ANALYTIC STUDY OF FERMIONS IN GRAPHENE; HEUN FUNCTIONS AND BEYOND

Starting with the wave function characterizing massless fermions evolving in orthogonal electric and magnetic fields, written in terms of Heun Biconfluent functions, we analyse some physically interesting cases. When the HeunB function truncates to a polynomial form, one may easily compute the essential components of the conserved current density. For a vanishing electric field, we get the familiar Hermite associated functions and discuss the current dependence on the sample width. In the opposite case, corresponding to an electric static field alone, one has to deal with HeunB functions of complex variable and parameters.