We propose a mechanism to directly measure the chiral anomaly in disorder Weyl semimetals (WSMs) by the Kondo effect. We find that in a magnetic and electric field driven WSM, the locations of the Kondo peaks can be modulated by the chiral chemical p
otential, which is proportional to $mathbf{E}cdot mathbf{B}$. The Kondo peaks come from spin fluctuations within the impurities, which apart from the temperature, relate closely to the hosts Fermi level. In WSMs, the chiral-anomaly-induced chirality population imbalance will shift the local Fermi levels of the paired Weyl valleys toward opposite directions in energy, and then affects the Kondo effect. Consequently, the Kondo effect can be tunable by an external electric field via the chiral chemical potential. This is unique to the chiral anomaly. Base on this, we argue that the electrically tunable Kondo effect can serve as a direct measurement of the chiral anomaly in WSMs. The Kondo peaks are robust against the disorder effect and therefore, the signal of the chiral anomaly survives for a relatively weak magnetic field.
We study the positive longitudinal magnetoconductivity (LMC) and planar Hall effect as emergent effects of the chiral anomaly in Weyl semimetals, following a recent-developed theory by integrating the Landau quantization with Boltzmann equation. It i
s found that, in the weak magnetic field regime, the LMC and planar Hall conductivity (PHC) obey $cos^{6}theta$ and $cos^{5}thetasin theta$ dependences on the angle $theta$ between the magnetic and electric fields. For higher magnetic fields, the LMC and PHC cross over to $cos^{2}theta$ and $costhetasintheta$ dependences, respectively. Interestingly, the PHC could exhibit quantum oscillations with varying $theta$, due to the periodic-in-$1/B$ oscillations of the chiral chemical potential. When the magnetic and electric fields are noncollinear, the LMC and PHC will deviate from the classical $B$-quadratic dependence, even in the weak magnetic field regime.
