Bound states in inhomogeneous magnetic field in graphene: Semiclassical approach

Abstract

We derive semiclassical quantization equations for graphene monolayer and bilayer systems where the excitations are confined by the applied inhomogeneous magnetic field. The importance of a semiclassical phase, a consequence of the spinor nature of the excitations, is pointed out. The semiclassical eigenenergies show good agreement with the results of quantum-mechanical calculations based on the Dirac equation of graphene and with numerical tight-binding calculations.