Abstract
We show that for graphene with any finite difference in the on-site energy between the two sub-lattices (), The optical absorption edge is determined by the . The universal conductance will be broken and the conductance near the band edge varies with frequency as . Moreover, we have identified another universal conductance for such systems without inversion symmetry, i.e., the onset conductance at the band edge is , independent of the size of the band gap. The total integrated optical response is nearly conserved despite of the opening of the band gap.
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