Quantum theory of the magnetochiral anisotropy coefficient in ZrTe$_5$

Recent experiments performed the nonreciprocal magneotransport in ZrTe$_5$ and obtained a giant magnetochiral anisotropy (MCA) coefficient $\gamma'$. The existing theoretical analysis was based on the semiclassical Boltzmann equation. In this paper, we develop a full quantum theory to calculate $\gamma'$ and further explore the underlying physics. We reveal that the $xz$-mirror symmetry breaking term also breaks the parity symmetry of the system and leads to mixed selection rules and nonvanishing second-order conductivity $\sigma_{xxx}$. The calculations show that $\gamma'$ decreases with the magnetic field, survives only to weak impurity scatterings, and exhibits a nonmonotonous dependence on the strength of the $xz$-mirror symmetry breaking. Our paper can provide a deeper insight into the intrinsic nonreciprocal magnetotransport phenomena in the topological semimetal material.