Spin and pseudospin in monolayer graphene: Part II. Competition between exchange and spin–orbit interactions

Abstract

Spin and pseudospin properties of monolayer graphene, when both the exchange and extrinsic spin–orbit (SO) interactions are taken into account, are analyzed within a framework of geometric algebra. The rotor equations for even and odd parts of electron bispinor are constructed in three-dimensional (3D) Euclidean space thus providing clear geometrical interpretation to the problem. It is shown that in the presence of combined action of exchange and SO interactions the spin and pseudospin fields in a monolayer graphene from two-dimensional become 3D, with spin and pseudospin components pointing out of the graphene plane. Also, the effect of both interactions on the Berry phase is considered analytically.