Thermal expansion of Josephson junctions as an elastic response to an effective stress field

TL;DR

This paper introduces a novel concept of thermal expansion in Josephson junctions as an elastic response to stress, analyzing its dependence on temperature and magnetic field through analytical and numerical methods.

Contribution

It presents the first detailed study of thermal expansion in Josephson junctions as an elastic response, including analytical and numerical analysis of flux-driven oscillations.

Findings

TE coefficient exhibits field oscillations due to Fraunhofer dependence

Strong flux-driven temperature oscillations occur near T_C in small junctions

Array response shows temperature oscillations under strong magnetic fields

Abstract

By introducing a concept of thermal expansion (TE) of a Josephson junction as an elastic response to an effective stress field, we study (both analytically and numerically) the temperature and magnetic field dependence of TE coefficient $\alpha $ in a single small junction and in a square array. In particular, we found that in addition to {\it field} oscillations due to Fraunhofer-like dependence of the critical current, $\alpha $ of a small single junction also exhibits strong flux driven {\it temperature} oscillations near $T_C$. We also numerically simulated stress induced response of a closed loop with finite self-inductance (a prototype of an array) and found that $\alpha $ of a $5\times 5$ array may still exhibit temperature oscillations provided the applied magnetic field is strong enough to compensate for the screening induced effects.