Supersymmetric Analysis of the Dirac-Weyl Operator within PT Symmetry

TL;DR

This paper explores the PT-symmetric properties of a two-dimensional Dirac electron system under hyperbolic magnetic fields, employing factorization and polynomial methods to analyze complex potentials and their supersymmetric extensions.

Contribution

It introduces a supersymmetric framework for analyzing the Dirac-Weyl operator with PT symmetry, including new solutions for complex Scarf II potentials and extensions to position-dependent Fermi velocities.

Findings

Solution of Dirac equation with complex Scarf II potential

Development of pseudo-supersymmetric models for effective potentials

Extension of previous work to PT symmetric and real partner potentials

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.