Tight-binding description of patterned graphene

The existence of an energy gap of graphene is vital as far as nano-electronic applications such as nano-transistors are concerned. In this paper, we present a method for introducing arbitrary energy gaps through breaking the symmetry point group of graphene. We investigate the tight-binding approximation for the dispersion of π and π* electronic bands in patterned graphene including up to five nearest neighbors. As we show by applying special …