We study the temperature and the interaction dependence of Green's function in the attractive Hubbard model using self-consistent T-matrix approximation (SCTMA). It is found that at low temperatures, the spectrum of electrons on the Fermi surface shows a three-peak structure. On the other hand, at high temperatures, the spectrum has only two peaks. We also find that by increasing the electron–electron attraction, the temperature at which the explained three-peak spectrum appears is decreased. These results are partially explained by the static superconducting fluctuation; however, at strong coupling we need to include the effect of dynamical fluctuation. The “preformed pair” scenario of the pseudogap in high- T c superconductors and the validity of SCTMA for the BCS–Bose Einstein condensation crossover problem are discussed.
We study the temperature and the interaction dependence of Green's function in the attractive Hubbard model using self-consistent T-matrix approximation (SCTMA). It is found that at low temperatures, the spectrum of electrons on the Fermi surface shows a three-peak structure. On the other hand, at high temperatures, the spectrum has only two peaks. We also find that by increasing the electron–electron attraction, the temperature at which the explained three-peak spectrum appears is decreased. These results are partially explained by the static superconducting fluctuation; however, at strong coupling we need to include the effect of dynamical fluctuation. The “preformed pair” scenario of the pseudogap in high- T c superconductors and the validity of SCTMA for the BCS–Bose Einstein condensation crossover problem are discussed.
We explore the effect of fluctuations for T≥Tc in the 2-D negative Hubbard model within the framework of the selfconsistent T-matrix formalism, which goes beyond the BCS approximation and includes pair fluctuations. We enter the regime where correlations are important, namely, U/t=−4.0, where t denotes the hopping matrix element between nearest neighboors and U is the strength of the on-site interaction. Our results include: 1) In comparison to the free case, the distribution function, n(k), reveals considerable renormalization. This fact makes us conclude that the Fermi surface is blurred for correlated electron systems; 2) There is a pseudogap in the density of states, N(ω), around the chemical potential, μ; and 3) The real part of the T-matrix, at zero frequency and zero momentum, vs T/t shows a divergence at a particular temperature. This last result shows that more approximate T-matrix calculations, extended to T=0 are meaningless.
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.
The effect of static fluctuations in the phase of the order parameter on the normal and superconducting properties of a 2D system with attractive four-fermion interaction has been studied. Analytic expressions for the fermion Green function, its spectral density and the density of states are derived. The resultant single-particle Green function clearly demonstrates non-Fermi liquid behavior. The results show that as the temperature increases through the 2D critical temperature the width of the quasiparticle peaks broadens significantly. At the same time one retains the gap in quasiparticle spectrum. The spectral density for the dynamical fluctuations can also be obtained. Clearly the dynamical fluctuations fill the gap giving the observed pseudogap behaviour.
We theoretically investigate strong-coupling properties of an attractively interacting Fermi atomic gas, where the Cooper-pair formation occurs between atoms belonging to different dimensional bands. Including pairing fluctuations within the framework of the self-consistent T-matrix approximation (SCTMA), we examine how the BCS-type superfluid phase transition temperature Tc varies as one moves from the 3D-3D to the 2D-3D system, in the wide parameter region with respect to the strength of the pairing interaction. In the 2D-3D limit, we find that, while the mean-field BCS theory predicts Tc>0 in the strong-coupling regime, Tc is remarkably suppressed down to zero by pairing fluctuations that are strongly enhanced by the mixed-dimensionality of the system. As the origin of this, we clarify that the lower-dimensional (2D) component dominates the superfluid instability, so that the vanishing Tc is the same phenomenon as that in the 2D-2D case. We also point out that this can already be seen in the mean-field level, when one examines the propagation of the Goldstone mode. On the other hand, we find that the pseudogap phenomenon, which is known as a precursor of Cooper-pair formation, exhibits a 3D character of the 2D-3D system. These results indicate that the dimensionality of a strongly interacting Fermi gas depends on what we observe.
Pair fluctuation effects above Tc
We explore the occurrence of pairing effects above Tc in the 2D attractive Hubbard model. The presence of pairs above Tc goes beyond the BCS approximation, in which pair formation and condensation occur at the same temperature. Using the fully self-conserving T-matrix formalism, which is valid above Tc, we find that (1) the distribution function, n(k), shows a 10\% change of the weight from ``below'' to ``above'' kF with respect to the free case, and (2) the phase shift, δϕ(ω,k), shows Θ-like behavior as a function of ω for large momentum k along the diagonal of the Brillouin zone. Our calculations have been carried out for an interaction of U/t=−4.0 and a temperature of T/t=0.125, where t is the hopping matrix element between nearest neighbors. We conclude that for such an interaction value the Fermi surface is not a well-defined quantity.
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.