Chiral Fermion Conductivity in Graphene-Like Samples Subjected to Orthogonal Fields

Starting with the U(1)−gauge covariant four-dimensional Dirac equation, we derive the analytic solutions describing the chiral massless fermions evolving in static orthogonal magnetic and electric fields. Working in cylindric coordinates, we compute the electric current density essential component and the off-diagonal conductivities. By summing up the conductivities of the two distinct species of electrons connected to the orientation of spin, the well-known 4n-quantization law is restored.