Ginzburg-Landau theory of superconductors with short coherence length

We consider fermions in two dimensions with an attractive interaction in the singlet d-wave channel of arbitrary strength. By means of a Hubbard-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 the Nelson-Kosterlitz jump in the superfluid density vanishes in the BCS limit, when mean-field theory becomes exact. Adjusting the interaction strength to the observed slope of H-c2 at T-c in the optimally doped high-T-c compounds Y-Ba-Cu-O and Bi-Sr-Ca-Cu-O, we determine the associated values of the Ginzburg-Landau correlation length xi and the London 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 are still on the weak-coupling side of the crossover to a Bose regime.