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