An Empirical Integer-Based Scaling Law for Predicting Superconductivity

Predicting which materials superconduct remains a central unsolved problem in condensed-matter physics, partly because there is no single, widely applicable descriptor analogous to band structure that cleanly separates superconductors from non-superconductors. Motivated by the practical value of historical empirical rules (for example, the Wiedemann-Franz relation for metals), we introduce a real-space, data-driven classifier that requires only elemental composition and atomic coordinates. By computing local potential energies and normalizing electrostatic interactions within repeating bond units by unit-cell volume, we obtain an integer-valued metric that discriminates superconductors from non-superconductors with high fidelity. Computationally inexpensive and physically transparent, our method complements conventional theories and serves as an empirical discovery tool to prioritize candidate materials.