Spectrally isomorphic Dirac systems: graphene in electromagnetic field

TL;DR

This paper introduces new one-dimensional Dirac Hamiltonians that are spectrally isomorphic to known models, providing explicit spectra and eigenstates, and applies them to describe graphene under inhomogeneous electromagnetic fields.

Contribution

The authors construct spectrally isomorphic Dirac Hamiltonians and demonstrate their application to modeling graphene in complex electromagnetic environments.

Findings

Explicit formulas for spectra and eigenstates of new Dirac Hamiltonians.

Examples of spectrally isomorphic systems with periodic and non-periodic barriers.

Application to Dirac fermions in graphene with electromagnetic fields.

Abstract

We construct the new one-dimensional Dirac Hamiltonians that are spectrally isomorphic (not isospectral) with the known exactly solvable models. Explicit formulas for their spectra and eigenstates are provided. The operators are utilized for description of Dirac fermions in graphene in presence of an inhomogeneous electromagnetic field. We discuss explicit, physically relevant, examples of spectrally isomorphic systems with both non-periodic and periodic electromagnetic barriers. In the latter case, spectrally isomorphic two- and three-gap systems associated with the Ablowitz-Kaup-Newell-Segur hierarchy are considered.