The BCS-BEC crossover within the two-dimensional attractive Hubbard model is studied by using the Cellular Dynamical Mean-Field Theory, both in the normal and superconducting ground states. Short-range spatial correlations incorporated in this theory remove the normal-state quasiparticle peak and the first-order transition found in the Dynamical Mean-Field Theory, rendering the normal state crossover smooth. For
U smaller than the bandwidth, pairing is driven by the potential energy, while in the opposite case it is driven by the kinetic energy, resembling a recent optical conductivity experiment in cuprates. Phase coherence leads to the appearance of a collective Bogoliubov mode in the density-density correlation function and to the sharpening of the spectral function.
We use the variational cluster approximation to study the superconducting ground state in the two-dimensional attractive Hubbard model, putting particular emphasis on the significance of quantum fluctuations of the system. We first show that the order parameter is suppressed in comparison with that obtained using the mean-field theory owing to the effects of spatial fluctuations in two-dimensional systems. We then show that the calculated Bogoliubov quasiparticle spectra and condensation amplitude clearly exhibit the character of Cooper pairs in momentum space and that the pair coherence length
ξ evaluated from the condensation amplitude demonstrates a smooth crossover in real space from a weakly paired BCS state (
ξ≫a) to a BEC state of tightly bound pairs (
ξ≪a), where
a is the lattice constant. The calculated kinetic and potential energies in the superconducting and normal ground states indicate that the superconducting state in the weak-coupling region is driven by the gain in potential energy, while that in the strongcoupling region is driven by the gain in kinetic energy.
We study the effects of phase fluctuations in 2D short-coherence length superconductors on the basis of the extended Hubbard model with intersite attraction.In the Kosterlitz-Thouless scenario the critical temperatures for anisotropic pairings were determined and compared with the ones from BCS Hartree-Fock approximation.The Uemura-type plots, i.e. the critical temperature vs. zero temperature phase stiffness, were obtained for extended s-wave and d x 2y 2-wave pairings.We also discuss the crossover from BCS to local pair superconductivity for d-wave pairing.