  Understanding the low-energy excitation state in three-dimensional layered
compound ZrTe5 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 ZrTe5, 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
Re(\sigma_x)\sim\omega^{1/2} and Re(\sigma_z)\sim{\omega}^{3/2}, which are
universal both in the gapped insulator phase and Weyl semimetal phase. For the
magneto-optical conductivity, on the contrary, Re(\sigma^B_{x/z}) 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 ZrTe5.
