Dynamics of electric transport in interacting Weyl semimetals

Abstract

The response to an electric field (dc and ac) of electronic systems in which the Fermi ``surface'' consists of a number of three-dimensional (3D) Weyl points (such as some pyrochlore iridates) exhibits a peculiar combination of characteristics usually associated with insulating and conducting behavior. Generically a neutral plasma in clean materials can be described by a tight-binding model with a strong spin-orbit interaction. A system of that type has a vanishing dc conductivity; however the current response to the dc field is very slow: The current decays with time in a powerwise manner, different from an insulator. The ac conductivity, in addition to a finite real part ${\ensuremath{\sigma}}^{\ensuremath{'}}(\ensuremath{\Omega})$ which is linear in frequency, exhibits an imaginary part ${\ensuremath{\sigma}}^{\ensuremath{'}\ensuremath{'}}(\ensuremath{\Omega})$ that increases logarithmically as a function of the UV cutoff (atomic scale). This leads to a substantial dielectric response like a large dielectric constant at low frequencies. This is in contrast to a two-dimensional (2D) Weyl semimetal-like graphene at a neutrality point where the ac conductivity is purely pseudodissipative. The Coulomb interaction between electrons is long range and sufficiently strong to make a significant impact on transport. The interaction contribution to the ac conductivity is calculated within the tight-binding model. The result for the real part expressed via the renormalized (at frequency $\overline{\ensuremath{\Omega}}$) Fermi velocity $v$ is $\ensuremath{\Delta}{\ensuremath{\sigma}}^{\ensuremath{'}}(\ensuremath{\Omega})={e}^{4}\ensuremath{\Omega}/(9{\ensuremath{\pi}}^{2}\ensuremath{\hbar}v)[2\mathrm{log}(\ensuremath{\Omega}/\overline{\ensuremath{\Omega}})\ensuremath{-}5]$.