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 ($\varphi$) 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, $D\to 1$, the formation of an Andreev bound state at ${ϵ}_{\text{b}}=\mathrm{\Delta }\cos (\varphi \mathrm{/}2)$ leads to suppression of the density of states for the continuum excitations that transport heat, and thus, to a reduction in the conductance for $\varphi \simeq \pi$. For low-transmission ($D\ll 1$) barriers resonant scattering at energies $ϵ\simeq (1+D\mathrm{/}2)\mathrm{\Delta }$ leads to an increase in the thermal conductance as $T$ drops below $T_c$ (for phase differences near $\varphi =\pi$).