Persistent current in a thin superconducting wire

TL;DR

This paper derives an exact formula for persistent current in thin superconducting wires, analyzing the effects of phase slips and the transition to non-superconducting states in long wires.

Contribution

It introduces a nonlinear integral equation approach to precisely calculate persistent currents, especially in strongly interacting regimes where perturbation theory fails.

Findings

Persistent current diminishes exponentially in long wires.

Phase slips potentially destroy superconductivity below BKT transition.

Exact results are obtained due to integrability of the model.

Abstract

In this paper, we explore the persistent current in thin superconducting wires and accurately examine the effects of the phase slips on that current. The main result of the paper is the formula for persistent current in terms of the solutions of certain (nonlinear) integral equation. This equation allows to find asymptotics of the current at long(small) length of the wire, in that paper, we interested in the region in which the system becomes strongly interacting and very few amounts of information can be extracted by perturbation theory. Nevertheless, due to the integrability, exact results for the current can be obtained. We observe that at the limit of a long wire, the current becomes exponentially small, we believe that it is the signal that phase slips may destroy superconductivity for long wires, below BKT phase transition.