Collisionless Transport Close to a Fermionic Quantum Critical Point in Dirac Materials

TL;DR

This paper investigates the universal behavior of optical conductivity near a relativistic quantum critical point in Dirac materials, revealing suppression effects due to strong fermion-boson coupling in the collisionless regime.

Contribution

It provides the first detailed calculation of optical conductivity scaling near a non-Gaussian quantum critical point in Dirac systems, including effects of Coulomb interactions and higher-dimensional generalizations.

Findings

Universal suppression of inter-band optical conductivity

Persistence of delta function in Drude peak

Quantitative predictions for Coulomb interaction effects

Abstract

Quantum transport close to a critical point is a fundamental, but enigmatic problem due to fluctuations, persisting at all length scales. We report the scaling of optical conductivity (OC) in the \emph{collisionless} regime ($\hbar \omega \gg k_B T$) in the vicinity of a relativistic quantum critical point, separating two-dimensional ($d=2$) massless Dirac fermions from a fully gapped insulator or superconductor. Close to such critical point gapless fermionic and bosonic excitations are strongly coupled, leading to a \emph{universal} suppression of the inter-band OC as well as of the Drude peak (while maintaining its delta function profile) inside the critical regime, which we compute to the leading order in $1/N_f$- and $\epsilon$-expansions, where $N_f$ counts fermion flavor number and $\epsilon=3-d$. Correction to the OC at such a non-Gaussian critical point due to the long-range Coulomb interaction and generalizations of these scenarios to a strongly interacting three-dimensional Dirac or Weyl liquid are also presented, which can be tested numerically and possibly from non-pertubative gauge-gravity duality, for example.