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

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 cannot 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 -> 0, where R is the radius of the 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.