Bound states in inhomogeneous magnetic field in graphene: a semiclassical approach

摘要

We derive semiclassical quantization equations for graphene mono- and bilayersystems where the excitations are confined by the applied inhomogeneousmagnetic field. The importance of a semiclassical phase, a consequence of thespinor nature of the excitations, is pointed out. The semiclassicaleigenenergies show good agreement with the results of quantum mechanicalcalculations based on the Dirac equation of graphene and with numerical tightbinding calculations.