Intrinsic optical absorption in Dirac metals

TL;DR

This paper investigates how electron-electron and electron-hole interactions influence optical absorption in Dirac metals below the direct threshold, revealing specific scaling behaviors and the overshadowing of Auger-Meitner processes.

Contribution

It provides a comprehensive analytical and numerical analysis of interaction effects on optical conductivity in 2D and 3D Dirac metals below the threshold, highlighting the dominance of certain scattering processes.

Findings

Optical conductivity scales as Ω²lnΩ in 2D and Ω² in 3D for low frequencies.

Auger-Meitner processes contribute a threshold singularity but are overshadowed by other interactions.

Reσ(Ω) remains small across most of the sub-threshold frequency range.

Abstract

A Dirac metal is a doped (gated) Dirac material with the Fermi energy ($E_\text{F}$) lying either in the conduction or valence bands. In the non-interacting picture, optical absorption in gapless Dirac metals occurs only if the frequency of incident photons ($\Omega$) exceeds the direct (Pauli) frequency threshold, equal to $2E_\text{F}$. In this work, we study, both analytically and numerically, the role of electron-electron ($ee$) and electron-hole ($eh$) interactions in optical absorption of two-dimensional (2D) and three-dimensional (3D) Dirac metals in the entire interval of frequencies below $2E_\text{F}$. We show that, for $\Omega\ll E_\text{F}$, the optical conductivity, $\Re\sigma(\Omega)$, arising from the combination of $ee$ and certain $eh$ scattering processes, scales as $\Omega^2\ln\Omega$ in 2D and as $\Omega^2$ in 3D, respectively, both for short-range (Hubbard) and long-range (screened Coulomb) interactions. Another type of $eh$ processes, similar to Auger-Meitner (AM) processes in atomic physics, starts to contribute for $\Omega$ above the direct threshold, equal to $E_\text{F}$. Similar to the case of doped semiconductors with parabolic bands studied in prior literature, the AM contribution to $\Re\sigma(\Omega)$ in Dirac metals is manifested by a threshold singularity, $\Re\sigma(\Omega)\propto (\Omega-E_\text{F})^{d+2}$, where $d$ is the spatial dimensionality and $0<\Omega-E_\text{F}\ll E_\text{F}$. In contrast to doped semiconductors, however, the AM contribution in Dirac metals is completely overshadowed by the $ee$ and other $eh$ contributions. Numerically, $\Re\sigma(\Omega)$ happens to be small in almost the entire range of $\Omega<2E_\text{F}$. This finding may have important consequences for collective modes in Dirac metals lying below $2E_\text{F}$.