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

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

1997-08-28

arxiv.org/abs/cond-mat/9708216v1

Physics

Condensed Matter

Superconductivity

4 pages RevTeX + 3 PS figures included

Scientific paper

10.1103/PhysRevB.57.5051

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 $\alpha$ is negative in this model and small compared to the classical BCS value $\alpha_{BCS} = 1/2$ or compared to typical observed values in non-optimally doped cuprate superconductors.

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