Threshold Perturbations in Current-Carrying Superconducting Bridges with a Finite Length near the Critical Temperature

TL;DR

This paper analyzes how the energy barrier for transitioning to a resistive state in superconducting bridges varies with length near the critical temperature, revealing size-dependent fluctuation effects.

Contribution

It provides a detailed calculation of the threshold perturbation energy in finite-length superconducting bridges near the critical temperature, highlighting size-dependent effects.

Findings

$ ext{δF}_{thr}$ increases as bridge length decreases for $L<\xi$.

$ ext{δF}_{thr}$ saturates for $L extgreater extgreater \xi$.

Minimum $ ext{δF}_{thr}$ at $L extasciitilde 2-3 \xi$ for certain geometries.

Abstract

Near the critical temperature of a superconducting transition, the energy of the threshold perturbation $\delta F_{thr}$ that transfers a superconducting bridge to a resistive state at a current below the critical current $I_c$ has been determined. It has been shown that $\delta F_{thr}$ increases with a decrease in the length of a bridge for short bridges with lengths $L<\xi$ (where $\xi$ is the coherence length) and is saturated for long bridges with $L\gg \xi$. At certain geometrical parameters of banks and bridge, the function $\delta F_{thr}(L)$ at the current $I\to 0$ has a minimum at $L\sim 2-3 \xi$. These results indicate that the effect of fluctuations on Josephson junctions made in the form of short superconducting bridges is reduced and that the effect of fluctuations on bridges with lengths $\sim 2-3 \xi$ is enhanced.