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arXiv:cond-mat/9703040 · Physical review. B, Condensed matter

Superconductivity in the Hubbard model with correlated hopping: Slave-boson study

Bogdan R. Bułka

Published May 1, 1998• 29 citations
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Abstract

Slave boson mean-field studies of the ground state of the Hubbard model with correlated hopping were performed. The approach qualitatively recovers the exact results for the case when the hopping integral $t$ equals the correlated hopping integral $X.$ The phase diagram for the strongly correlated state with only singly occupied sites, the weakly correlated state, where single and double occupation is allowed, and for the superconducting state, was determined for any value of $X$ and any electron concentration $n.$ At the half-filled band $(n=1)$ a direct transition from the superconductor to the Mott insulator was found. In the region of strong correlations the superconducting solution is stable for $n$ close to 1, in contrast to the case of weak correlations, in which superconductivity occurs at $n\ensuremath{\approx}0$ and $n\ensuremath{\approx}2.$ We have also found that strong correlations change the characteristics of the superconducting phase, e.g., the gap in the excitation spectrum exhibits a nonexponential dependence on the on-site Coulomb integral $U$ close to the phase-transition point.

DOI
10.1103/physrevb.57.10303

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Slave boson mean-field studies of the ground state of the Hubbard model with correlated hopping were performed. The approach qualitatively recovers the exact results for the case when the hopping integral ttt equals the correlated hopping integral X.X.X. The phase diagram for the strongly correlated state with only singly occupied sites, the weakly correlated state, where single and double occupation is allowed, and for the superconducting state, was determined for any value of XXX and any electron concentration n.n.n. At the half-filled band (n=1)(n=1)(n=1) a direct transition from the superconductor to the Mott insulator was found. In the region of strong correlations the superconducting solution is stable for nnn close to 1, in contrast to the case of weak correlations, in which superconductivity occurs at n\ensuremath≈0n\ensuremath{\approx}0n\ensuremath≈0 and n\ensuremath≈2.n\ensuremath{\approx}2.n\ensuremath≈2. We have also found that strong correlations change the characteristics of the superconducting phase, e.g., the gap in the excitation spectrum exhibits a nonexponential dependence on the on-site Coulomb integral UUU close to the phase-transition point.
Using the slave-boson method in its spin-and charge-rotational invariant representation we determine stability of the superconducting state in the Hubbard model with correlated hopping.In general the term with correlated hopping violates electron-hole symmetry, however, in the special case when the correlated hopping integral X is equal to the uncorrelated hopping inte- gral t the electron-hole symmetry remains.We investigate this case and show that correlations induced by onsite Coulomb interactions U yield to the nor- mal state with exactly single occupied sites (corresponding to |U = oo)).The phase diagram of the superconducting state is determined for the different electron concentration n.At the half-filled band (n = 1) a direct transition from the Mott insulator to the superconducting state occurs.
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 single-band Hubbard model with random site energies in the strong-repulsion limit, as represented by the slave-boson formulation of the t-J model. It is essential to include the correlations between the slave-boson mean field and the disorder. This leads to the widening of the non-Fermi-liquid (``generalized Mott insulating'') region around half filling. In the Fermi-liquid regime we apply the renormalization-group method. The resulting phase diagram has superconducting, magnetic, and insulating phases. The disorder generally suppresses superconductivity and gives rise to the formation of localized magnetic moments.
The ground-state phase diagram of the one-dimensional Hubbard chain with pair-hopping interaction is studied. The analysis of the model is performed using the continuum-limit field theory approach and exact diagonalization studies. At half-filling the phase diagram is shown to consist of two superconducting states with Cooper-pair center-of-mass momentum $Q=0 (\mathrm{BCS}\ensuremath{-}{\ensuremath{\eta}}_{0}$ phase) and $Q=\ensuremath{\pi} ({\ensuremath{\eta}}_{\ensuremath{\pi}}$ phase) and four insulating phases corresponding to the Mott antiferromagnet, the Peierls dimerized phase, the charge-density-wave (CDW) insulator, and an unconventional insulating phase characterized by the coexistence of a CDW and a bond-located staggered magnetization. Away from half-filling the phase diagram consists of the superconducting $\mathrm{BCS}\ensuremath{-}{\ensuremath{\eta}}_{0}$ and ${\ensuremath{\eta}}_{\ensuremath{\pi}}$ phases and the metallic Luttinger-liquid phase. The $\mathrm{BCS}\ensuremath{-}{\ensuremath{\eta}}_{0}$ phase exhibits a smooth crossover from a weak-coupling BCS type to a strong-coupling local-pair regime. The ${\ensuremath{\eta}}_{\ensuremath{\pi}}$ phase shows the properties of the doublon (zero-size Cooper-pair) superconductor with Cooper-pair center-of-mass momentum $Q=\ensuremath{\pi}.$ The transition into the ${\ensuremath{\eta}}_{\ensuremath{\pi}}$-paired state corresponds to an abrupt change in the ground-state structure. After the transition the conduction band is completely destroyed and a new ${\ensuremath{\eta}}_{\ensuremath{\pi}}$-pair band, corresponding to the strongly correlated doublon motion, is created.
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.
Recently a new phenomenological Hamiltonian was proposed to describe the superconducting cuprates in which correlations and on-site Coulomb repulsion are introduced by partial Gutzwiller projection. This Gossamer Hamiltonian has an exact ground state and differs from the t-J and Hubbard Hamiltonians in possessing a powerful attractive interaction among electrons responsible for Cooper pairing in the d-wave channel. It is a faithful description for a superconductor with strong on-site electronic repulsion. The superconducting tunneling gap remains intact and despite on-site repulsion. Near half-filling the Gossamer superconductor with strong repulsion has suppressed photoemission intensities and superfluid density, is unstable toward an antiferromagnetic insulator and possesses an incipient Mott-Hubbard gap. The Gossamer technique can be applied to metallic ground states thus possibly serving as an apt description of strongly correlated metals. Such a Gossamer metallic phase, just as the Gossamer superconducting one, becomes arbitrarily hard to differentiate from an insulator as one turns the Coulomb correlations up near half-filling. Both the metallic and superconducting states undergo a quantum phase transition to an antiferromagnetic insulator as one increases the on-site Coulomb repulsion. In the Gossamer model we reach the critical point at half-filling by fully projecting out the double occupancy. Such a critical point might be the Anderson Resonating Valence bond state.