Ritus functions for graphene-like systems with magnetic fields generated by first-order intertwining operators

TL;DR

This paper develops a method to construct exact Dirac fermion propagators in graphene-like systems with complex magnetic fields using supersymmetric techniques, expanding the range of solvable magnetic profiles.

Contribution

It introduces a supersymmetric framework to generate and analyze magnetic field profiles for which the fermion propagator can be explicitly obtained in closed form.

Findings

Exact propagator constructed for non-trivial magnetic fields

Propagator expressed in a simple diagonal form in momentum space

Electric charge and current densities derived and compared with other methods

Abstract

In this work, we construct the exact propagator for Dirac fermions in graphene-like systems immersed in external static magnetic fields with non-trivial spatial dependence. Such field profiles are generated within a first-order supersymmetric framework departing from much simpler (seed) magnetic field examples. The propagator is spanned on the basis of the Ritus eigenfunctions, corresponding to the Dirac fermion asymptotic states in the non-trivial magnetic field background which nevertheless admits a simple diagonal form in momentum space. This strategy enlarges the number of magnetic field profiles in which the fermion propagator can be expressed in a closed-form. Electric charge and current densities are found directly from the corresponding propagator and compared against similar findings derived from other methods.