Distinct Spatiotemporal Dynamics of Thermoelectric Transport Across Superconducting 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 T c , 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 T c , results in a steady and spatially uniform heat current governed by linear diffusion. By contrast, Type-II relaxation, relevant below T c , 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.