Dirac-Weyl equation on a hyperbolic graphene surface under perpendicular magnetic fields

Abstract

In this paper the Dirac-Weyl equation on a hyperbolic surface of graphene under magnetic fields is considered. In order to solve this equation analytically for some cases, we will deal with vector potentials symmetric under rotations around the z axis. Instead of using tetrads we will get this equation from a more intuitive point of view by restriction from the Dirac-Weyl equation of an ambient space. The eigenvalues and corresponding eigenfunctions for some magnetic fields are found by means of the factorization method. The existence of a zero energy ground level and its degeneracy is also analysed in relation to the Aharonov-Casher theorem valid for flat graphene.

arXiv comment15 pages, 5 figures

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• Graphene Dirac fermions in symmetric electric and magnetic fields: the case of an electric square well
• The solutions of Dirac equation on the hyperboloid under perpendicular magnetic fields
• Dirac-like Hamiltonians associated to Schrödinger factorizations
• Dirac systems with magnetic field and position dependent mass: Darboux transformations and equivalence with generalized Dirac oscillators