Orateur
Description
Mixed-order phase transitions, which combine abrupt phase switching with critical behavior, are uncommon in condensed-matter systems. Here, we demonstrate a mixed-order normal metal to superconductor transition in a single two-dimensional disordered superconducting network, driven by the interplay of two types of interactions: local electrical connectivity and long-range thermally mediated coupling generated by self-heating. Transport measurements reveal an abrupt, hysteretic transition that coexists with critical scaling exponents near the transition. Time-dependent measurements during the non-stationary abrupt transition further uncover a long-lived metastable resistance plateau, whose lifetime increases sharply as the bias current approaches the critical value. Scanning SQUID current imaging directly distinguishes the underlying current-flow morphologies: at low bias current, the transition is continuous and evolves through a complex percolative network of current paths, whereas at high bias current, the transition is abrupt and the current distribution changes discontinuously between normal and superconducting states. By fabricating otherwise identical networks on substrates with strongly different thermal conductivities, we show that the onset and strength of the abrupt transition are tunable, confirming the key role of thermal diffusion and heat retention. These results establish electro-thermal coupling as a practical route to engineer mixed-order criticality in single-layer superconducting networks.