Quantum Transport of Disordered Weyl Semimetals at the Nodal Point

Weyl semimetals are paradigmatic topological gapless phases in three dimensions. We here address the effect of disorder on charge transport in Weyl semimetals. For a single Weyl node with energy at the degeneracy point and without interactions, theory predicts the existence of a critical disorder strength beyond which the density of states takes on a nonzero value. Predictions for the conductivity are divergent, however. In this work, we present a numerical study of transport properties for a disordered Weyl cone at zero energy. For weak disorder, our results are consistent with a renormalization group flow towards an attractive pseudoballistic fixed point with zero conductivity and a scale-independent conductance; for stronger disorder, diffusive behavior is reached. We identify the Fano factor as a signature that discriminates between these two regimes.

Figure 1

Dimensionless conductance $g$ referred to a cubic sample of size $L$ (top) and Fano factor $F$ (bottom) for a single Weyl cone with a random potential for disorder strengths $K=1$, 2, and 3 in the pseudoballistic regime. The data represent a disorder average over at least 10 realizations. The dashed lines refer to the clean limits $g_0$ and $F_0$ for an isotropic Weyl cone ($c=1$). For comparison, diffusive scaling of $g$ for $K=6$, 10 is shown in the insets.

Figure 2

Resistance $R$ (top) and Fano factor $F$ (bottom) for a single Weyl cone vs system length $L$, for disorder strengths $K=6$, 10, and 18. The thin solid lines indicate the linear fit for the conductivity $\sigma$. The dashed lines refer to the pseudoballistic and diffusive limits for the Fano factor $F$. The data represent a disorder average over at least 100 realizations.

Figure 3

Conductivity $\sigma$ for the disordered Weyl cone as a function of the disorder strength $K$. The data represent a disorder average over at least 50 disorder realizations. The dashed line refers to the SCBA theory of Ref. [31].

Figure 4

Diagrammatic representation of the SCBA self-energy ${\mathrm{\Sigma }}^{\text{SCBA}}$ (a) and the leading correction $\delta \mathrm{\Sigma }$ (b). The double solid lines denote the SCBA propagator; dashed lines are disorder correlators.