The effect of spin-orbit coupling in band structure of few-layer graphene

Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator but have protected conducting states on their edge or surface. This can be happened due to spin-orbit coupling and time-reversal symmetry. Moreover, the edge current flows through their edge or surface depends on its spin orientation and also it is robust against non-magnetic impurities. Therefore, topological insulators are predicted to be useful ranging from spintronics to quantum computation. Graphene was first predicted to be the precursor of topological insulator by Kane-Mele. They developed a Hamiltonian model to describe the gap opening in graphene. In this work, we investigate the band structure of few-layer graphene by using this model with analytical approach. The results of our calculations show that the gap opening occurs at K and K’ point, not only in single layer, but also in bilayer and trilayer graphene.