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

By introducing a concept of thermal expansion (TE) of a Josephson junction as an elastic response to an effective stress field, we studied (both analytically and numerically) the temperature and magnetic field dependences of the TE coefficient alpha in a single small junction and in a square array. In particular, we found that in addition to field oscillations due to Fraunhofer-type dependence of the critical current, alpha of a small single junction also exhibits strong flux driven 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 5x5 array may still exhibit temperature oscillations provided the applied magnetic field is strong enough to compensate for the screening-induced effects.