Analysis of transport in a graphene ribbon with an antidot lattice, based on the scattering matrix solution of the Dirac equation

We have performed a simplified numerical simulation of the transport properties of a graphene ribbon with an antidot lattice. We have used an envelope function model for graphene, in which a space-dependent mass term approximately reproduces the effect of the regions of the ribbon where the carbon atoms are absent. The envelope function equation has been solved in proper subregions of the ribbon and then the results have been composed using a scattering matrix approach. Our simulator has been used to study the dependence of the energy gap and of the conductance of the ribbon on the different geometrical parameters of the antidot lattice, such as the size of the antidots, the distance between them and the tilt angle of the antidot lattice.