Temperature dependence of the energy band gap in ZrTe$_5$: implications for the topological phase

Using Landau level spectroscopy, we determine the temperature dependence of the energy band gap in zirconium pentatelluride (ZrTe$_5$). We find that the band gap reaches $E_g=(5 \pm 1)$ meV at low temperatures and increases monotonously when the temperature is raised. This implies that ZrTe$_5$ is a weak topological insulator, with non-inverted ordering of electronic bands in the center of the Brillouin zone. Our magneto-transport experiments performed in parallel show that the resistivity anomaly in ZrTe$_5$ is not connected with the temperature dependence of the band gap.