Graphene in complex magnetic fields

TL;DR

This paper derives exact solutions for electrons in graphene under complex magnetic fields using supersymmetric quantum mechanics, revealing unique probability and current behaviors compared to real magnetic fields.

Contribution

It introduces a novel analytical approach to solve the non-hermitian Dirac-Weyl Hamiltonian in complex magnetic fields, with physical interpretations related to strained graphene.

Findings

Exact eigenvalues and eigenfunctions are obtained.

Distinct probability and current density behaviors are observed.

Analogies with non-uniform strained graphene are established.

Abstract

Exact analytic solutions for an electron in graphene interacting with external complex magnetic fields are found. The eigenvalue problem for the non-hermitian Dirac-Weyl Hamiltonian leads to a pair of intertwined Schr{\"o}dinger equations, which are solved by means of supersymmetric quantum mechanics. Making an analogy with the non-uniform strained graphene a prospective physical interpretation for the complex magnetic field is given. The probability and currents densities are explored and some remarkable differences as compared with the real case are observed.