Hysteresis in superconducting short weak links and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>μ</mml:mi></mml:math>-SQUIDs

Abstract

Thermal hysteresis in a micron-size superconducting quantum interference device ($\ensuremath{\mu}$-SQUID), with weak links as Josephson junctions, is an obstacle for improving its performance for magnetometry. Following the ``hot-spot'' model of Skocpol et al. [J. Appl. Phys. 45, 4054 (1974)] and by incorporating the temperature dependence of the superconductor thermal conductivity under 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 $\ensuremath{\mu}$-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 nonhysteretic regimes. We also discuss the effect of the weak link geometry in order to widen the temperature range of hysteresis-free operation.