Phonons and d-wave pairing in the two-dimensional Hubbard model

TL;DR

This study investigates how different phonon modes influence d-wave pairing in the 2D Hubbard model, revealing that some phonons enhance pairing while others suppress it, with combined effects potentially favoring superconductivity.

Contribution

It introduces a functional renormalization group approach with frequency-dependent interactions to analyze phonon effects on d-wave pairing in the Hubbard model.

Findings

B1g buckling mode enhances pairing.

Other phonon modes decrease pairing.

Combined phonon effects can tip the balance towards superconductivity.

Abstract

We analyze the influence of phonons on the d-wave pairing instability in the Hubbard model on the two-dimensional square lattice at weak to moderate interaction U, using a functional renormalization group scheme with frequency-dependent interaction vertices. As measured by the pairing scale, the B1g buckling mode enhances the pairing, while other phonon modes decrease the pairing. When various phonon modes are included together, the net effect on the scale is small. However, in situations where d-wave superconductivity and other tendencies, e.g. antiferromagnetism, are closely competing, the combined effect of different phonons may be able to tip the balance towards pairing.