Phase Modulated Thermal Conductance of Josephson Weak Links

Abstract

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 ${\epsilon }_{\text{b}}=\Delta \cos (\varphi /2)$ 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 $\epsilon \simeq (1+D/2)\Delta$ leads to an increase in the thermal conductance as $T$ drops below $T_c$ (for phase differences near $\varphi =\pi$).

4 pages, 3 figures Expanded discussion of boundary conditions for Ricatti amplitudes

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