Rashba spin-orbit interaction enhanced by graphene in-plane deformations

TL;DR

This paper investigates how in-plane deformations of graphene under a perpendicular electric field can significantly enhance Rashba spin-orbit coupling, affecting the electronic band structure near the K points.

Contribution

It introduces a gauge field framework to analyze the impact of uniform stretching on spin-orbit interactions in graphene, revealing a notable enhancement of Rashba coupling.

Findings

Rashba coupling increases by 30-50% with small bond deformations.

Deformation direction influences the band structure modifications.

Accessible changes in electronic properties can be controlled via strain.

Abstract

Graphene consists in a single-layer carbon crystal where 2$p_z$ electrons display a linear dispersion relation in the vicinity of the Fermi level, conveniently described by a massless Dirac equation in $2+1$ spacetime. Spin-orbit effects open a gap in the band structure and offer perspectives for the manipulation of the conducting electrons spin. Ways to manipulate spin-orbit couplings in graphene have been generally assessed by proximity effects to metals that do not compromise the mobility of the unperturbed system and are likely to induce strain in the graphene layer. In this work we explore the $\rm{U(1)}\times SU(2)$ gauge fields that result from the uniform stretching of a graphene sheet under a perpendicular electric field. Considering such deformations is particularly relevant due to the counter-intuitive enhancement of the Rashba coupling between 30-50% for small bond deformations well known from tight-binding and DFT calculations. We report the accessible changes that can be operated in the band structure in the vicinity of the K points as a function of the deformation strength and direction.