Phase Modulated Thermal Conductance of Josephson Weak Links

We present a theory for quasiparticle heat transport through superconducting weak links. The thermal conductance depends on the phase difference ([Formula presented]) of the superconducting leads. Branch-conversion processes, low-energy Andreev bound states near the contact, and the suppression of the local density of states near the gap edge are related to phase-sensitive transport processes. Theoretical results for the influence of junction transparency, temperature, and disorder, on the conductance, are reported. For high-transmission weak links, [Formula presented], the formation of an Andreev bound state leads to suppression of the density of states for the continuum excitations, and thus, to a reduction in the conductance for [Formula presented]. For low-transmission ([Formula presented]) barriers resonant scattering leads to an increase in the thermal conductance as [Formula presented] drops below [Formula presented] (for phase differences near [Formula presented]).