Envelope-Function-Based Transport Simulation of a Graphene Ribbon with an Antidot Lattice

We have performed numerical simulations to study the effect of a regular lattice of antidots on the conductance, and in particular on the gap, of an armchair graphene ribbon. We have used an envelope-function approach, with a nonzero mass term mimicking the presence of the antidots. With a very efficient simulation procedure, consisting in a reciprocal space solution of the envelope-function equation in the transverse direction followed by a recursive scattering matrix calculation in the transport direction, we have been able to analyze the impact of the different geometrical parameters characterizing the structure. We have observed that the conductance of the device rapidly reaches an asymptotic value when the length of the region containing the antidot lattice is increased. The dependence of the energy gap on the geometrical features of the antidot lattice is quite similar to that observed in unconfined graphene, excluding the cases of very small or distant antidots, for which the energy gap of the pristine graphene ribbons is recovered. The tilt angle of the lattice with respect to the transport direction has a negligible influence on the gap, which is also quite robust with respect to the introduction of disorder in the antidot lattice.