Effective Properties of Graphene with Large Periodic Anti-dots

Antidot graphene is an interesting material system which can exhibit a bandgap. In this work we present the effective properties of graphene with large periodic anti-dots, obtained by solving the Weyl equation numerically, as well as through the k dot p theory calculation. We find the dispersion relation to be hyperbolic in character, leading to an effective mass m* with an altered Fermi velocity v$_{\mathrm{eff}}$ as compared to the pristine case. The gap is exactly given by 2m*c$^{\mathrm{2}}$, where c is the speed of light. The dependence of m* and v$_{\mathrm{eff}}$ on geometric parameters is investigated. A remarkable enhancement of the Coulomb interaction parameter is seen in the antidot graphene, in the region close to the bottom of the band. This can explain the appearance of a Coulomb quasi-gap discovered recently in this material system.