Short Note on the Density of States in 3D Weyl Semimetals

The average density of states in a disordered three-dimensional Weyl system is discussed in the case of a continuous distribution of random scattering. Our results clearly indicate that the average density of states does not vanish, reflecting the absence of a critical point for a metal-insulator transition. This calculation supports recent suggestions of an avoided quantum critical point in the disordered three-dimensional Weyl semimetal. However, the effective density of states can be very small such that the saddle-approximation with a vanishing density of states might be valid for practical cases.

Figure 1

Poles of the one-particle Green’s function and the Cauchy-Lorentz distribution. The contour of the $U_{\mathbf{r}}$ integration encloses only one pole of the Cauchy-Lorentz distribution but not the other poles.

Figure 2

Dividing the system into cubes $\{S\}$ of size $|S|$ with boundary $\partial S$.