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Thin superconducting films form a unique platform for geometrically-confined,strongly-interacting electrons. They allow an inherent competition betweendisorder and superconductivity, which in turn enables the intriguingsuperconducting-to-insulator transition and believed to facilitate thecomprehension of high-Tc superconductivity. Furthermore, understanding thinfilm superconductivity is technologically essential e.g. for photo-detectors,and quantum-computers. Consequently, the absence of an established universalrelationships between critical temperature ($T_c$), film thickness ($d$) andsheet resistance ($R_s$) hinders both our understanding of the onset of thesuperconductivity and the development of miniaturised superconducting devices.We report that in thin films, superconductivity scales as $d^.$$T_c(R_s)$. Wedemonstrated this scaling by analysing the data published over the past 46years for different materials (and facilitated this database for furtheranalysis). Moreover, we experimentally confirmed the discovered scaling for NbNfilms, quantified it with a power law, explored its possible origin anddemonstrated its usefulness for superconducting film-based devices.

Universal scaling of the critical temperature for thin films near the superconducting-to-insulating transition