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.

Figure 1

(Color online) Joint density of states for two characteristic values of the energy gap.

Figure 2

(Color online) Analytical conductivity spectra for two examples of gapped graphene.

Figure 3

(Color online) Comparison of spectra for graphene antidot lattices and gapped graphene. The energy gaps have been adjusted to fit two particular antidot lattice geometries.

Figure 4

(Color online) Complex conductivity of gapped graphene assuming a broadening of 50 meV.

Figure 5

(Color online) Comparison of spectra with and without excitons for gapped graphene on a ${\text{SiO}}_2$ substrate. The two panels illustrate cases of medium and large band gaps.