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

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 $1\mathrm{/}{N}_f$- and $ϵ$-expansions, where $N_f$ counts fermion flavor number and $ϵ=3-d$. 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.