Semiclassical Boltzmann transport theory for multi-Weyl semimetals

Multi-Weyl semimetals (m-WSMs) are a new type of Weyl semimetal that have linear dispersion along one symmetry direction but anisotropic nonlinear dispersion along the two transverse directions with a topological charge larger than one. Using the Boltzmann transport theory and fully incorporating the anisotropy of the system, we study the dc conductivity as a function of carrier density and temperature. We find that the characteristic density and temperature dependence of the transport coefficients at the level of Boltzmann theory are controlled by the topological charge of the multi-Weyl point and distinguish m-WSMs from their linear Weyl counterparts.

Figure 1

Density dependence of dc conductivity (a)–(c) ${\sigma }_{xx}$ and (d)–(f) ${\sigma }_{zz}$ for charged impurities with $g\alpha =1000$. Here, ${\sigma }_0$ and $n_0$ are density-independent normalization constants in units of conductivity and density, respectively, defined in SM [19]. Red dashed lines represent analytic forms in the strong screening limit given by Eq. (24) in SM [19].

Figure 2

(a)–(c) $dlog{\sigma }_{xx}/dlogn$ and (d)–(f) $dlog{\sigma }_{zz}/dlogn$ as a function of the screening strength $g\alpha$ for charged impurities. Red dashed and blue dashed-dotted lines represent the density exponents obtained from $\zeta =\frac{1}{J}$ (or in the strong screening limit) and $\zeta =1$ in Eq. (9), respectively. Here, $n=n_0$ is used for the calculation.

Figure 3

${\sigma }_{xx}/{\sigma }_{zz}$ as a function of density for m-WSMs with $J=1,2,3$ for (a) short-range impurities, (b) charged impurities with $g\alpha =1000$, and (c) charged impurities with $g\alpha =1$. Dashed lines in (b) represent analytic forms in the strong screening limit given by Eq. (24) in SM [19].

Figure 4

Temperature dependence of dc conductivity (a)–(c) ${\sigma }_{xx}$ and (d)–(f) ${\sigma }_{zz}$ for charged impurities with $g\alpha =1000$. The insets in each panel show the low-temperature behavior. Red dashed and blue dashed-dotted lines represent fitting by Eq. (14) with $\zeta =\frac{1}{J}$ in the high- and low-temperature limits, respectively.