Non-Linear and Non-Local Meissner Effect in Superconducting Wires

The structure of the Meissner effect in a current-carrying cylindrical wire with arbitrary disorder is studied using a numerical procedure that is exact within the semiclassical approximation. A distribution of currents is found that is non-monotonous as a function of the radial coordinate. For high currents, a robust gapless superconducting state develops at the surface of both clean and dirty leads. Our calculation provides a quantitative theory of the critical current in realistic wires.