
⁴ Institute for Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany
⁵ Universidad de Investigación de Tecnología Experimental YACHAY Ciudad del Conocimiento, 100119 San Miguel de Urcuqui, Ecuador

^a e-mail: bertrand.berche@univ-lorraine.fr

Received: 30 March 2015
Received in final form: 2 June 2015
Published online: 10 August 2015

Abstract

Inclusion of spin-dependent interactions in graphene in the vicinity of the Dirac points can be posed in terms of non-Abelian gauge potentials. Such gauge potentials being surrogates of physical electric fields and material parameters, only enjoy a limited gauge freedom. A general gauge transformation thus changes the physical model. We argue that this property can be useful in connecting reference physical situations, such as free particle or Rashba interactions to non-trivial physical Hamiltonians with a new set of spin-orbit interactions, albeit constrained to being isoenergetic. We analyse different combinations of spin-orbit interactions in the case of monolayer graphene and show how they are related by means of selected non-Abelian gauge transformations.