S. Stintzing et W. Zwerger, GINZBURG-LANDAU-THEORY OF SUPERCONDUCTORS WITH SHORT COHERENCE LENGTH, Physical review. B, Condensed matter, 56(14), 1997, pp. 9004-9014
We consider fermions in two dimensions with an attractive interaction
in the singlet d-wave channel of arbitrary strength. By means of a Hub
bard-Stratonovich transformation a statistical Ginzburg-Landau theory
is derived, which describes the smooth crossover from a weak-coupling
BCS superconductor to a condensate of composite bosons. We show that t
he Nelson-Kosterlitz jump in the superfluid density vanishes in the BC
S limit, when mean-field theory becomes exact. Adjusting the interacti
on strength to the observed slope of H-c2 at T-c in the optimally dope
d high-T-c compounds Y-Ba-Cu-O and Bi-Sr-Ca-Cu-O, we determine the ass
ociated values of the Ginzburg-Landau correlation length xi and the Lo
ndon penetration depth lambda. The resulting dimensionless ratio k(F)
xi(0)approximate to 5-8 and the Ginzburg-Landau parameter kappa=lambda
/xi approximate to 90-100 agree well with the experimentally observed
values. These parameters indicate that the optimally doped materials a
re still on the weak-coupling side of the crossover to a Bose regime.