Tomonaga-Luttinger liquid and localization in Weyl semimetals

We study both noncentrosymmetric and time-reversal breaking Weyl semimetal systems under a strong magnetic field with the Coulomb interaction. The three-dimensional bulk system is reduced to many mutually interacting quasi-one-dimensional wires. Each strongly correlated wire can be approached within the Tomonaga-Luttinger liquid formalism. Including impurity scatterings, we inspect the localization effect and the temperature dependence of the electrical resistivity. The effect of a large number of Weyl points in real materials is also discussed.

Figure 1

1D linear dispersions along $k_z$. There are two [four] Weyl points at $\pm k_0[\pm k_R,\pm k_L]$ with topological charges denoted by $\pm$ for the (a) TRB [(b) IB] case. We label 1D channels with chirality index $r=R/L$, written as $r=\pm 1$ in the calculation, in both cases and side index $j=\pm 1$ only in (b). $|\uparrow /\downarrow \rangle$ are pseudospin states. Two modes at each side in (b) have unequal Fermi velocities $v_R\ne v_L>0$ in general.

Figure 2

Exponents (a) $\gamma$ and (b) $\eta$ depend on $v_g$ and the number $N$ of opposite-chirality Weyl-point pairs. Left: TRB case ($v=1$). Right: IB case ($v_R=3,v_L=1$). Fermi velocities and the interaction strength measured in $v_g$ are in units of $\frac{k_e{e}^2}{h}$. $\gamma =1$ and $\eta =2$ for the noninteracting case.