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

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