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Physical review. B, Condensed matter

Slave-boson mean-field theory for the negative-UHubbard model

Jorge O. Sofo, C. A. Balseiro

Published Jan 1, 1992• 21 citations
Publisher

Abstract

We study the negative-U Hubbard model for arbitrary values of the attractive interaction U and band filling by means of the slave-boson mean-field theory. We analyze both the normal and the superconducting states. We show that for the superconducting state our approach gives results similar to those obtained in the usual BCS mean field; only small renormalization of the bare parameters are obtained for U of the order of the bandwidth W. The energy difference between the normal and the superconducting states is maximum for U\ensuremath{\simeq}W. This energy difference is a measure of the superconducting critical temperature, which increases exponentially for small U and decreases as 1/U for large U. We discuss briefly the pair-breaking excitations.

DOI
10.1103/physrevb.45.377

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Physical review. B, Condensed matter•Dec 1, 1988•14 citations
We study the negative-U Hubbard model for arbitrary values of the attractive interaction U and band filling by means of the slave-boson mean-field theory. We analyze both the normal and the superconducting states. We show that for the superconducting state our approach gives results similar to those obtained in the usual BCS mean field; only small renormalization of the bare parameters are obtained for U of the order of the bandwidth W. The energy difference between the normal and the superconducting states is maximum for U\ensuremath{\simeq}W. This energy difference is a measure of the superconducting critical temperature, which increases exponentially for small U and decreases as 1/U for large U. We discuss briefly the pair-breaking excitations.
The superfluid characteristics of the attractive Hubbard model are analyzed for any coupling |U| and arbitrary electron concentration (0n2) by means of the slave-boson mean-field method and also by the perturbative treatment of the strong-coupling limit. The slave boson method takes into account correlations of electrons and yields a reliable description of the crossover from BCS-type superconductivity to local pair (composite bosons) superconductivity with increasing |U|. The results for the ground state (the free energy, the gap in the excitation spectrum) and the electromagnetic characteristics (the critical magnetic field, the London penetration depth, the coherence length) are compared with those obtained by the Hartree-Fock approximation and by the self-consistent second-order perturbation theory in the weak-coupling limit as well as with those obtained using perturbational approaches in the strong-coupling limit. We show that the slave-boson method, in contrast to the Hartree-Fock approximation, gives credible results for all investigated quantities in the whole interaction range, interpolating smoothly between the BCS and local pair regimes. A comparison of theoretical predictions for our simple model with experimental data for various families of short-coherence-length superconductors suggests that the best agreement can be obtained for intermediate values of the local attraction. \textcopyright{} 1996 The American Physical Society.
The attractive Hubbard model for normal and superconducting ground states is examined for arbitrary electron concentration by the use of the slave-boson mean-field approximation (SBMFA) technique. This approach, at a saddle-point level, is equivalent to the Gutzwiller approximation. Several superfluid characteristics of the model are shown for hypercubic lattices of all dimensions, including , and a comparison with the Bardeen-Cooper-Schrieffer Hartree-Fock approximation (BCS-HFA) calculations and exact results is made. Our results show quantitative and qualitative corrections of the SBMFA to the HFA. The improvement of the SBMFA over the HFA diminishes with increasing lattice dimensionality. We have also evaluated the energy difference between the superconducting and the normal states; this is compared with available results for the superconducting critical temperatures in various dimensions and Uemura-type plots are obtained. The results confirm and substantiate the assertion of a continuous evolution of the superfluid properties of the model from the weak-coupling (BCS-like) to the strong-coupling (composite-boson superconductivity) limit.
We have developed a method for studying superconductivity in the negative-U Hubbard model. It is based on the Hubbard-alloy-analogy approximation applied to the Gor'kov equation for the model. We find that, unlike the case of the BCS solution, the formation of pairs and their condensation into a superconducting ground state take place at two different temperatures. We calculate the condensation temperature Tc{\mathit{T}}_{\mathit{c}}Tc​ for all U and discuss the nature of the normal state which, for large enough U, features a macroscopically large number of pairs. Briefly, we argue that the model has relevance for high-temperature superconductors.
The phase diagrams and superconducting properties of the extended Hubbard model with pair hopping interaction, i.e., the Penson-Kolb-Hubbard model are studied. The analysis of the model is performed for d-dimensional hypercubic lattices, including d=1d=1d=1 and $d=\ensuremath{\infty},$ by means of the (broken symmetry) Hartree-Fock approximations and, for $d=\ensuremath{\infty},$ by the slave-boson mean-field method. For d=1,d=1,d=1, at half filling the phase diagram is shown to consist of nine different phases including two superconducting states with center-of-mass momentum q=0q=0q=0 and q=Qq=Qq=Q $(\ensuremath{\eta}$ pairing), site and bond-located antiferromagnetic and charge-density wave states as well as three mixed phases with coexisting site and bond orderings. The stability range of the bond-type orderings shrinks with increasing lattice dimensionality d and for $d=\ensuremath{\infty}$ the corresponding diagram consists of four phases only, involving exclusively site-located orderings. Comparing the pair hopping model with the attractive Hubbard model we found in both cases gradual evolution from the BCS-like limit to the tightly bound pairs regime and a monotonic increase of the gap in the excitation spectrum with increasing coupling. However, the dynamics of electron pairs in both models is qualitatively different, which results in different dependences of condensation energies and critical temperatures on interaction parameters as well as in different electrodynamic properties, especially in a strong coupling regime.
We investigate the possibility of superconductivity in the large-UUU limit of the Hubbard model near half filling, using a slave-boson representation. The local constraint is treated in a novel way, incorporating short-range fluctuations in addition to the global constraint. We find slave-boson pairing and a superconducting extended sss-wave phase at hole concentrations $\ensuremath{\delta}$-above 4% and below 32%.