Phase Modulated Thermal Conductance of Josephson Weak Links

TL;DR

This paper develops a theoretical model for phase-dependent quasiparticle heat transport in superconducting weak links, highlighting how junction transparency, temperature, and disorder influence thermal conductance and phase modulation effects.

Contribution

It introduces a comprehensive theory linking phase difference to thermal conductance in Josephson weak links, accounting for transparency, temperature, and disorder effects.

Findings

High-transmission links suppress conductance near = due to Andreev bound states.

Low-transmission barriers increase conductance below T_c near = because of resonant scattering.

Thermal conductance is strongly phase-dependent, especially near = and for different transparency regimes.

Abstract

We present a theory for quasiparticle heat transport through superconducting weak links. The thermal conductance depends on the phase difference ($\phi$) 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 $\epsilon_{\text{\tiny b}}=\Delta\cos(\phi/2)$ leads to suppression of the density of states for the continuum excitations that transport heat, and thus, to a reduction in the conductance for $\phi\simeq\pi$. 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 $\phi=\pi$).