Spin-Fluctuation Superconductivity in the Hubbard Model

Abstract

The theory of the superconductivity mediated by kinematic and exchange interactions in t−J and two-band Hubbard models in a paramagnetic state is formulated. The Dyson equations for the matrix Green functions in terms of the Hubbard operators are obtained in the non-crossing approximation. To calculate superconducting T c a numerical solution of self-consistent Eliashberg equations is proposed.

Evaluation of the two-particle propagator for the Hubbard model with the help of the Hubbard-I approximation

“…Technically speaking, the 1/r 3 decay of the Hubbard-I propagator is a consequence of the fact that the interaction in the equation of motion, (21), is important in the s-channel only, whereas in the d-channel its effect decreases when r increases.…”

“…A related approach, that using the twopole approximation (which, in some respects, is superior to the Hubbard-I approximation), and its generalization are applied to study possible superconductivity of the usual Hubbard model [19] and of the multi-band Hubbard model [20]. Similar techniques are used in [21,22]. Systematic expansion in orders of t/U is developed in [23].…”

“…In such an equation the quantity P iilm is decoupled from P ijlm , i = j, which is equivalent to the condition P iilm = 0. Expression (21) corresponds to the propagation of two interacting particles: the terms with the Kronecker symbols may be regarded as an effective repulsive interaction between electrons on neighbouring sites with a coupling constant of the order of t (1 − n iσ ). Thus, we reduce the strong coupling many-body problem to the intermediate coupling two-body one.…”

“…The fact that the MC propagator decays like the freeelectron propagator is a surprising revelation of [10]. The ability of the Hubbard-I approximation to capture the 1/r 3 law is a rather simple consequence of the equation of motion, (21). Indeed, in the latter equation, if r is large, the interaction terms (the terms with the Kronecker symbols) contribute to the swave channel only; as for the d-wave propagator, its equation of motion coincides, up to a normalization factor, with that for free fermions.…”

Hubbard-I approximation as a tool for study of superconducting properties of the Hubbard model with repulsive interaction

“…A related approach, the two-pole approximation (which, in some respects, is superior to Hubbard-I approximation), and its generalization are applied to study possible superconductivity of the usual Hubbard model [19] and of the multi-band Hubbard model [20]. Similar techniques are used in [21,22]. Systematic expansion in orders of t/U is developed in [23].…”