Non-Drude universal scaling laws for the optical response of local Fermi liquids

TL;DR

This paper derives universal scaling laws for the optical response of local Fermi liquids, revealing non-Drude features that serve as signatures of Fermi-liquid behavior and differ from traditional models.

Contribution

It provides explicit analytical expressions for the optical conductivity and memory function, demonstrating universal scaling laws and identifying non-Drude features in Fermi liquids.

Findings

Universal scaling forms for optical conductivity and memory function.

Non-Drude 'foot' in optical conductivity as a Fermi-liquid signature.

Excellent agreement between analytical laws and numerical DMFT results.

Abstract

We investigate the frequency and temperature dependence of the low-energy electron dynamics in a Landau Fermi liquid with a local self-energy. We show that the frequency and temperature dependencies of the optical conductivity obey universal scaling forms, for which explicit analytical expressions are obtained. For the optical conductivity and the associated memory function, we obtain a number of surprising features that differ qualitatively from the Drude model and are universal characteristics of a Fermi liquid. Different physical regimes of scaling are identified, with marked non-Drude features in the regime where hbar omega ~ kB T. These analytical results for the optical conductivity are compared to numerical calculations for the doped Hubbard model within dynamical mean-field theory. For the "universal" low-energy electrodynamics, we obtain perfect agreement between numerical calculations and analytical scaling laws. Both results show that the optical conductivity displays a non-Drude "foot", which could be easily mistaken as a signature of breakdown of the Fermi liquid, while it actually is a striking signature of its applicability. The aforementioned scaling laws provide a quantitative tool for the experimental identification and analysis of the Fermi-liquid state using optical spectroscopy, and a powerful method for the identification of alternative states of matter, when applicable.