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

## TL;DR

This paper investigates how the positive longitudinal magnetoconductivity and planar Hall effect in Weyl semimetals depend on magnetic field strength and orientation, revealing angle-dependent behaviors and quantum oscillations due to chiral anomaly effects.

## Contribution

It introduces a theoretical framework combining Landau quantization with Boltzmann equation to analyze angle and field strength effects on magnetotransport in Weyl semimetals.

## Key findings

- LMC and PHC follow specific angular dependences in weak magnetic fields.
- Quantum oscillations of PHC occur with varying angle due to chiral chemical potential.
- Deviations from classical B-quadratic dependence arise in noncollinear fields.

## Abstract

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.