Superconducting properties of the attractive Hubbard model: A slave-boson study

The superfluid characteristics of the attractive Hubbard model are analyzed for any coupling /U/ and arbitrary electron concentration (0 < n < 2) by means of the slave-boson mean-field method and also by the perturbative treatment of the strong-coupling limit. The slave boson method takes into account correlations of electrons and yields a reliable description of the crossover from BCS-type superconductivity to local pair (composite bosons) superconductivity with increasing /U/. The results for the ground state (the free energy, the gap in the excitation spectrum) and the electromagnetic characteristics (the critical magnetic field, the London penetration depth, the coherence length) are compared with those obtained by the Hartree-Fock approximation and by the self-consistent second-order perturbation theory in the weak-coupling limit as well as with those obtained using perturbational approaches in the strong-coupling limit. We show that the slave-boson method, in contrast to the Hartree-Fock approximation, gives credible results for all investigated quantities in the whole interaction range, interpolating smoothly between the BCS acid local pair regimes. A comparison of theoretical predictions for our simple model with experimental data for various families of short-coherence-length superconductors suggests that the best agreement can be obtained for intermediate values of the local attraction.