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

TL;DR

This paper investigates the Dirac-Weyl equation on a hyperbolic graphene surface under magnetic fields, deriving analytical solutions for certain cases and analyzing zero-energy states and degeneracy.

Contribution

It introduces a novel approach to solving the Dirac-Weyl equation on hyperbolic surfaces using restriction from ambient space, avoiding tetrads, and applies the factorization method.

Findings

Eigenvalues and eigenfunctions for specific magnetic fields are obtained.

Existence and degeneracy of zero-energy ground states are analyzed.

The results relate to the Aharonov-Casher theorem for flat graphene.

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.