Quantum theory of the magnetochiral anisotropy coefficient in ${\mathrm{ZrTe}}_5$

Recent experiments performed nonreciprocal magnetotransport studies in ${\mathrm{ZrTe}}_5$ and obtained a giant magnetochiral anisotropy (MCA) coefficient ${\gamma }^{\prime }$. The existing theoretical analysis was based on the semiclassical Boltzmann equation. In this paper, we develop a full quantum theory to calculate ${\gamma }^{\prime }$ 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 ${\gamma }^{\prime }$ decreases with the magnetic field, survives only to the weak impurity scatterings, and exhibits a nonmonotonous dependence on the strength of the $xz$-mirror symmetry breaking. In this paper, we provide deeper insights into the intrinsic nonreciprocal magnetotransport phenomena in the topological semimetal material.