Optical conductivity of an interacting Weyl liquid in the collisionless regime

Optical conductivity can serve as an indispensable probe of correlation effects in a wide range of materials, from high-Tc superconductors, heavy fermion systems, Fe-based superconductors to graphene, as well as Weyl and Dirac semimetals. As we will show, the long range Coulomb interaction yields a universal enhancement of the zero-temperature optical conductivity that depends solely on the number of Weyl points at the Fermi level [1]. To this end, we use dimensional regularization about three spatial dimensions, since this regularization scheme explicitly preserves gauge invariance. The scaling of optical conductivity is a remarkable consequence of an interplay between the quantum-critical nature of an interacting Weyl liquid, marginal irrelevance of the long-range Coulomb interaction and the violation of hyperscaling in three spatial dimensions. Experimental consequences of this effect in recently discovered Weyl and Dirac materials will be outlined.

[1] B. Roy and V. Juricic, Phys. Rev. B 96, 155117 (2017).