Graphene under the influence of Aharonov-Bohm flux and constant magnetic field

TL;DR

This paper studies the effects of combined homogeneous magnetic fields and Aharonov-Bohm vortices on graphene's electronic properties, revealing impurity-like behavior and calculating associated vacuum and electric currents.

Contribution

It introduces a model of graphene under combined magnetic influences, deriving wave functions, energy spectra, and current properties, highlighting the vortex's role as a charge impurity.

Findings

Aharonov-Bohm vortex acts as a charge impurity in graphene.

Derived electronic wave functions and energy spectra for the combined magnetic field.

Calculated vacuum and electric currents in specific magnetic field configurations.

Abstract

Investigation of real two-dimensional systems with Dirac-like electronic behavior under the influence of magnetic field is challenging and leads to many interesting physical results. In this paper we study 2D graphene model with a particular form of magnetic field as a superposition of a homogeneous field and an Aharonov-Bohm vortex. For this configuration, electronic wave functions and energy spectrum were obtained and it was shown that the magnetic Aharonov-Bohm vortex plays the role of a charge impurity. As a demonstration of vacuum properties of the system, vacuum current, as well as an electric current, is calculated and their representation for particular limiting cases of magnetic field is obtained.