Induced Currents and Aharonov–Bohm Effect in Effective Fermion Models and in Spaces with a Compact Dimension

Abstract

We consider fermion models in 3D- and 5D-space-time with an Aharonov–Bohm potential and a domain wall. Induced current is calculated, which is due to vacuum effects in the topologically nontrivial space-time. Violation of chiral symmetry and appearance of induced current is demonstrated in a simple example of quantum mechanical violation of symmetry in a model of a massless Dirac fermion moving in a background vector field and domain walls as barriers for the electron propagation. The effective Dirac equation for massless electrons modeling monolayer graphene is used. One of the solutions to the problem of describing domain walls in planar systems is reduced to finding exact analytic solutions. In this paper, we consider appearance of induced current in two-fermion model with a compact dimension as a result of vacuum polarization in the field of the external gauge field in the 4 + 1 and the 2 + 1 dimensional models with one type of fermions and with two types of fermions living in the brane and in the bulk. Two different approaches (Kaluza–Klein and Aharonov–Bohm) to the problem of induced current are used. Production of an induced current in a planar model with a thin solenoid is also studied.