Spontaneous superconducting islands and Hall voltage in superconductors with large electric penetration depth

We study a superconductor in the Hall configuration, in the framework of a purely dissipative time-dependent Ginzburg-Landau model. For electric penetration depths in the range 3.5-10 coherence lengths we find situations in which the order parameter differs significantly from zero in a set of islands that appear to form a periodic structure. When the pattern of islands becomes irregular, it moves in or against the direction of the current and a Hall voltage is found. Tiny differences in the initial state may reverse the sign of the Hall voltage. When the average Hall voltage vanishes, the local Hall voltage does not necessarily vanish. We examine the influence that several boundary conditions at the electrodes have on these effects.