Ballistic transport in disordered Dirac and Weyl semimetals

We study the dynamics of Dirac and Weyl electrons in disordered point-node semimetals. The ballistic feature of the transport is demonstrated by simulating the wave-packet dynamics on lattice models. We show that the ballistic transport survives under a considerable strength of disorder up to the semimetal-metal transition point, which indicates the robustness of point-node semimetals against disorder. We also visualize the robustness of the nodal points and linear dispersion under broken translational symmetry. The speed of the wave packets slows down with increasing disorder strength, and vanishes toward the critical strength of disorder, hence becoming the order parameter. The obtained critical behavior of the speed of the wave packets is consistent with that predicted by the scaling conjecture.

Figure 1

(a) Time evolution of wave packets for DSM at (a) the clean limit $W=0$, (b) a weak disorder $W=3$, and (c) a strong disorder $W=6$. The vertical axis is $F(x,t)$, and the horizontal axis is distance from the center of the initial wave packet $x-x_0$. The size of the cross section $L=35$.

Figure 2

(a) Traveled distance of the peak of wave packet $r$ as a function of time $t$ at $W=6$, $L=95$, averaged over 200 samples. The solid line is a linear fitting. (b) Speed of ballistic mode $v\left(L\right)$ in Q1D DSM samples with $W=6$ as a function of cross-section size $L$. The solid line is a fitting curve Eq. (14).

Figure 3

Speed of ballistic mode in the 3D limit $v=v(L\to \infty )$ as a function of disorder strength $W$, in (a) DSM and (b) WSM. The solid line is a fitting curve Eq. (13) with $W_{\text{c}}=6.4$ and $\nu =0.8$ for DSM, and $W_{\text{c}}=6.3$ and $\nu =0.9$ for WSM.

Figure 4

Spectral feature ${\rho }_{(k_x,0,0)}\left(E\right)$ of disordered (a)–(d) DSM and (e)–(h) WSM with different disorder strengths: (a), (e) clean; (b), (f) weak; (c), (g) strong; and (d), (h) critical. The horizontal axis is $k_x$ and the vertical axis is $E$. The system size is $360\times 50\times 50$ sites for DSM and $360\times 100\times 100$ sites for WSM. Averaged over up to six samples.