Mean-field study of superconductivity in the t−J square lattice model with three-site hopping

Abstract

It remains an open question whether the two-dimensional single-band pure Hubbard model and its related pure t−J model truly capture the superconducting order in cuprates. Recent numerical studies on this issue have raised a notable disparity in superconducting order between the pure Hubbard model and the pure t−J model. Inspired by these works, we investigate the role of the three-site hopping term in d-wave superconductivity, such a term is usually neglected in the effective Hamiltonian of the Hubbard model, although its amplitude is of the same order as the superexchange coupling J in the t−J model. Our slave-boson mean-field solution demonstrates the suppression of d-wave superconducting order by incorporating the three-site hopping term, consistent with numerical observations by the density-matrix renormalization group. This suppression could be understood as a result of competition between superexchange interaction and three-site hopping, the former favors d-wave pairing while the latter favors s-wave pairing. We also discussed its role in quasiparticle dispersion and boson-condensation temperature. Our findings may offer an alternative understanding of the recent numerical contrasting findings in the strong-coupling regime: the absent or weak superconductivity in the pure Hubbard model, while the robust superconductivity in the t−J model without including the three-site hopping term.

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