Persistent currents for Coulomb interacting electrons on 2d disordered lattices - Sign and interaction dependence in the Wigner crystal regime

A Wigner crystal structure of the electronic ground state is induced by str ong Coulomb interactions at low temperature in clean or disordered two-dime nsional (2d) samples. For fermions on a mesoscopic disordered 2d lattice, b eing closed to a torus, we study the persistent current in the regime of st rong interaction at zero temperature. We perform a perturbation expansion s tarting from the Wigner crystal limit which yields power laws for the depen dence of the persistent current on the interaction strength. The sign of th e persistent current in the strong interaction Emit is independent of the d isorder realization and strength. It depends only on the electro-statically determined configuration of the particles in the Wigner crystal.