Optical response and excitons in gapped graphene

Graphene can be rendered semiconducting via energy gaps introduced in a variety of ways, e.g., coupling to substrates, electrical biasing, or nanostructuring. To describe and compare different realizations of gapped graphene we propose a simple two-band model in which a ``mass'' term is responsible for the gap. The optical conductivity predicted for this model is obtained as a simple closed-form expression. In addition, analytical estimates for the binding energy of excitons are derived and the impact of excitons on the optical response is analyzed.