Quantum oscillations and three-dimensional quantum Hall effect in ZrTe$_5$

Recent experiments have reported a lot of spectacular transport properties in topological materials, such as quantum oscillations and three-dimensional (3D) quantum Hall effect (QHE) in ZrTe$_5$. In this paper, by using a strong topological insulator model to describe ZrTe$_5$, we study the magnetotransport property of the 3D system. With fixed carrier density, we find that there exists a deferring effect in the chemical potential, which favors distinguishing the saddle points of the inverted LLs. On the other hand, with fixed chemical potential, the features of 3D QHE are demonstrated and we attribute the underlying mechanisms to the interplay between Dirac fermions, magnetic field and impurity scatterings.