# Mesoscopic effects in the heat conductance of superconducting-normal-superconducting and normal-superconducting junctions

## TL;DR

This paper investigates how superconducting gaps and phases affect heat conductance in hybrid junctions, revealing universal fluctuation behaviors and a generalized Wiedemann-Franz law in specific conditions.

## Contribution

It provides a detailed analysis of heat conductance in mesoscopic superconducting junctions, highlighting the persistence of phase effects in fluctuations and establishing a generalized Wiedemann-Franz law.

## Key findings

- Superconducting gaps and phases influence heat conductance in single-channel and diffusive junctions.
- Heat conductance fluctuations exhibit near-universal behavior despite deviations in average properties.
- A generalized Wiedemann-Franz law is derived for Josephson junctions with equal gaps and zero phase difference.

## Abstract

We study the heat conductance of hybrid superconducting junctions. Our analysis involves single-channel junctions with arbitrary transmission as well as diffusive connectors and shows the influence of the superconducting gaps and phases of the contacts on the heat conductance. If the junction is diffusive, these effects are completely quenched on average, however, we find that their influence persists in weak-localization corrections and conductance fluctuations. While these statistical properties strongly deviate from the well-known analogues for the charge conductance, we demonstrate that the heat conductance fluctuations maintain a close to universal behavior. We find a generalized Wiedemann-Franz law for Josephson junctions with equal gaps and vanishing phase difference.