Graphene and Relativistic Quantum Physics

The honeycomb lattice structure of graphene requires an additional degree of freedom, termed as pseudo spin, to describe the orbital wave functions sitting in two different sublattices of the honeycomb lattice. In the low energy spectrum of graphene near the charge neutrality point, where the linear carrier dispersion mimics the quasi-relativistic dispersion relation, pseudo spin replaces the role of real spin in the usual Dirac Fermion spectrum. The exotic quantum transport behavior discovered in graphene, such as the unusual half-integer quantum Hall effect and Klein tunneling effect, are a direct consequence of the pseudo spin rotation. In this chapter we will discuss the non-trivial Berry phase arising from the pseudo spin rotation in monolayer graphene under a magnetic field and its experimental consequences.