Abstract
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- T c cuprates. Utilizing in addition a phenomenological link between k B T c and a characteristic energy ε c=ℏ 2/2m ∗ξ 2 , with m ∗ the effective mass, major differences are exposed in the functional relation between k B T c and ε c for s-wave materials and for non-conventional superconductors. The relation between critical temperature and ε c thereby proposed correctly reflects the qualitative properties of heavy Fermion superconductors.
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