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

TL;DR

This study investigates the d-wave superconducting instability in the two-dimensional Holstein-Hubbard model using a novel numerical renormalization group approach, revealing how electron-phonon interactions influence the phase diagram and critical temperature.

Contribution

A new numerical renormalization group method is developed to analyze the Holstein-Hubbard model's superconducting properties with full fluctuation exchange approximation.

Findings

Optimal T_c at electron concentration ~0.9 in the Hubbard model

Electron-phonon interaction suppresses d-wave T_c

Negative isotope exponent smaller than BCS value

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 <n> ~ 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.