Gauge transformations of Spin-Orbit interactions in graphene

TL;DR

This paper explores how non-Abelian gauge transformations relate different spin-orbit interaction models in graphene, revealing connections between various physical Hamiltonians and their underlying gauge structures.

Contribution

It demonstrates the use of gauge transformations to connect and analyze different spin-orbit interaction configurations in graphene, highlighting their physical equivalence under certain conditions.

Findings

Gauge transformations relate different spin-orbit Hamiltonians in graphene.

Physical models can be transformed while preserving energy levels.

Connections between free particle, Rashba, and other interactions are established.

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 in general 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.