Non-divergent Chiral Charge Pumping in Weyl Semimetal

Recent studies suggest that the nonlinear transport properties in Weyl semimetal may be a measurable consequence of its chiral anomaly. Nonlinear responses in transport are estimated to be substantial, because in real materials such as TaAs or Bi$_{1-x}$Sb$_x$, the Fermi level resides near the Weyl nodes where the chiral charge pumping is said to diverge. However, this work presents semiclassical Boltzmann analysis that indicates that the chiral charge pumping is non-divergent even at the zero-temperature limit. We demonstrate that the divergence in common semiclassical calculation scheme is not a problem of the scheme itself, but occurs because a commonly-used approximation of the change in particle number breaks down near the Weyl nodes. Our result suggests the possibility that the nonlinear properties in WSMs can be overestimated, and provides the validity condition for the conventional approximation. We also show the distinct Fermi level dependencies of the chiral magnetic effect and the negative longitudinal magnetoresistance, as a consequence of non-diverging chiral charge pumping.