Thermal Conductance of Andreev Interferometers

We calculate the thermal conductance G^T of diffusive Andreev interferometers, which are hybrid loops with one superconducting arm and one normal-metal arm. The presence of the superconductor suppresses G^T; however, unlike a conventional superconductor, G^T/G_N^T does not vanish as the temperature T→0, but saturates at a finite value that depends on the resistance of the normal-superconducting interfaces, and their distance from the path of the temperature gradient. The reduction of G^T is determined primarily by the suppression of the density of states in the proximity-coupled normal metal along the path of the temperature gradient. G^T is also a strongly nonlinear function of the thermal current, as found in recent experiments.