Electric field dependence of thermal conductivity of a granular superconductor: Giant field-induced effects predicted

The temperature and electric field dependence of electronic contribution to the thermal conductivity (TC) of a granular superconductor is considered within a 3D model of inductive Josephson junction arrays. In addition to a low-temperature maximum of zero-field TC $\kappa (T,0)$ (controlled by mutual inductance $L_0$ and normal state resistivity $R_n$), the model predicts two major effects in applied electric field: (i) decrease of the linear TC, and (ii) giant enhancement of the nonlinear (i.e. $\nabla T$-dependent) TC with $\Delta \kappa (T,E)/\kappa (T,0)$ reaching $500\%$ for parallel electric fields $E\simeq E_T$ ($E_T=S_0|\nabla T|$ is an «intrinsic» thermoelectric field). A possiblity of experimental observation of the predicted effects in granular superconductors is discussed.