Decay of near-critical currents in superconducting nanowires

We consider decay of supercurrent via phase slips in a discrete one-dimensional superconductor (a chain of nodes connected by superconducting links), aiming to explain the experimentally observed power-3/2 scaling of the activation barrier in nanowires at currents close to the critical. We find that, in this discrete model, the power-3/2 scaling holds for both long and short wires even in the presence of bulk superconducting leads, despite the suppression of thermal fluctuations at the ends. We also consider decay via tunneling (quantum phase slips), which becomes important at low temperatures. We find numerically the relevant Euclidean solutions (periodic instantons) and determine the scaling of the tunneling exponent near the critical current. The scaling law is power-5/4, different from that of the thermal activation exponent.