Rashba coupling and Lifshitz transition in monolayer graphene

TL;DR

This paper explores the effects of Rashba spin-orbit coupling and external electric fields on monolayer and bilayer graphene, analyzing their influence on electronic properties and Lifshitz transitions, with a focus on differences between the two systems.

Contribution

It provides a comparative analysis of Rashba coupling effects in monolayer and bilayer graphene, highlighting the absence of Lifshitz transition features in monolayer graphene under similar conditions.

Findings

Rashba coupling does not induce Lifshitz transition in monolayer graphene.

Trigonal warping and Lifshitz transition are observed in bilayer graphene with interlayer hopping.

No replication of bilayer graphene Lifshitz transition features in monolayer graphene with Rashba coupling.

Abstract

We take a wide-angle view of the problem of monolayer graphene (MLG) where spin-degeneracy lifting is assumed to be possible by wedging in the tunable Rashba spin-orbit coupling(RSOC) and the sub-lattice staggered potential. We next consider the AB-stacked bi-layer graphene (BLG) system (the A-carbon of the upper sheet lying on top of the B-carbon of the lower one) and assume that a perpendicular electric field is created by the external gates deposited on the BLG surface. This system exhibits the occurrence of trigonal warping due to a (skew) interlayer hopping leading to the well-known Lifshitz transition(LT)[Y. Lemonik, I.L. Aleiner, C. Toke, and V.I. Fal'ko; arXiv:1006.1399]. We do not observe the replication of the features associated with BLG-LT in MLG in the presence of RSOC.