Ginzburg-Landau theory of superconductors with short coherence length

S. Stintzing; W. Zwerger

doi:10.1103/PhysRevB.56.9004

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Ginzburg-Landau theory of superconductors with short coherence length

S. Stintzing, W. Zwerger

DOI 10.1103/PhysRevB.56.9004 · Physical Review B

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Abstract

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, where mean-field theory becomes exact. Adjusting the interaction strength to the observed slope of Hc2 at Tc in the optimally doped high-Tc compounds Y-Ba-Cu-O and Bi-Sr-Ca-Cu-O, we determine the associated values of the Ginzburg-Landau correlation length ξ and the London penetration depth λ. The resulting dimensionless ratio kFξ(0)≈5−8 and the Ginzburg-Landau parameter κ=λ/ξ≈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.