Induced Current and Aharonov-Bohm Effect in Graphene

TL;DR

This paper investigates the vacuum polarization effects, specifically the induced current, in graphene subjected to a magnetic flux from an infinitesimally thin solenoid, revealing a periodic dependence on the flux with zero current at certain flux values.

Contribution

It provides an exact expression for the induced current as a periodic function of magnetic flux in graphene, highlighting the effects of vacuum polarization and the Aharonov-Bohm effect.

Findings

Induced charge density is zero.

Induced current is a finite periodic function of magnetic flux.

Current vanishes at integer and half-integer flux ratios.

Abstract

The effect of vacuum polarization in the field of an infinitesimally thin solenoid at distances much larger than the radius of solenoid is investigated. The induced charge density and induced current are calculated. Though the induced charge density turned out to be zero, the induced current is finite periodical function of the magnetic flux $\Phi$. The expression for this function is found exactly in a value of the flux. The induced current is equal to zero at the integer values of $\Phi/\Phi_0$ as well as at half-integer values of this ratio, where $\Phi_0=2\pi\hbar c/e$ is the elementary magnetic flux. The latter is a consequence of the Furry theorem and periodicity of the induced current with respect to magnetic flux. As an example we consider the graphene in the field of solenoid perpendicular to the plane of a sample.