Influence of the boundary conditions on the current flow pattern along a superconducting wire

TL;DR

This paper investigates how different boundary conditions affect current flow patterns in a 1D superconducting wire near the critical temperature, revealing complex regimes and the conditions for stationary states.

Contribution

It provides a detailed analysis of current flow patterns under various boundary conditions, highlighting the existence of multiple periodic regimes and the impact of contact types.

Findings

Superconducting contacts prevent stationary regimes, which can only be approached asymptotically.

Weak superconducting contacts lead to multiple periodic regimes with phase slip centers.

Normal contacts allow for stable stationary current flow.

Abstract

We study the patterns at which the current flow stabilizes in a 1D superconducting wire, for various experimentally reasonable boundary conditions, for small fixed current densities and temperatures close to $T_c$. We pay special attention to the possible existence of a stationary regime. If the contacts are superconducting, truly stationary or normal regimes do not exist, but can be approached as a limit. In the case of weak superconducting contacts, a rich phase diagram is found, with several periodic regimes that involve two phase slip centers. For some of these regimes, the density of Cooper pairs does not have mirror symmetry. If the contacts are normal, the stationary regime is possible.