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

TL;DR

This paper investigates the behavior of induced currents in a (2+1)-dimensional Dirac system with a small-radius magnetic flux tube, revealing universal flux-dependent current characteristics relevant to graphene.

Contribution

It provides a detailed analysis of the induced current in the limit of a small magnetic flux tube radius, showing universal behavior independent of internal magnetic field distribution.

Findings

Induced current is an odd periodic function of magnetic flux when electrons cannot penetrate the flux region.

If electrons can penetrate, the current is not periodic in flux.

In the limit of zero radius, the current's form becomes universal, independent of flux distribution.

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.