Current-carrying states in FFLO superconductors

We show that nonuniform superconductors of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type conduct electric current in the way which is very different from the usual case. We discuss both equilibrium and nonequilibrium properties using a modified Ginzburg-Landau formalism. Among the novel features are the existence of two different critical currents and two distinct stable states able to carry a given current, the possibility of superconducting domain walls, and also a spontaneous supercurrent in a ring geometry.