Disorder usually destroys superconductivity. Impurities scatter Cooper pairs, disrupt the lattice periodicity that electrons need to maintain phase coherence, and fragment the delicate quantum state that allows resistance-free current flow. Anderson's theorem says non-magnetic impurities preserve s-wave superconductivity in the weak-disorder limit, but strong disorder or unconventional pairing always degrades performance. The hierarchy is clear: perfect crystal first, imperfect crystal worse.
Slebarski and Maska (arXiv 2602.22448, February 2026) find the opposite in tin-based cage compounds. In Y_{5-x}Ca_xRh_6Sn_{18} and La_{3-x}Ca_xRh_4Sn_{13}, substituting calcium for rare-earth atoms on the cage sites enhances superconductivity. Not marginally — in the lanthanum system, the local critical temperature doubles relative to the bulk. The enhancement is nonmonotonic: it rises with increasing disorder, peaks, then falls when coherence loss finally dominates. But at intermediate concentrations, the dirty material superconducts better than the clean one.
The mechanism is spatial. Each calcium dopant, sitting where a lanthanum or yttrium atom should be, creates a local structural inhomogeneity on the scale of the superconducting coherence length — about 10 to 20 nanometers. Near the dopant, the pairing interaction strengthens. A small region around the impurity becomes superconducting at a temperature T_c* above the bulk transition temperature T_c.
Cool the material below T_c* and these islands appear: disconnected patches of superconductivity floating in a normal-metal matrix. Each island has local phase coherence but no connection to its neighbors. Cool further and the islands grow, overlap, and eventually percolate — establishing long-range coherence at the lower bulk T_c. The upper critical field H_c2(T) shows two distinct branches: one for the islands, one for the connected bulk, with the island branch curving positively in a characteristic signature of percolation.
The picture is an archipelago. Each impurity nucleates its own island. The islands don't communicate until the gaps close. The transition from local to global superconductivity happens through geometry — the percolation threshold — not through uniform strengthening of the pairing interaction across the whole material.
This inverts the usual design principle. In conventional superconductor engineering, you start with the cleanest possible material and carefully introduce dopants to shift the Fermi level or modify the phonon spectrum. The goal is uniform improvement. Here, the improvement is intrinsically non-uniform. The impurities don't make the whole material better — they make small regions much better and rely on connectivity to propagate the enhancement.
The entropy measurements confirm this is a genuine thermodynamic effect, not a surface artifact. The largest entropy maxima coincide with the largest separation between T_c* and T_c, when the gap between island formation and bulk coherence is widest. The disorder functions as a thermodynamic control parameter.
At high disorder concentrations, the mechanism self-destructs. Too many islands fragment the matrix so severely that percolation fails — the archipelago becomes too dense, paradoxically, disrupting the normal-metal channels that carry current between islands. The coherence length shrinks, the percolating pathways break, and both local and bulk superconductivity are suppressed. The optimal point is intermediate: enough islands to enhance, few enough to connect.
The material doesn't conduct despite its disorder. It conducts because of it, up to a point — and the point is set by geometry.