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. In this talk, we discuss the scaling of optical conductivity (OC) in the collisionless regime (ω»T) in the vicinity of a relativistic Gross-Neveu-Yukawa quantum critical point, separating two-dimensional (d=2) massless Dirac fermions from a fully gapped insulator or superconductor. In particular, we show that close to such a critical point a universal suppression of both the inter-band OC and the Drude peak (while maintaining its delta function profile) inside the critical regime occurs due to strongly coupled gapless fermionic and bosonic excitations [1]. We carry out the computation to the leading order in 1/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.

[1] B. Roy and V. Juričić, Phys. Rev. Lett. 121, 137601 (2018).