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 K(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., grad T-dependent) TC with [K(T,E)-K(T,0)]/K(T,0) reaching 500% for parallel electric fields E=E_T (E_T=S_0|grad T| is an "intrinsic" thermoelectric field). A possiblity of experimental observation of the predicted effects in granular superconductors is discussed. 
Sergei Sergeenkov