Spectrally isomorphic Dirac systems: graphene in electromagnetic field

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.

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• Bound states of the two-dimensional Dirac equation for an energy-dependent hyperbolic Scarf potential
• Coherent states for graphene under the interaction of crossed electric and magnetic fields
• Darboux partners of Heun-class potentials for the two-dimensional massless Dirac equation
• A New Class of Solvable Two-dimensional Scalar Potentials for Graphene
• Solvable Two-dimensional Dirac Equation with Matrix Potential: Graphene in External Electromagnetic Field