Abstract
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 bilayer grapheme and also its edge states by using this model with analytical approach. The results of our calculation show that the gap opening occurs at K and K’ point in bilayer graphene.In addition, a pair of gapless edge modes occurs both in the zigzag and arm-chair configurations are no longer exist. There are gap created at the edge even though thery are very small.
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