Empirical understanding of superconducting critical temperature based on valence electron parameters

• Concave triangle-like relation is shown between Tc/N(atom) and electronegativity.
• Maximum Tc (or Tc/N(atom)) is obtained at around the threshold electronegativity.
• Tc value can be empirically estimated by the linear equation of N(ν)r(eff)3.
• Enhancement of sp2d2-hybridization is the important factor to attain higher Tc value.

It is tried to empirically understand the superconducting critical temperature Tc of various materials (24 elements, 286 AnB (n = 1, 2, 3) compounds, 34 Fe- and 49 Cu-based compounds) by the effective pseudopotential radius, r(eff), and the effective orbital electronegativity, χ(eff)(=[N(v)/r(eff)]1/2). By giving the sets of values of r(eff) and the number of effective electron, N(v), for 65 elements under the assumption that both the hybridization state and N(v) can be assigned to 65 elements in advance by considering their electronic characters, the Tc/N(atom)–χ(eff) and Tc–N(v)r(eff)3 relations are examined, where N(atom) is the number of atom in compounds. It is found that a convex triangle-like relation is obtained between Tc/N(atom) and χ(eff) and the maximum of Tc/N(atom) is observed at around the threshold χ(eff) corresponding to metal–semiconductor transition. The cuprates and Fe-compounds with the χ(eff) closer to the threshold value show the higher Tc value. Applying the linear relation between Tc and N(v)r(eff)3 empirically obtained for the elements to the compounds, it is indicated that about two-thirds of AnB compounds as well as the Fe- and Cu-based compounds are well placed along the linear relation. These results allow us to estimate the Tc value in compound materials empirically based on the effective pseudopotential radius determined by the assumed hybridization.