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arXiv:cond-mat/0011255 · Physical review. B, Condensed matter

Influence of spin fluctuations on the superconducting transition temperature and resistivity in thet-Jmodel at largeN

A. Greco, R. Zeyher

Published Jan 23, 2001• 7 citations
arXivHTMLPDF

Abstract

Spin fluctuations enter the calculation of the superconducting transition temperature ${T}_{c}$ only in the next-to-leading order [i.e., in ${O(1/N}^{2})]$ of the $1/N$ expansion of the $t\ensuremath{-}J$ model. We have calculated these terms and show that they have only little influence on the value for ${T}_{c}$ obtained in the leading order $O(1/N)$ in the optimal and overdoped region, i.e., for dopings larger than the instability towards a flux phase. This result disagrees with recent spin-fluctuation mediated pairing theories. The discrepancies can be traced back to the fact that in our case the coupling between electrons and spins is determined by the $t\ensuremath{-}J$ model and not adjusted and that the spin susceptibility is rather broad and structureless and not strongly peaked at low energies as in spin-fluctuation models. Relating ${T}_{c}$ and transport we show that the effective interactions in the particle-particle and particle-hole channels are not simply related within the $1/N$ expansion by different Fermi surface averages of the same interaction as in the case of phonons or spin fluctuations. As a result, we find that large values for ${T}_{c}$ and rather small scattering rates in the normal state as found in the experiments can easily be reconciled with each other. We also show that correlation effects heavily suppress transport relaxation rates relative to quasiparticle relaxation rates in the case of phonons but not in the case of spin fluctuations.

DOI
10.1103/physrevb.63.064520

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A microscopical theory of electron spectrum and superconductivity within the two-dimensional $t\ensuremath{-}J$ model in paramagnetic state is proposed. By employing the projection technique for the Green functions in terms of the Hubbard operators self-consistent Eliashberg equations are derived. A strong coupling of electrons with spin and charge fluctuations due to exchange and kinematical interactions is obtained. In the normal state, one-electron spectral functions reveal narrow quasiparticle peaks close to the Fermi surface (FS) with an additional broad incoherent band. The FS changes from holelike at low doping to electronlike for hole concentrations $\ensuremath{\delta}>0.3.$ In the superconducting state we observe d-wave pairing with the maximal ${T}_{c}\ensuremath{\simeq}0.04t$ at optimal doping $\ensuremath{\delta}\ensuremath{\simeq}0.3.$
A microscopic theory of superconductivity in the extended Hubbard model which takes into account the intersite Coulomb repulsion and electron-phonon interaction is developed in the limit of strong correlations. The Dyson equation for normal and pair Green functions expressed in terms of the Hubbard operators is derived. The self-energy is obtained in the noncrossing approximation. In the normal state, antiferromagnetic short-range correlations result in the electronic spectrum with a narrow bandwidth. We calculate superconducting Tc by taking into account the pairing mediated by charge and spin fluctuations and phonons. We found the d-wave pairing with high-Tc mediated by spin fluctuations induced by the strong kinematic interaction for the Hubbard operators. Contributions to the d-wave pairing coming from the intersite Coulomb repulsion and phonons turned out to be small.
Away from half filling and above its Neel temperature, the three-dimensional Hubbard model is a paramagnetic metal with antiferromagnetic spin fluctuations, where controlled momentum-resolved results have been lacking. Using connected-determinant diagrammatic Monte Carlo, we compute the momentum-resolved self-energy for n = 0.4-0.95, T/t = 0.05-0.33 and U/t = 4-8, and the full-zone spin susceptibility at twelve of these points, focusing on U/t = 4. At U/t = 4 and toward half filling the spin fluctuations become strong: for n = 0.7-0.9 at T/t = 0.14 they enhance the susceptibility peak up to sevenfold and raise the momentum-dependent part of the scattering rate to four to five times its second-order value. They are driven by an effective spin interaction screened to about 2U/3 and nearly uniform over the zone. Yet the peak height is set by the slightly smaller value of this interaction at the peak wave vector, and near magnetic order this small difference changes the height by a large factor. Two-particle self-consistent theory reproduces the peak because its sum rule fixes its single constant interaction near this value, but for n = 0.7-0.9 at T/t = 0.14 its self-energy overestimates the local scattering rate and underestimates the momentum-dependent part. Though strong, the fluctuations are short ranged, with a correlation length of at most about two lattice spacings, and for n = 0.7-0.9 and T/t >= 0.14 the scattering rate near the Fermi surface varies by at most about 1% at fixed band energy, without hot spots. At U/t = 4 dynamical mean-field theory (DMFT) reproduces the local scattering rate and quasiparticle weight within a few percent, and the nonlocal part it misses is approximately a function of the band energy. Strong spin fluctuations thus coexist with nearly isotropic quasiparticles, and the results provide a benchmark for extensions of DMFT and for spin-fluctuation theories.
We study d-wave superconductivity in the extended Hubbard model in the strong correlation limit for a large intersite Coulomb repulsion V. We argue that in the Mott-Hubbard regime with two Hubbard subbands there emerges a new energy scale for the spin-fluctuation coupling of electrons of the order of the electronic kinetic energy W much larger than the exchange energy J. This coupling is induced by the kinematic interaction for the Hubbard operators which results in the kinematic spin-fluctuation pairing mechanism for V < W . The theory is based on the Mori projection technique in the equation of motion method for the Green functions in terms of the Hubbard operators. The doping dependence of superconductivity temperature Tc is calculated for various values of U and V.
We have used exact diagonalization and quantum Monte Carlo methods to study the one-dimensional t-J model including the three-site hopping term derived from the strong-coupling limit of the Hubbard model. The three-site term may be important to superconducting correlations since it allows direct hopping of local singlet electron pairs. The phase diagram is determined for several values of the strength of the three-site term and compared with that of the t-J and Hubbard models. Phase separation, which exists in the t-J model, is suppressed. In the low electron density region the formation of local singlet electron pairs is enhanced, leading to stronger superconducting correlations even for values J/t2. A large spin gap region extends from low electron densities up to high densities. In the low hole density region the superconducting correlations are suppressed at J/t>2.8 in spite of enhanced pair formation. This is because the three-site term, while enhancing the formation of electron pairs, leads to a repulsion between holes.