Universal correlation of the superconducting transition temperature with the linear-in-T coefficient, electron packing parameter, and the numbers of valence and conduction electrons.

Abstract

A generic conductivity equation, developed in our previous work, is used to predict the universal superconducting transition temperature, Tc. Our prediction shows that Tc and the linear-in-T scattering coefficient, A1, have a scaling relationship of Tc ∼ A10.5, where A1 comes from the empirical experimental equation ρ = ρ0 + A1T with ρ as the resistivity, which is consistent with recent experimental observations. However, our theory suggests that 1/ρ has a linear relationship with 1/T, rather than the empirical relationship between ρ and T postulated in the literature. The physical meaning of A1 is made clear by the equations, and it is related to the electron packing parameter, α, the number of valence electrons per unit cell, the number of conduction electrons in the entire system, and the volume of the material under study, among others. In general, Tc increases with α and the number of valence electrons per unit cell, but decreases sharply with the number of conduction electrons. A ridge appears when α is around 30, suggesting that Tc may reach a maximum at this point. Our findings not only provide theoretical support for recent experimental observations but also offer insight into achieving high Tc by fine-tuning material properties and have broader implications for understanding superconductivity in a universal manner.