Examining the validity of the two-dimensional conical model to describe the three-dimensional ZrTe5

Understanding the low-energy excitation state in three-dimensional layered compound ${\mathrm{ZrTe}}₅$ remains a challenging problem in the study of novel topological materials. Recently, a two-dimensional conical model was proposed to explain the experimental optical spectroscopy in the 3D ${\mathrm{ZrTe}}₅$, Martino et al. [Phys. Rev. Lett. 122, 217402 (2019)]. Motivated by this work, in this paper, we perform a systematic theoretical study on the optical conductivity of this model in both cases without and with an external magnetic field to further demonstrate the validity of this model and to recover new physics. We find that there exist completely different characteristics for optical conductivity along different directions, due to anisotropic low-energy excitations in this two-dimensional conical model. Specifically, for the interband optical conductivity, we find asymptotic dependence on the optical frequency as $\mathrm{Re}({\ensuremath{\sigma}}_x)\ensuremath{\sim}{\ensuremath{\omega}}^{\frac{1}{2}}$ and $\mathrm{Re}({\ensuremath{\sigma}}_z)\ensuremath{\sim}{\ensuremath{\omega}}^{\frac{3}{2}}$, which are universal both in the gapped insulator phase and Weyl semimetal phase. For the magneto-optical conductivity, on the contrary, $\mathrm{Re}({\ensuremath{\sigma}}_x/z^B)$ shows distinct signatures in the gapped insulator phase and Weyl semimetal phase, which can help distinguish the two phases. Our results, to be verified in future experiments, could provide more insights into the understanding of the topological nature of ${\mathrm{ZrTe}}₅$.