Phase Modulated Thermal Conductance of Josephson Weak Links

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We present a theory for quasiparticle heat transport through superconducting weak links. The thermal conductance depends on the phase difference (ϕ) 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 phase modulation of the conductance are reported. For high-transmission weak links, D→ 1, the formation of an Andreev bound state at ε b=Δ(ϕ/2) leads to suppression of the density of states for the continuum excitations that transport heat, and thus, to a reduction in the conductance for ϕ≃π. For low-transmission (D≪ 1) barriers resonant scattering at energies ε≃(1+D/2)Δ leads to an increase in the thermal conductance as T drops below Tc (for phase differences near ϕ=π).