Induced current and Aharonov-Bohm effect in graphene

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 a finite periodical function of the magnetic flux $\ensuremath{\Phi}$. 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 $\ensuremath{\Phi}/{\ensuremath{\Phi}}_{0}$ as well as at half-integer values of this ratio, where ${\ensuremath{\Phi}}_{0}=2\ensuremath{\pi}\ensuremath{\hbar}c/e$ 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.