| Summary: | In this paper, we give a systematic theoretical study on the Landau levels (LLs) and magneto-optical conductivity Re( σ _αα ) in a gapped Dirac semimetal model with mixed linear and parabolic dispersions under a magnetic field, which was recently proposed by Jiang et al (2020 Phys. Rev. Lett.
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125 046403 ) to explain the experimental magnetoinfrared spectroscopy in the three-dimensional ZrTe _5 crystal. We find that the strong magnetic field can drive the LLs become noninverted and thus the strong topological insulator phase in ZrTe _5 turns to be a trivial insulator. In the different magnetic field regions, the density of states and Re( σ _αα ) can exhibit distinct signatures. Moreover, when the magnetic field is weak, a qualitative relation in Re( σ _zz ) between the peaks at the saddle points is revealed as Re $({\sigma }_{zz}^{{\zeta }_{n}}) > $ Re $({\sigma }_{zz}^{{\Gamma}})$ , which is in good agreement with the experiment.
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