Quantum-oscillation-modulated angular dependences of the positive longitudinal magnetoconductivity and planar Hall effect in Weyl semimetals

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 is found that, in the weak magnetic field regime, the LMC and planar Hall conductivity (PHC) obey $\cos^{6}\theta$ and $\cos^{5}\theta\sin \theta$ 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 $\cos\theta\sin\theta$ 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.