Non-Fermi Liquid Fixed Point in 2+1 Dimensions

TL;DR

This paper constructs models showing deviations from Fermi liquid behavior due to coupling with a Chern-Simons gauge field, revealing a new stable fixed point in 2+1 dimensions with potential relevance to quantum Hall states and high-temperature superconductors.

Contribution

It introduces a novel class of models with calculable non-Fermi liquid fixed points arising from gauge field interactions, expanding understanding of low-energy metallic states.

Findings

Fermi liquid fixed point is unstable for x<1

A new infrared-stable fixed point is identified in a (1-x)-expansion

Logarithmic approach to zero coupling at Coulomb interaction (x=1)

Abstract

We construct models of excitations about a Fermi surface that display calculable deviations from Fermi liquid behavior in the low-energy limit. They arise as a consequence of coupling to a Chern-Simons gauge field, whose fluctations are controlled through a ${1\over{k^x}}$ interaction. The Fermi liquid fixed point is shown to be unstable in the infrared for $x<1$, and an infrared-stable fixed point is found in a $(1-x)$-expansion, analogous to the $\epsilon$-expansion of critical phenomena. $x=1$ corresponds to Coulomb interactions, and in this case we find a logarithmic approach to zero coupling. We describe the low-energy behavior of metals in the universality class of the new fixed point, and discuss its possible application to the compressible $\nu={1\over2}$ quantum Hall state and to the normal state of copper-oxide superconductors.