Dynamics of electric transport in interacting Weyl semimetals

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 ${\sigma }^{\prime }\left(\Omega \right)$ which is linear in frequency, exhibits an imaginary part ${\sigma }^{\prime \prime }\left(\Omega \right)$ 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 $\overline{\Omega }$) Fermi velocity $v$ is $\Delta {\sigma }^{\prime }\left(\Omega \right)=e^4\Omega /\left(9{\pi }^2\hslash v\right)[2\log (\Omega /\overline{\Omega })-5]$.

Figure 1

The response of the free Weyl semimetal to a dc electric field, multiplied by $t,$ is shown as a function of time. The current's asymptotic value of zero is approached powerwise.

Figure 2

The response of the free Weyl semimetal to an ac electric field (green lines) is shown as a function of time for two different frequencies (magenta lines). The value of $v/a$ is typically of order $\sim$$3\times {10}^{15}$ Hz.

Figure 3

(a) The real part and (b) the imaginary part of the ac conductivity of the Weyl semimetal (magenta line) are compared with those of a band insulator (red line) and of a metal (blue line). The parameter values are given in the text.

Figure 4

(a) The real part and (b) the imaginary part of the dielectric constant of the Weyl semimetal (magenta line) are compared with those of a band insulator (red line) and of a metal (blue line). The parameter values are given in the text.