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Europhysics Letters (EPL)

Superconductivity in the Hubbard Model with Strong Coulomb Repulsion

Yu. A. Izyumov, B. M. Letfulov

Published Oct 1, 1991• 4 citations
Publisher

Abstract

We calculated an effective electron interaction in Cooper's channel for the t-J model with the help of the diagram technique for the Hubbard operators. We derived equations which are similar to the superconducting strong-coupling theory equations and investigated the possibility of superconducting pairing due to spin fluctuations in different regions of ( t/U, n )-plane corresponding to different magnetic regimes of the system.

DOI
10.1209/0295-5075/16/5/015

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We calculated an effective electron interaction in Cooper's channel for the t-J model with the help of the diagram technique for the Hubbard operators. We derived equations which are similar to the superconducting strong-coupling theory equations and investigated the possibility of superconducting pairing due to spin fluctuations in different regions of ( t/U, n )-plane corresponding to different magnetic regimes of the system.
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.
A microscopic theory of electronic spectrum and superconducting pairing within the Hubbard model is formulated.The Dyson equation for the normal and anomalous Green functions in terms of the Hubbard operators is derived by applying the Mori-type projection technique.The self-energy is evaluated in the noncrossing approximation for electron scattering on spin and charge fluctuations induced by kinematic interaction for Hubbard operators.Numerical results for electron dispersion in the strong correlation limit are presented.Superconducting pairing mediated by antiferromagnetic exchange and spin fluctuations is discussed.
A new method for estimating the parameter ensuring the fulfillment of the Mermin-Wagner theorem in the strong coupling diagram technique (SCDT) for the two-dimensional Hubbard model is suggested. With the precise parameter value, calculated magnetic quantities are in good agreement with the results of numeric and optical-lattice experiments. Obtained spin and charge vertices are used for investigating superconductivity in the ttt-UUU and ttt-t′t't′-t"t"t"-UUU Hubbard models in the regime of strong correlations. We found no superconducting transition in the ttt-UUU model. In the ttt-t′t't′-t"t"t"-UUU model, the transition occurs for the singlet dx2−y2d_{x^2-y^2}dx2−y2​ pairing at Tc≈0.016tT_c\approx0.016tTc​≈0.016t. The difference between the two models is in the renormalized hopping describing electron motion in SCDT. In the ttt-UUU model, it vanishes for momenta (π,0)(π,0)(π,0), (0,π)(0,π)(0,π) of extrema of the ddd-wave order parameter, while the hopping is finite in the ttt-t′t't′-t"t"t"-UUU model. In the one-band model, there are optimal values of t′t't′ and t"t"t" ensuring the highest TcT_cTc​.
Abstract The possibility of the superconducting transition in the repulsive Hubbard model on a square lattice is studied using the ladder approximation of the strong coupling diagram technique. The t – U and t – t ′– t ″– U models are considered in the regime of strong correlations, for the on-site Coulomb repulsion U = 8 t , in the range of temperatures 0.02 t ≲ T ≲ 0.3 t . To avoid the influence of the phase separation and size effects the calculations are performed in an infinite crystal, in the part of the phase diagram without inhomogeneities, for the electron concentration n ¯ = 0.92 . Solutions of the Eliashberg equation for singlet and triplet pairing, which are transformed according to one-dimensional representations of the lattice point group D 4 , are considered. For both models and all considered symmetries, eigenvalues of the Eliashberg equation are less than unity and demonstrate no upward trend with decreasing temperature. This result points to the absence of superconductivity in the Hubbard model in the strong-coupling regime. We discuss the reason for the small eigenvalue of the Eliashberg equation in the case of the singlet d x 2 − y 2 pairing.
The effect of spin-fluctuation scattering processes on the region of the superconducting phase in the strongly correlated electrons (Hubbard fermions) has been investigated by the diagram technique for Hubbard operators. It is shown that spin fluctuations in the one-loop approximation for the − t' − t − J*- model taking into account long-range hoppings and three-center interactions are reflected by components of the strength operator. In this approximation for the d-type symmetry of the order parameter for the superconducting phase a system of infinite integral equations has been derived. Obtained dependencies of critical temperature on the electron concentrations show that joint effect of long-range hoppings, three-center interactions, and dynamical spin-fluctuation processes leads to strong renormalization of the superconducting phase region. It was shown that these processes essentially modify distribution functions of Hubbard fermions in normal phase.
It is important to understand the mechanism of high-temperature superconductivity. It is obvious that the interaction with large energy scale is responsible for high critical temperature T c . The Coulomb interaction is one of candidates that bring about high-temperature superconductivity because its characteristic energy is of the order of eV. There have been many works for the Hubbard model including three-band d-p model with the on-site Coulomb repulsion to investigate a possibility of high-temperature superconductivity. It is, of course, not trivial whether the on-site Coulomb interaction leads to a pairing interaction between two electrons. We argue that high-temperature superconductivity is possible in the strongly correlated region by using the variational Monte Carlo method for the two-dimensional t-U-J-V model. The exchange interaction J and the nearest-neighbour attractive interaction V cooperate with U and will act to enhance the critical temperature.