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arXiv:cond-mat/0503466 · Physical Review B

High- Tc superconductivity due to coexisting wide and narrow bands: A fluctuation exchange study of the Hubbard ladder as a test case

Kazuhiko Kuroki, Takafumi Higashida, Ryotaro Arita

Published Dec 15, 2005• 58 citations
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Abstract

We propose that when the Fermi level lies within a wide band and also lies close to but not within a coexisting narrow band, high-${T}_{c}$ superconductivity may take place due to the large number of interband pair scattering channels and the small renormalization of the quasiparticles. We show using the fluctuation exchange method that this mechanism works for the Hubbard model on a ladder lattice with diagonal hoppings. From this viewpoint, we give a possible explanation for the low ${T}_{c}$ for the actual hole-doped ladder compound, and further predict a higher ${T}_{c}$ for the case of electron doping.

DOI
10.1103/physrevb.72.212509

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We propose that when the Fermi level lies within a wide band and also lies close to but not within a coexisting narrow band, high-Tc{T}_{c}Tc​ superconductivity may take place due to the large number of interband pair scattering channels and the small renormalization of the quasiparticles. We show using the fluctuation exchange method that this mechanism works for the Hubbard model on a ladder lattice with diagonal hoppings. From this viewpoint, we give a possible explanation for the low Tc{T}_{c}Tc​ for the actual hole-doped ladder compound, and further predict a higher Tc{T}_{c}Tc​ for the case of electron doping.
One promising way to enhance superconductivity is to have coexisting wide and incipient narrow bands, where the Fermi level intersecting the wide band lies just above the narrow band, by which finite-energy spin fluctuations act as glue to mediate pair scattering. As an extreme case of the narrow band dispersion, we investigate spin-fluctuation-mediated superconductivity in two-dimensional Hubbard models with an incipient flat band. For all of the systems investigated in this study, the Kagome, Lieb, and bilayer square lattices with a flat band, we find that spin-singlet pairing superconductivity is enhanced when the flat band is nearly fully filled, due to the interband pair scattering even when the flat band becomes dispersive by correlation effects. Among these models, enhancement of superconductivity is weak in the Lieb lattice, possibly because the density of states of the wide band goes to zero at the Dirac point where the flat and wide bands intersect. Also, when the electron density is smaller so that the flat band approaches half-filling, ferromagnetic spin fluctuations and spin-triplet pairing arises, which does not develop strongly compared to the case of the spin-singlet pairing for the incipient band situation.
Quasiparticle bands of the two-dimensional Hubbard model are calculated using the Roth two-pole approximation to the one-particle Green's function. Excellent agreement is obtained with recent Monte Carlo calculations, including an anomalous volume of the Fermi surface near half-filling, which can possibly be explained in terms of a breakdown of Fermi liquid theory. The calculated bands are very flat around the (\ensuremath{\pi},0) points of the Brillouin zone in agreement with photoemission measurements of cuprate superconductors. With doping there is a shift in spectral weight from the upper band to the lower band. The Roth method is extended to deal with superconductivity within a four-pole approximation allowing electron-hole mixing. It is shown that triplet p-wave pairing never occurs. A self-consistent solution with singlet ${\mathit{d}}_{{\mathit{x}}^{2}\mathrm{\ensuremath{-}}{\mathit{y}}^{2}}$-wave pairing is found and optimal doping occurs when the van Hove singularity, corresponding to the flat band part, lies at the Fermi level. Nearest-neighbor antiferromagnetic correlations play an important role in flattening the bands near the Fermi level and in favoring superconductivity. However, the mechanism for superconductivity is a local one, in contrast to spin-fluctuation exchange models. For reasonable values of the hopping parameter the transition temperature Tc{\mathit{T}}_{\mathit{c}}Tc​ is in the range 10--100 K. The optimum doping ${\mathrm{\ensuremath{\delta}}}_{\mathit{c}}$ lies between 0.14 and 0.25, depending on the ratio U/t. The gap equation has a BCS-like form and 2${\mathrm{\ensuremath{\Delta}}}_{\mathrm{max}}$/kTc{\mathit{kT}}_{\mathit{c}}kTc​\ensuremath{\simeq}4.
Full or empty narrow bands near the Fermi level are known to enhance superconductivity by promoting scattering processes and spin fluctuations. Here, we demonstrate that doublon-holon fluctuations in systems with half-filled narrow bands can similarly boost the superconducting Tc{T}_{c}Tc​. We study the half-filled attractive bilayer Hubbard model on the square lattice using dynamical mean-field theory. The band structure of the noninteracting system contains a wide band formed by bonding orbitals and a narrow band formed by antibonding orbitals, with bandwidths tunable by the interlayer hopping. The shrinking of the narrow band can lead to a substantial increase in the superconducting order parameter and phase stiffness in the wide band. At the same time, the coupling to the wide band allows the narrow band to remain superconducting---and to reach the largest order parameter---in the flat band limit. We develop an anomalous worm sampling method to study superconductivity in the limit of vanishing effective hopping. By analyzing the histogram of the local eigenstates, we clarify how the interplay between different interaction terms in the bonding/antibonding basis promotes pair fluctuations and superconductivity.
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We study within the fluctuation exchange approximation the trilayer Hubbard model where three layers of the Hubbard model are coupled by large interlayer hoppings so that the overlap of the bonding, nonbonding, and antibonding bands is relatively small. We pay special attention to the band fillings close to 1/3, for which the bonding and nonbonding bands as a whole are close to half filling. For relatively small values of the onsite UUU, superconductivity roughly exhibits electron-hole symmetric behavior, as expected for a nearly half-filled two-band system. By contrast, an asymmetry appears when UUU becomes large, where superconductivity is more favored in the hole-doped regime, i.e., in the regime where electrons are removed from 1/3 filling. We attribute this asymmetry to the asymmetric renormalization of the bonding, nonbonding, and antibonding bands when UUU is large.