Quantum transport in three-dimensional Weyl electron system in the presence of charged impurity scattering

We theoretically study the quantum transport in a three-dimensional Weyl electron system in the presence of the charged impurity scattering using a self-consistent Born approximation. The scattering strength is characterized by the effective fine-structure constant $\alpha$, which depends on the dielectric constant and the Fermi velocity of the linear band. We find that the Boltzmann theory fails at the band touching point, where the conductivity takes a nearly constant value almost independent of $\alpha$, even though the density of states linearly increases with $\alpha$. There the magnitude of the conductivity only depends on the impurity density. The qualitative behavior is quite different from the case of the Gaussian impurities, where the minimum conductivity vanishes below a certain critical impurity strength.

Figure 1

Boltzmann conductivity [Eq. (16)] plotted as a function of the Fermi energy.

Figure 2

Density of states calculated by the SCBA, as a function of the Fermi energy at several values of $\alpha$.

Figure 3

Conductivity as a function of the Fermi energy in different plot ranges. In each panel, the solid lines represent the SCBA and the dashed lines represent the Boltzmann theory. The inset in (b) shows the detailed plot for the SCBA conductivity around the Weyl point.

Figure 4

Density of states and the conductivity as a function of $\alpha$. The solid line represents the numerical result and the dashed line represents the approximate analytical expression (see text).

Figure 5

The diagrammatic representations of (a) the self-energy for the SCBA and (b) the leading correction term for the SCBA.