  Zirconium pentatelluride (ZrTe$_{5}$), a system with a Dirac linear band
across the Fermi level and anomalous transport features, has attracted
considerable research interest for it is predicted to be located at the
boundary between strong and weak topological insulators separated by a
topological semimetal phase. However, the experimental verification of the
topological phase transition and the topological ground state in ZrTe$_{5}$ is
full of controversies, mostly due to the difficulty of precisely capturing the
small gap evolution with single-particle band structure measurements.
Alternatively, the collective excitations of electric charges, known as
plasmons, in Dirac systems exhibiting unique behavior, can well reflect the
topological nature of the band structure. Here, using reflective
high-resolution electron energy loss spectroscopy (HREELS), we investigate the
temperature-dependent collective excitations of ZrTe$_{5}$, and discover that
the plasmon energy in ZrTe$_{5}$ is proportional to the $1/3$ power of the
carrier density $n$, which is a unique feature of plasmons in three-dimensional
Dirac systems. Based on this conclusion, the origin of the resistivity anomaly
of ZrTe$_{5}$ can be attributed to the temperature-dependent chemical potential
shift in extrinsic Dirac semimetals.
