Persistent currents due to point obstacles

We discuss properties of the two-dimensional Landau Hamiltonian perturbed by a family of identical $\delta$ potentials arranged equidistantly along a closed loop. It is demonstrated that for the loop size exceeding the effective size of the point obstacles and the cyclotronic radius such a system exhibits persistent currents at the bottom of the spectrum. We also show that the effect is sensitive to a small disorder.