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

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 a 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 the energy spectrum are obtained and it is 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 a magnetic field is obtained.