# Distinct Spatiotemporal Dynamics of Thermoelectric Transport Across Superconducting Transition

## TL;DR

This paper explores how heat transport dynamics change across the superconducting transition, revealing distinct linear and nonlinear relaxation behaviors above and below Tc with implications for experimental probing.

## Contribution

It introduces two classes of relaxation diffusion equations capturing the fundamental shift in heat transport mechanisms across the superconducting transition.

## Key findings

- Type I relaxation leads to uniform heat current above Tc.
- Type II relaxation shows inhomogeneous, propagating hot spots below Tc.
- Distinct dynamics highlight a fundamental change in transport across the transition.

## Abstract

We investigate the relaxation dynamics of heat transport in superconductors, shaped by the interplay of diffusion, nonlinearity, and magnetic fields. Focusing on regimes near the critical temperature Tc, we analyze two classes of relaxation diffusion equations that give rise to qualitatively distinct dynamics, which we denote as Type I (linear) and Type II (nonlinear). Type I relaxation, characteristic of the normal state above Tc, results in a steady and spatially uniform heat current governed by linear diffusion. By contrast, Type II relaxation, relevant below Tc, exhibits non steady dynamics marked by pronounced spatial inhomogeneities and an evolving pattern, in which an initially localized hot spot propagates transiently through the system. The striking distinction between these regimes underscores a fundamental shift in transport mechanisms across the superconducting phase transition and provides experimentally relevant predictions in light of emerging techniques for probing local dissipation.