# Phase-coherent caloritronics with ordinary and topological Josephson junctions

## TL;DR

This paper reviews recent advances in phase-coherent caloritronics involving ordinary and topological Josephson junctions, highlighting experimental breakthroughs and theoretical insights into heat transport phenomena.

## Contribution

It provides a comprehensive overview of phase-dependent thermal conductance in Josephson junctions, including recent experimental and theoretical developments in topological systems.

## Key findings

- Experimental realization of thermal interferometers and modulators
- Observation of phase-dependent heat transport phenomena
- Theoretical predictions of unique heat transport in topological Josephson junctions

## Abstract

We provide a brief and comprehensive overview over recent developments in the field of phase-coherent caloritronics in ordinary and topological Josephson junctions. We start from the simple case of a short, one-dimensional superconductor-normal metal-superconductor (S-N-S) Josephson junction and derive the phase-dependent thermal conductance within the Bogoliubov-de Gennes formalism. Then, we review the key experimental breakthroughs that have triggered the recent growing interest into phase-coherent heat transport. They include the realization of thermal interferometers, diffractors, modulators and routers based on superconducting tunnel junctions. Finally, we discuss very recent theoretical findings based on superconductor-topological insulator-superconductor (S-TI-S) Josephson junctions that show interesting heat transport properties due to the interplay between topological band structures and superconductivity.