Spectral properties of the attractive Hubbard model (original) (raw)
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Physical Review Letters, 2007
Recent excperiments (ARPES, Raman) suggest the presence of two distinct energy gaps in high-Tc superconductors (HTSC), exhibiting different doping dependences. Results of a variational cluster approach to the superconducting state of the two-dimensional Hubbard model are presented which show that this model qualitatively describes this gap dichotomy: One gap (antinodal) increases with less doping, a behavior long considered as reflecting the general gap behavior of the HTSC. On the other hand, the near-nodal gap does even slightly decrease with underdoping. An explanation of this unexpected behavior is given which emphasizes the crucial role of spin fluctuations in the pairing mechanism.
Superconductivity in a Hubbard-Fröhlich model and in cuprates
Physical Review B, 2009
Using the variational Monte-Carlo method we find that a relatively weak long-range electronphonon interaction induces a d-wave superconducting state of doped Mott-Hubbard insulators and/or strongly-correlated metals with a condensation energy significantly larger than can be obtained with Coulomb repulsion only. Moreover, the superconductivity is shown to exist for infinite on-site Coulomb repulsion, removing the requirement for additional mechanisms such as spin fluctuations to mediate d-wave superconductivity. We argue that the superconducting state is robust with respect to a more intricate choice of the trial function and that the true origin of high-temperature superconductivity lies in a proper combination of strong electron-electron correlations with poorly screened Fröhlich electron-phonon interaction.
Superconductivity in an extended Hubbard model with attractive interaction
Superconductor Science and Technology, 2011
In this work, a two-dimensional one-band Hubbard model is investigated within a two-pole approximation. The model presents a non-local attractive potential U (U < 0) that allows the study of d-wave superconductivity and also includes hopping up to second-nearest-neighbors. The twopole scheme has been proposed to improve the Hubbard-I approximation. The analytical results
Superconductivity in the Attractive Hubbard Model: The Double Hubbard--I Approximation
arXiv (Cornell University), 1998
Using the Dyson equation of motion for both the diagonal one-particle Green function, G(k, ω) and off-diagonal Green function, F (k, ω), at the level of the Hubbard-I decoupling scheme, we have found that they have four poles symmetric in pairs, justifying a more elaborated calculation done by the Zürich group by means of the T-Matrix approach (Pedersen et al, Z. Physik B 103, 21 (1997)) and the moment approach of Nolting (Z. Physik 255, 25 (1972)). We find that the energy spectra and the weights of G(k, ω) and F (k, ω) have to be calculated self-consistently. G(k, ω) satisfies the first two moments while F (k, ω) the first sum rule. Our order parameter α(T) is given by 1/Ns k ε(k)∆(k). Due to the fact that we have a purely local attractive interaction ∆(k) can be of any s-type wave. However, for a pure s-wave, for which α(T) = 0, we go back to the mean-field BCS results, with a renormalized chemical potential. In this case, the off-diagonal Green function, F (k, ω), satisfies the first two off-diagonal sum rules. We explicitly state the range of validity of our approximation.
Pairing and superconductivity from weak to strong coupling in the attractive Hubbard model
New Journal of Physics, 2005
The finite-temperature phase diagram of the attractive Hubbard model is studied by means of the Dynamical Mean Field Theory. We first consider the normal phase of the model by explicitly frustrating the superconducting ordering. In this case we obtain a first-order pairing transition between a metallic phase and a paired phase formed by strongly coupled incoherent pairs. The transition line ends in a finite temperature critical point, but a crossover between two qualitatively different solutions still occurs at higher temperature. Comparing the superconducting and the normal phase solutions, we find that the superconducting instability always occurs before the pairing transition in the normal phase takes place, i.e., Tc > Tpairing. Nevertheless, the high-temperature phase diagram at T > Tc is still characterized by a crossover from a metallic phase to a preformed pair phase. We characterize this crossover by computing different observables that can be used to identify the pseudogap region, like the spin susceptibility, the specific heat and the single-particle spectral function.
Orbital Currents in Extended Hubbard Models of High-Tc Cuprate Superconductors
Physical Review Letters, 2009
Motivated by the recent report of broken time-reversal symmetry and zero momentum magnetic scattering in underdoped cuprates, we investigate under which circumstances orbital currents circulating inside a unit cell might be stabilized in extended Hubbard models that explicitly include oxygen orbitals. Using Gutzwiller projected variational wave functions that treat on an equal footing all instabilities, we show that orbital currents indeed develop on finite clusters, and that they are stabilized in the thermodynamic limit if additional interactions, e.g. strong hybridization with apical oxygens, are included in the model. Despite intensive efforts in the last twenty years, the physics of high Tc superconductors remains largely mysterious [1]. This is especially true of the pseudogap phase of underdoped cuprates, for which various explanations have been put forward ranging from preformed superconducting pairs [5] to the existence of orbital currents with or without broken translational symmetry. The latter case has received considerable attention due on one hand to recent neutron experiments indicating the presence of magnetic moments, compatible with the translation invariant pattern of currents predicted by Varma , and on the other hand to Kerr effect measurements showing evidence of time-reversal symmetry breaking.
Physical Review B, 2005
We investigate by means of Dynamical Mean-Field Theory the crossover from BCS superconductivity to Bose-Einstein (BE) condensation of preformed pairs which occurs in the attractive Hubbard model by increasing the attraction strength. We follow the evolution of the two energy scales underlying the superconducting phenomenon, the gap ∆0 and the superfluid stiffness DS, which controls the phase coherence. The BCS-BE crossover is clearly mirrored in a change in the hierarchy of these two scales, the smallest of the two controlling the critical temperature. In the whole intermediate-to-strong coupling region Tc scales with DS, while TC is proportional to ∆0 only in the BCS regime. This evolution as a function of the interaction qualitatively resembles what happens in the cuprates when the doping is decreased towards the Mott insulator.
Superconductivity in inhomogeneous Hubbard models
We present a controlled perturbative approach to the low temperature phase diagram of highly inhomogeneous Hubbard models in the limit of small coupling, t ′ , between clusters. We apply this to the dimerized and checkerboard models. The dimerized model is found to behave like a doped semiconductor, with a Fermi-liquid groundstate with parameters (e.g. the effective mass) which are smooth functions of the Hubbard interaction, U . By contrast, the checkerboard model has a nodeless d-wave superconducting state (preformed pair condensate, d-BEC) for 0 < U < Uc, which smoothly crosses over to an intermediate BCS-like superconducting phase (d-BCS), also with no nodal quasi-particles, for |U − Uc| < O(t ′ ), which gives way to a Fermi liquid phase at large U > Uc = 4.58.