Coherence length in non-conventional superconductors

authors: A. Toschi , L. Benfatto, S. Caprara and C. Castellani

In the standard BCS superconductors the Cooper-pair size xi_pair and the coherence length for the gap fluctuations xi_0 are of the same order, being both settled by the ratio between the Fermi velocity v_F and the gap amplitude Delta_0. In the superconducting cuprates the coherence length xi_0 calculated from upper critical field measurements turns out to be sensibly shorter than in conventional materials and even smaller values (10-15 AA) are deducted from a very recent experiment of STS and STM [1]. A detailed study of the various length scales in these non conventional superconductors is then requested: in particular the effects of the d-wave symmetry of the gap and of the not small strength of the pairing interaction have to be taken into account. Within a (generalized) attractive Hubbard model, we show [2] that at weak coupling the presence of the nodal points in the d-wave gap, while producing the divergence of the Cooper-pair size, corrects only by a numerical factor the BCS estimate for xi_0. The strong coupling regime has to be treated more carefully since it is not possible to study the gap fluctuations separately from the density fluctuations. We show explicitly [2](in the s-wave case, but we do not expect significant differences for d-wave superconductors) that the coherence length xi_0 is effectively reduced to the order of a lattice spacing at finite density, while in the extreme diluted limit we recover the expected divergence for the coherence length of a weakly-interacting bosonic system.

[1.] S.H. Pan et al. Nature 413, 282 (2001).
[2.] L. Benfatto, A. Toschi, S. Caprara and C. Castellani Phys. Rev. B, 66, 054515 (2002).