Ginzburg-Landau theory of superconductors with short coherence length

TL;DR

This paper develops a Ginzburg-Landau theory for 2D fermionic superconductors with d-wave pairing, describing the crossover from BCS to Bose-Einstein condensation, and compares theoretical parameters with high-T_c materials.

Contribution

It derives a statistical Ginzburg-Landau theory for d-wave superconductors across the BCS-BEC crossover and applies it to high-T_c compounds to estimate key parameters.

Findings

The dimensionless ratio k_F xi(0) is approximately 5-8.

The Ginzburg-Landau parameter kappa is approximately 90-100.

Parameters suggest high-T_c materials are near the weak-coupling side of the crossover.

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. Adjusting the interaction strength to the observed slope of H_c2 at T_c in the optimally doped high-T_c compounds YBCO and BSCCO, 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) approx 5-8 and the Ginzburg-Landau parameter kappa=lambda xi approx 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.