Effective medium model for graphene superlattices with electrostatic and magnetic vector potentials

In this article we develop an effective medium model to characterize the electron wave propagation in graphene based nanostructures with electrostatic and magnetic vector potentials imposed on their surface. We use a numerical algorithm determine parameters of heterostructure calculate electronic band structure system. apply our formalism analyze superlattices solely potential reveal that response remains reciprocal is characterized by decrease velocity charge carriers. also study both superimposed show system becomes nonreciprocal dispersion tilted Dirac cone. demonstrate it possible alternate between type-I, type-II, or type-III cones properly tuning amplitude potentials.