Magnetic-field-dependent intervalley relaxation time in Weyl semimetals

The zeroth Landau levels in Weyl semimetals (WSMs) are singular, which result in the anomalous nonsaturated positive longitudinal magnetoconductivity (LMC). The LMC exhibits periodic-in-$1/B$ quantum oscillations attributable to the the oscillating electron density of states in a magnetic field. The intervalley relaxation time ${\ensuremath{\tau}}^{a}$ is a key material parameter determining the magnitude of the LMC directly. In existing theories of the LMC, the magnetic field dependence of ${\ensuremath{\tau}}^{a}$ is usually neglected. Based upon the Boltzmann equation, we derive analytical expression for the intervalley relaxation time for short-range impurity scattering potential and arbitrary magnetic field strength. Taking the magnetic field dependence of ${\ensuremath{\tau}}^{a}$ into consideration, we find that the quantum oscillations of the LMC are enhanced. Numerical calculations are also carried out to verify the analytical derivations. Moreover, we provide an explanation for the anomalous behavior of the LMC observed in WSMs that the amplitude of LMC first increases and then decreases with increasing temperature.