Some universal relations between the gap and thermodynamic functions plausible for various models of superconductors

TL;DR

This paper establishes universal relations linking the energy gap to thermodynamic functions in various superconducting models, enabling the calculation of thermodynamic properties from the gap function and vice versa.

Contribution

It introduces universal formulas connecting the energy gap with thermodynamic quantities across multiple superconducting models, facilitating easier computation of thermodynamic functions.

Findings

Universal relations between gap and thermodynamic functions derived.

Formulas enable calculation of specific heat and magnetic field from gap data.

Inverse relations allow determining the gap from thermodynamic measurements.

Abstract

It is proven that there exist some universal relations between the energy gap and the differences of the thermodynamic potential, entropy, specific heat and critical magnetic field for many two- and three-dimensional models of superconductivity with spin-singlet Cooper pairs forming \textit{s} or \textit{d} or \textit{g} etc. states. The obtained formulae make it possible to derive thermodynamic functions and, in particular, the superconducting specific heat and the critical magnetic induction in the whole temperature range $0\leq T\leq T_{c}$ employing the form of $\Delta(T)$ only. The inverse formula allowing us to find $\Delta(T)$, when the temperature dependence of the specific heat difference is known, is also presented. The results are referred to some obtained within the McMillan formalism, and some remarks on an application of the present formulae to the {\textit{t--J}} model are given.