Correlation between characteristic energies in non-s-wave pairing superconductors

TL;DR

This paper derives and confirms a relation between coherence length and binding energy in non-s-wave superconductors, revealing key differences from s-wave materials and explaining properties of heavy Fermion superconductors.

Contribution

It provides an approximate analytic relation between coherence length and binding energy, validated by numerical solutions, specifically for non-conventional superconductors like heavy Fermions and cuprates.

Findings

Derived a relation between coherence length and binding energy.

Confirmed the relation through numerical solutions across coupling regimes.

Highlighted differences in Tc-energy relations between s-wave and non-s-wave superconductors.

Abstract

By solution of the Bethe-Goldstone equation for the Cooper pairing problem, an approximate analytic relation is derived between coherence length xi and the binding energy of the Cooper pair. This relation is then qualitatively confirmed by numerically solving the corresponding self-consistent gap equations, following the crossover from weak to strong coupling, in non-s-wave superconductors. The relation applies to non-conventional superconductors, and in particular to heavy Fermions and to high-Tc cuprates. Utilizing in addition a phenomenological link between kB*Tc and a characteristic energy epsilon_c = hbar^2 / 2m^* xi^2, with m^* the effective mass, major differences are exposed in the functional relation between kB*Tc and epsilon_c for s-wave materials and for non-conventional superconductors. The relation between critical temperature and epsilon_c thereby proposed correctly reflects the qualitative properties of heavy Fermion superconductors.