Universal Correlation between Critical Temperature of Superconductivity and band structure features

The critical temperature (${T}_\text{c}$) of superconductors varies a lot. The factors governing the ${T}_\text{c}$ may hold key clues to understand the nature of the superconductivity. Thereby, ${T}_\text{c}$-involved correlations, such as Matthias laws, Uemura law, and cuprates doping phase diagrams, have been of great concern. However, the electronic interaction being responsible for the carriers pairing in high-${T}_\text{c}$ superconductors is still not clear, which calls for more comprehensive analyses of the experimental data in history. In this work, we propose a novel perspective for searching material gene parameters and ${T}_\text{c}$-involved correlations. By exploring holistic band structure features of diverse superconductors, we found a universal correlation between the ${T}_\text{c}$ maxima and the electron energy levels for all kinds of superconducting materials. It suggests that the ${T}_\text{c}$ maxima are determined by the energy level of secondary-outer orbitals, rather than the band structure nearby the Fermi level. The energy level of secondary-outer orbitals is a parameter corresponding to the ratio of atomic orbital hybridization, implying that the fluctuation of the orbital hybridization is another candidate of pairing glue.