Hysteresis in superconducting short weak links and $\mu$-SQUIDs

TL;DR

This paper improves understanding of thermal hysteresis in Nb-based $$-SQUIDs by refining the hot-spot model with temperature-dependent thermal conductivity, explaining hysteresis disappearance at higher temperatures, and exploring geometric effects.

Contribution

It introduces an enhanced hot-spot model incorporating temperature-dependent thermal conductivity to better match experimental data and analyzes how geometry affects hysteresis in superconducting weak links.

Findings

Better agreement with observed temperature dependence of retrapping current.

Hysteresis disappears above a certain temperature.

Geometry influences the temperature range of hysteresis-free operation.

Abstract

Thermal hysteresis in a micron-size Superconducting Quantum Interference Device ($\mu$-SQUID), with weak links as Josephson junctions, is an obstacle for improving its performance for magnetometery. Following the "hot-spot" model of Skocpol et al. [J. Appl. Phys. {\bf 45}, 4054 (1974)] and by incorporating the temperature dependence of thermal conductivity of superconductor using a linear approximation, we find a much better agreement with the observed temperature dependence of the retrapping current in short superconducting Nb-based weak links and $\mu$-SQUIDs. In addition, using the temperature dependence of the critical current, we find that above a certain temperature hysteresis disappears. We analyze the current-voltage characteristics and the weak link temperature variation in both the hysteretic and non-hysteretic regimes. We also discuss the effect of the weak link geometry in order to widen the temperature range of hysteresis-free operation.