Decoupling intranode and internode scattering in Weyl fermions

A series of recent papers claimed that intranode scattering alone can contribute to positive longitudinal magnetoconductance (LMC) due to the chiral anomaly (CA) in Weyl semimetals (WSMs) in the quasiclassical limit. We revisit the problem of CA-induced LMC in WSMs in the quasiclassical limit and show that intranode scattering, by itself, does not result in enhancement of LMC. In the limit of zero internode scattering, chiral charge must remain conserved, which is shown to actually decrease LMC. Only in the presence of a finite nonzero internode scattering does one obtain a positive LMC due to nonconservation of the chiral charge. Even weak internode scattering suffices in generating positive LMC since it redistributes charges across both the nodes, although on a timescale larger than that of the intranode scattering. Our work is fundamental to correctly interpret the recent experiments on magnetoconductance in Weyl semimetals that claim to have observed chiral anomaly. Furthermore, our calculations reveal that, in contrast to recent works, in inhomogeneous WSMs strain-induced axial magnetic field $B_5$, by itself, leads to negative longitudinal magnetoconductance and a negative planar Hall conductance.

Figure 1

(a) LMC for an isolated Weyl node is always negative due to chiral charge conservation. (b) ${\mathrm{\Lambda }}^{\chi }\left(\theta \right)$ between 0 and $\pi$ at $B=1T$. (c) The corresponding normalized deviation in the distribution function (proportional to $\delta g_{\mathbf{k}}^{\chi }$), which integrates to zero. Here $\chi =1$.

Figure 2

(a) LMC for a pair of Weyl nodes of opposite chiralities becomes negative beyond a critical intervalley scattering strength ${\alpha }_c$. Here $\alpha$ is increased from 0.1 to 1. (b) The normalized deviation in distribution functions at both the valleys for three different values of $\alpha$.

Figure 3

Conditions to observe positive or negative LMC.

Figure 4

(a) Strain-induced LMC for a pair of Weyl nodes of opposite chiralities is always negative. Here $\alpha$ is increased from 0.1 to 1. (b) The normalized deviation in distribution functions at both the valleys for three different values of $\alpha$. $B_5$ field is chosen parallel to $\mathbf{E}$.

Figure 5

(a) Minimal model of inversion asymmetric WSM with four nodes. Chirality of a node is indicated by $\chi$ and internode scattering from node $i$ to $j$ (and vice versa) is denoted by ${\alpha }^{ij}$. The sign of LMC as a function of internode scattering without strain is plotted in (b) and with only strain in (c). Strain, alone does not increase LMC.

Figure 6

(a) Planar Hall conductivity as a function of magnetic field in the absence of strain and (b) as a function of the axial magnetic field $B_5$ in the absence of external magnetic field. The angle of the magnetic field in (a) and axial field (b) are chosen to be the same.