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(T)(N) 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.