  Three-dimensional topological insulators (3D TIs) represent novel states of
quantum matters in which surface states are protected by time-reversal symmetry
and an inversion occurs between bulk conduction- and valence-bands. However,
the bulk-band inversion which is intimately tied to the topologically
nontrivial nature of 3D TIs has rarely been investigated by experiments.
Besides, 3D massive Dirac fermions with nearly near band dispersions were
seldom observed in TIs. Recently, a van der Waals crystal, ZrTe5, was
theoretically predicted to be a TI. Here, we report an infrared transmission
study of a high-mobility (~33,000 cm$^2$/(Vs)) multilayer ZrTe5 flake at
magnetic fields ($B$) up to 35 T. Our observation of a linear relationship
between the zero-magnetic-field optical absorption and the photon energy, a
bandgap of ~10 meV and a $\sqrt{B}$ dependence of the Landau level (LL)
transition energies at low magnetic fields demonstrates 3D massive Dirac
fermions with nearly linear band dispersions in this system. More importantly,
the reemergence of the intra-LL transitions at magnetic fields higher than 17 T
reveals the energy cross between the two zeroth LLs, which reflects the
inversion between the bulk conduction- and valence-bands. Our results not only
provide spectroscopic evidence for the TI state in ZrTe5 but also open up a new
avenue for fundamental studies of Dirac fermions in van der Waals materials.
