Induced current in the presence of magnetic flux tube of small radius

Abstract

The induced current density, corresponding to the massless Dirac equation in (2+1) dimensions in a magnetic flux tube of small radius is considered. This problem is important for graphene. In the case, when an electron can not penetrate the region of nonzero magnetic field, this current is the odd periodical function of the magnetic flux. If the region inside the magnetic tube is not forbidden for penetration of electron, the induced current is not a periodical function of the magnetic flux. However in the limit $R\to 0$, where $R$ is the radius of magnetic flux tube, this function has the universal form which is independent of the magnetic field distribution inside the magnetic tube at fixed value of the magnetic flux.

5 pages, 1 figure

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• Electric Field Effect in Atomically Thin Carbon Films
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• Vacuum polarization of charged massless fermions in Coulomb and Aharonov--Bohm fields
• Finite temperature fermion condensate, charge and current densities in a (2+1)-dimensional conical space
• Graphene under the influence of Aharonov-Bohm flux and constant magnetic field
• Ferromagnetic phase in graphene-based planar heterostructures induced by charged impurity