Vanishing Density of States in Weakly Disordered Weyl Semimetals

The Brillouin zone of the clean Weyl semimetal contains points at which the density of states (DOS) vanishes. Previous work suggested that below a certain critical concentration of impurities this feature is preserved including in the presence of disorder. This result got criticized for its neglect of rare disorder fluctuations which might bind quantum states and hence generate a finite DOS. We here show that in spite of their existence these states are so fragile that their contribution effectively vanishes when averaged over continuous disorder distributions. This means that the integrity of the nodal points remains protected for weak disorder.

Figure 1

Top: phase shift $\delta (\omega )$ for three configurations, $\lambda =\pi /b+\mathrm{\Delta }$, $\mathrm{\Delta }=0.01$ (dashed curve), 0.02 (solid curve), 0.06 (dotted curve). With decreasing $\mathrm{\Delta }$, a resonance of width $\sim \mathrm{\Delta }$ moves closer to the origin. At the origin, $\delta (0)={\delta }^{\prime }(0)=0$ touches zero (inset). Bottom: the corresponding shift in the DOS $\delta \nu \equiv {\nu }_{\lambda }-{\nu }_0$ compared to the clean Weyl problem assumes the form of narrow peaks. Their positive spectral weight is screened by a negative background in such a way that $\nu (0)=0$, always (inset). This includes the limit, $\mathrm{\Delta }\to 0$, in which the singular derivative of the phase shift reflects the presence of a bound state.

Figure 2

Exemplary DOS of a system of two impurities ($r=15/M$, $U_1=-75/M^2$, $U_2=150/M^2$ in the units discussed in the text). Left inset: enlargement of the DOS near zero energy. Right inset: dashed curve, integrated spectral weight around the resonance centers; solid curve, the same for a resonance at zero energy.