Supersymmetric Analysis of the Dirac-Weyl Operator within PT Symmetry

Abstract: Two dimensional effective Hamiltonian for a massless Dirac electron interacting with a hyperbolic magnetic field is discussed within PT symmetry. Factorization method and polynomial procedures are used to solve Dirac equation for the constant Fermi velocity and the effective potential which is complex Scarf II potential. The more general effective Scarf II potential models are also obtained within pseudo-supersymmetry. Finally, an extension of Panella and Roy's work [12] to the both PT symmetric and real Scarf II partner potentials are given using the position dependent Fermi velocity.