Marginal Fermi Liquid with a Two-Dimensional Patched Fermi Surface

TL;DR

This paper models a two-dimensional Fermi surface with patches and flat regions to explain marginal Fermi liquid behavior observed in cuprates, revealing instability of Fermi liquid theory due to flat sectors.

Contribution

It introduces a patched Fermi surface model with flat regions to demonstrate the emergence of marginal Fermi liquid behavior through renormalization group analysis.

Findings

Self-energy scales as ω ln ω, indicating marginal Fermi liquid behavior.

Forward scattering coupling is never infrared stable due to flat FS sectors.

Fermi liquid state is destabilized within each FS patch.

Abstract

We consider a model composed of Landau quasiparticle states with patched Fermi surfaces (FS) sandwiched by states with flat FS to simulate the ``cold'' spot regions in cuprates. We calculate the one particle irreducible function and the self-energy up to two-loop order. Using renormalization group arguments we show that in the forward scattering channel the renormalized coupling constant is never infrared stable due to the flat FS sectors. Furthemore we show that the self-energy scales with energy as ${\rm Re} \Sigma \sim \omega \ln \omega $ as $\omega \to 0$, and thus the Fermi liquid state within each FS patch is turned into a marginal Fermi liquid.