The response to an electric field (DC and AC) of electronic systems in which the Fermi surface consists of a number of 3D Weyl points (such as some pyrochlore iridates) exhibits a peculiar combination of characteristics usually associated with insulating and conducting behaviour. 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 which is linear in frequency, exhibits an imaginary part that increases logarithmically as function of the UV cutoff (atomic scale). This leads to substantial dielectric response like a large dielectric constant at low frequencies. This is in contrast to a 2D Weyl semimetal like graphene at neutrality point where the AC conductivity is purely pseudo-dissipative. 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.
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