Spin and pseudospin in monolayer graphene: Part I. Representation by geometric algebra and simple cases

Properties of spin and pseudospin in monolayer graphene are investigated in terms of geometric algebra (GA). Specifically, Cl algebra that describes Minkowski relativistic spacetime is used for this purpose. Influence of exchange and spin–orbit (SO) interactions on spin and pseudospin are discussed in detail. It is shown how the eigenvalue problem can be depicted by GA rotors in 3D Euclidean space and solved geometrically. In this first part, the connection between Cl algebra and the Hilbert space formulation is established and spin/pseudospin properties in the presence of either exchange or SO interaction are studied. In the second part (2015 Phys. Scr. 90 025808) the effect of simultaneous action of both SO and exchange interactions on spin, pseudospin and Berry phase will be considered within the framework of GA.