We study the thermodynamic properties of short coherence length superconductors in the pseudogap phase. Our description is based on the attractive Hubbard model that reproduces well these features in the intermediate coupling regime
(U=4t). Basing ourselves on the self-consistent T-matrix approximation, we perform an analytical calculation that yields an expression for the thermodynamic grand potential of the electronic system. It shows that the relevant degrees of freedom above the critical temperature are well-defined bosonic fluctuations describing virtual Cooper pairing. The latter are described by the low-energy expansion of the T matrix whose evaluation reveals that these pairing fluctuations behave quite similarly to free bosons undergoing a Bose-Einstein condensation (BEC). We then carefully analyze the conditions allowing for this interpretation and finally consider the case of underdoped high-temperature superconductors where typical BEC features have been observed experimentally.
One-particle spectral properties in the normal phase of the two-dimensional attractive Hubbard model are investigated in the weak-coupling regime using the non-self-consistent T-matrix approximation. The corresponding equations are evaluated numerically directly on the real-frequency axis. For temperatures sufficiently close to the superconducting transition temperature, a pseudogap in the one-particle spectral function is observed, which can be assigned to the increasing importance of pair fluctuations.
The attractive Hubbard model on a 2-D square lattice is studied at low electronic densities using the ladder approximation for the pair susceptibility. This model includes (i) the short coherence lengths known to exist experimentally in the cuprate superconductors, and (ii) two-particle bound states that correspond to electron pairs. We study the quasiparticle lifetimes in both non self-consistent and self-consistent theories, the latter including interactions between the pairs. We find that if we include the interactions between pairs the quasiparticle lifetimes vary approximately linearly with the inverse temperature, consistent with experiment.
We consider a lattice version of the ``negative-
U′′ Hubbard model in three dimensions, to study the crossover from a superconducting phase transition (dominated by phase fluctuation) to a regime where the amplitude of the superconducting order parameter controls the critical temperature. Starting from a fermionic Hamiltonian, we give a microscopic derivation of the effective action in terms of the relevant physical fields: the modulus and phase of the superconducting order parameter. Furthermore, by employing to the resulting coarse--grained quantum
XY model the phase fluctuation algebra between number and phase operators (given by the Euclidean group
E2), we map the ``phase-only'' action onto a solvable quantum spherical model. We establish the self--consistent theory (involving both fermionic and bosonic degrees of freedom), and calculate the superconducting phase coherence transition temperature
Tc as a function of the coupling strength
∣U∣, exhibiting a maximum where the behavior crosses over from BCS to Bose-Einstein (BE) condensation. We examine a pseudogap in the normal state which emerges naturally as a precursor of superconductivity at the second characteristic temperature
Tg due to a state with bound pairs but without long--range phase coherence. Furthermore, we demonstrate that the reduced gaps of the model $2{\ensuremath{\Delta}}_{0}{/k}_{B}{T}_{g}\ensuremath{\sim}4$ is almost independent on the pairing strength
∣U∣/t, whereas $2{\ensuremath{\Delta}}_{0}{/k}_{B}{T}_{c}$ increases with increasing
∣U∣---in striking analogy with the phenomenology of the high--temperature cuprate superconductors when interpreted in terms of the BCS-BC crossover scenario.
The understanding of an electron gas with short coherence length pairs formed by an attractive interaction is believed to be one of the major keys to our theoretical knowledge of the high-T_c-superconductors. Mainly the deviations of the cuprates from usual metallic Fermi liquid behaviour already in the normal state like e.g. a linear resistivity or the observation of a pseudo gap can result from electron-electron correlations. We therefore investigate the negative U Hubbard model in two dimensions at low densities using the T-matrix approximation. In the non selfconsistent formulation of the theory the system always shows an instability towards Bose condensation of pairs into an infinite lifetime two-particle bound state. If the calculations are performed selfconsistently pair-pair scattering is included which causes the pairs to have finite lifetime. The physics of these finite lifetime pairs is discussed.
We study the phase diagram for the attractive ({\it i.e.,} negative-
U) Hubbard model on a simple cubic lattice, through Monte Carlo simulations. We obtain the critical temperature,
Tc, for superconductivity from a finite-size scaling analysis of the data for the pairing correlations. For fixed on-site attraction,
U,
Tc displays a maximum near the filling factor 0.9, roughly independent of
U. For fixed filling we estimate the crossover temperature
T×(U), separating the normal states: metallic and spin-gap. There is also a critical value
Up for pair formation, the magnitude of which seems to be independent of doping. The relevance of these results to the high-
Tc oxides is discussed.