Vertex corrections in antiferromagnetic spin fluctuation theories

Abstract

We calculate the first vertex correction $\delta {\Lambda }_{\mathbf{k}}$ to the bare vertex ${\Lambda }_{\circ }$ in the nearly antiferromagnetic spin fluctuation Fermi liquid theory of the cuprate superconductor $\mathrm{YB}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_7$. It is calculated for $\mathbf{k}$ on the Fermi surface, and $\mathbf{Q}=(\pm \frac{\pi }{a},\pm \frac{\pi }{a})$. We find that the dimensionless ratio $|\delta {\Lambda }_{\mathbf{k}}|/{\Lambda }_{\circ }$, which parametrizes the vertex correction, is not small. It is a maximum for $\mathbf{k}={\mathbf{k}}_{\mathbf{h}}$, where ${\mathbf{k}}_{\mathbf{h}}$ is a ``hot spot'' on the Fermi surface. This makes large quantitative corrections to the theory.

13 pages, RevTeX, 2 figures, Minor changes including tabular values have been made. The main conclusions have not been changed.The revised version is to appear in Phys. Rev. Lett. 77, 3017 (1996)

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• On the low energy properies of fermions with singular interactions
• Toward a Unified Magnetic Phase Diagram of the Cuprate Superconductors
• Renormalization Group Approach to Low Temperature Properties of a Non-Fermi Liquid Metal
• Quantum Phase Transition in Frustrated Two-Dimensional Antiferromagnets
• Theory of single-particle properties of the Hubbard model
• Non-Fermi Liquid Behavior In Quantum Critical Systems
• Quasiparticle spectrum in a nearly antiferromagnetic Fermi liquid: shadow and flat bands

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• A Vertex Correction in the Gap Equation for the High Temperature Superconductors
• Vertex Corrections in the Spin-fluctuation-induced Superconductivity