Thermal expansion of granular superconductors based on elastic response of Josephson junction arrays

We introduce the concept of thermal expansion (TE) in Josephson systems as an elastic response to an effective stress field. The temperature and magnetic field dependences of TE coefficient can be studied both analytically and numerically in a single junction and in a square array of Josephson junctions (JJA). We found that in addition to field oscillations due to Fraunhofer-type dependence of the critical current, both single junction and JJAs may exhibit flux driven temperature oscillations of the TE coefficient near Tc provided the applied magnetic field is strong enough to compensate for the screening-induced effects. We briefly discuss possible consequences of TE coefficient temperature oscillations for the local penetration of magnetic field in granular systems modelled as JJAs