Optical conductivity of a metal near an Ising-nematic quantum critical point

TL;DR

This paper investigates the optical conductivity behavior of a two-dimensional metal near an Ising-nematic quantum critical point, revealing how Fermi surface shape influences frequency scaling and identifying distinct scaling laws for different geometries.

Contribution

It provides a detailed analysis of optical conductivity near a nematic quantum critical point, highlighting the role of Fermi surface shape and deriving specific frequency scaling laws.

Findings

Optical conductivity scales as |ω|^{2/3} for isotropic and convex Fermi surfaces.

Leading order terms cancel for isotropic and convex Fermi surfaces, leaving subleading contributions.

For concave Fermi surfaces, the dominant term scales as |ω|^{-2/3}.

Abstract

We study the optical conductivity of a pristine two-dimensional electron system near an Ising-nematic quantum critical point. We discuss the relation between the frequency scaling of the conductivity and the shape of the Fermi surface, namely, whether it is isotropic, convex, or concave. We confirm the cancellation of the leading order terms in the optical conductivity for the cases of isotropic and convex Fermi surfaces and show that the remaining contribution scales as $|\omega|^{2/3}$ at $T=0$. On the contrary, the leading term, $\propto |\omega|^{-2/3}$, survives for a concave FS. We also address the frequency dependence of the optical conductivity near the convex-to-concave transition. Explicit calculations are carried out for the Fermi-liquid regime using the modified (but equivalent to the original) version of the Kubo formula, while the quantum-critical regime is accessed by employing the space-time scaling of the $Z=3$ critical theory.