Efficient numerical method to study the transport behavior of a graphene armchair nanoribbon in the presence of a generical potential using an envelope function approach

We describe the numerical method we have developed to efficiently study transport in armchair graphene nanoribbons in the presence of an external potential using an approach based on the solution of the Dirac equation. The original problem with the exact boundary conditions is recasted in an equivalent problem with periodic boundary conditions and a solution in the Fourier space. Applying this technique inside each slice with a longitudinally constant potential and then using a scattering matrix approach, we can obtain the transmission of the device in the presence of a generical potential.