Introduction

Having studied a prototype model Hamiltonian in one-dimensional (1D), we turn our focus towards two-dimensional (2D), now with the lens on graphene. Particularly, we shall explore whether graphene possesses the credibility of becoming a topological insulator. That may happen, provided by some means, we are able to open a spectral gap at the Dirac cones. Since a non-zero Berry phase can be a smoking gun for non-trivial properties, let us first look at the Berry phase of graphene.