Universal correlation of the superconducting transition temperature with the linear-in-T coefficient, electron...

A generic conductivity equation, developed in our previous work, is used to predict the universal superconducting transition temperature, T_c. Our prediction shows that T_c and the linear-in-T scattering coefficient, A₁, have a scaling relationship of T_c ∼ A₁^0.5, 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, T_c 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 T_c 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 T_c by fine-tuning material properties and have broader implications for understanding superconductivity in a universal manner.