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Superconducting instability in the Holstein-Hubbard model: A numerical renormalization group study

C. -H. Pao·H. -B. Schüttler
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Abstract

We have studied the d-wave pairing-instability in the two-dimensional Holstein-Hubbard model at the level of a full fluctuation exchange approximation which treats both Coulomb and electron-phonon (EP) interaction diagrammatically on an equal footing. A generalized numerical renormalization group technique has been developed to solve the resulting self-consistent field equations. The $d$-wave superconducting phase diagram shows an optimal T_c at electron concentration ~ 0.9 for the purely electronic Hubbard system. The EP interaction suppresses the d-wave T_c which drops to zero when the phonon-mediated on-site attraction $U_p$ becomes comparable to the on-site Coulomb repulsion $U$. The isotope exponent $α$ is negative in this model and small compared to the classical BCS value $α_{BCS} = 1/2$ or compared to typical observed values in non-optimally doped cuprate superconductors.

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C. -H. Pao, H. -B. Schüttler. 1997-08-28. Superconducting instability in the Holstein-Hubbard model: A numerical renormalization group study. https://doi.org/10.1103/physrevb.57.5051

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