POLYNOMIAL SOLUTIONS OF HEUN EQUATION DESCRIBING FERMIONS IN GRAPHENE

Abstract

The wavefunctions describing the massless fermions evolving in a static magnetic field orthogonal to a radially planar electric field are obtained, as solutions to Dirac equation. In the case of the magnetic field alone, the corresponding HeunB confluent functions turn into the usual Hermite polynomials and the energy spectrum has the familiar form which has been reported for graphene samples. Within a more involved analysis with both electric and magnetic orthogonal static fields, we compute the conserved current density component and the quantized off-diagonal conductivity.