Charge transport gap in graphene antidot lattices

Graphene antidot lattices (GALs) offer an attractive approach to band-gap engineering in graphene. Theoretical studies indicate that the size of the opened gap is sensitive to the shape, size, and architecture of the nanoholes introduced into the graphene sheet. We have investigated the temperature-dependent electrical conductivity of GALs comprising 50-nm-diameter nanoholes with a pitch of 80, 100, and 200 nm, respectively. The data reveal the presence of localized states within a transport gap, whose interactions lead to a soft Coulomb gap and associated Efros-Shklovskii variable range hopping (ES-VRH). This conduction type is preserved upon application of magnetic fields up to 1 Tesla, above which a transition to Mott variable range hopping occurs. Such a crossover can alternatively be introduced at zero magnetic fields by increasing either the nanohole spacing or the gate-controlled carrier concentration. Furthermore, at intermediate magnetic fields, the hopping exponent assumes a value of 2/3, as predicted by percolation theory for ES-VRH under this condition.