Vertex corrections in antiferromagnetic spin fluctuation theories

TL;DR

This paper calculates the first vertex correction in a spin fluctuation theory for cuprate superconductors, finding it to be significant and impacting the quantitative accuracy of the model.

Contribution

It provides the first calculation of vertex corrections in the nearly antiferromagnetic spin fluctuation theory for cuprates, revealing their non-negligible size.

Findings

Vertex correction ratio is not small, especially at hot spots.

Large quantitative corrections to the spin fluctuation theory.

Implications for the accuracy of existing theoretical models.

Abstract

We calculate the first vertex correction $\delta\Lambda_{\bf k}$ to the bare vertex $\Lambda_\circ$ in the nearly antiferromagnetic spin fluctuation Fermi liquid theory of the cuprate superconductor ${\rm YBa_2Cu_3O_7}$. It is calculated for $\bf k$ on the Fermi surface, and ${\bf Q}=(\pm {\pi\over a}, \pm {\pi\over a})$. We find that the dimensionless ratio $|\delta\Lambda_{\bf k}|/\Lambda_\circ$, which parametrizes the vertex correction, is not small. It is a maximum for ${\bf k=k_h}$, where ${\bf k_h}$ is a ``hot spot'' on the Fermi surface. This makes large quantitative corrections to the theory.