Onset of superconductivity in a voltage-biased NSN microbridge

TL;DR

This paper investigates the conditions under which superconductivity emerges in a voltage-biased mesoscopic NSN junction, revealing how bias voltage and relaxation mechanisms influence the stability of the normal state and the formation of superconducting states.

Contribution

It introduces a detailed analysis of the instability line V_{inst}(T) in NSN junctions using the linearized time-dependent Ginzburg-Landau equation, highlighting the impact of bias voltage and relaxation mechanisms.

Findings

Superconductivity nucleates below the instability line V_{inst}(T).

High biases lead to non-stationary bimodal superconducting states.

The instability line's behavior is sensitive to inelastic relaxation details.

Abstract

We study the stability of the normal state in a mesoscopic NSN junction biased by a constant voltage V with respect to the formation of the superconducting order. Using the linearized time-dependent Ginzburg-Landau equation, we obtain the temperature dependence of the instability line, V_{inst}(T), where nucleation of superconductivity takes place. For sufficiently low biases, a stationary symmetric superconducting state emerges below the instability line. For higher biases, the normal phase is destroyed by the formation of a non-stationary bimodal state with two superconducting nuclei localized near the opposite terminals. The low-temperature and large-voltage behavior of the instability line is highly sensitive to the details of the inelastic relaxation mechanism in the wire. Therefore, experimental studies of V_{inst}(T) in NSN junctions may be used as an effective tool to access parameters of the inelastic relaxation in the normal state.