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

By solution of the Bethe-Goldstone equation for the Cooper pairing problem, an approximate analytic relation is derived between coherence length ξ 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 kBTc and a characteristic energy εc = h̄ /2m∗ξ2, with m the effective mass, major differences are exposed in the functional relation between kBTc and εc for s-wave materials and for non-conventional superconductors. The relation between critical temperature and εc thereby proposed correctly reflects the qualitative properties of heavy Fermion superconductors.