We study the three-dimensional (3D) attractive Hubbard model by means of the Determinant Quantum Monte Carlo method. This model is a prototype for the description of the smooth crossover between BCS superconductivity and Bose-Einstein condensation. By detailed finite-size scaling we extract the finite-temperature phase diagram of the model. In particular, we interpret the observed behavior according to a scenario of two fundamental temperature scales; T * associated with Cooper pair formation and Tc with condensation (giving rise to long-range superconducting order). Our results also indicate the presence of a recently conjectured phase transition hidden by the superconducting state. A comparison with the 2D case is briefly discussed, given its relevance for the physics of high-Tc cuprate superconductors.
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 (Uϭ4t). 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 ͑BEC͒. 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.
The fluctuation induced diamagnetism of underdoped high temperature superconductors is studied in the framework of the Lawrence-Doniach model. By taking into account the fluctuations of the phase of the order parameter only, the latter reduces to a layered XY-model describing a liquid of vortices which can be either thermally excited or induced by the external magnetic field. The diamagnetic response is given by a current-current correlation function which is evaluated using the Coulomb gas analogy. Our results are then applied to recent measurements of fluctuation diamagnetism in underdoped YBCO. They allow to understand both the observed anomalous temperature dependence of the zero-field susceptibility and the two distinct regimes appearing in the magnetic field dependence of the magnetization.
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