Coherence length in superconductors from weak to strong coupling

We investigate the evolution of the superconducting coherence length xi(0) from weak to strong coupling, within both an s-wave and a d-wave lattice model. We show that the identification of xi(0) with the Cooper-pair size xi(pair) in the weak-coupling regime is meaningful only for a fully gapped (e.g., s-wave) superconductor. Instead in a d-wave superconductor, where xi(pair) diverges, we show that xi(0) is finite (and of the expected order of magnitude) when properly defined as the characteristic length scale for the correlation function of the amplitude of the superconducting order parameter. The strong-coupling regime is quite intriguing, since the interplay between the particle-particle and the particle-hole channel is no more negligible. In the case of s-wave pairing, which allows for an analytical treatment, we show that xi(0) is of the order of the lattice spacing at finite densities. In the diluted regime xi(0) diverges, recovering the behavior of the coherence length of an effective bosonic system. Similar results are expected to hold for d-wave superconductors. We also comment on the consequences of our results with respect to the physics of high-T-c superconducting cuprates.