Temperature dependence of the energy band gap in ${\mathrm{ZrTe}}_5$: Implications for the topological phase

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

Figure 1

(a) Stacked plot of relative magnetoreflectivity spectra, $R_B\left(\omega \right)/R_0\left(\omega \right)$, collected on ${\mathrm{ZrTe}}_5$ at $T=80\mathrm{K}$ and plotted for selected values of $B$. (b) The false-color plot of $R_B/R_0$ plotted with a step of 40 mT. Weakly $B$-dependent features, nearly horizontal in the plot, are phonons, accompanied at low energies (below 10 meV) by an interference pattern. This appears since ${\mathrm{ZrTe}}_5$ becomes transparent at low energies when a sufficiently strong magnetic field is applied. The vertical line in (a) at 23 meV shows the position of the most pronounced phonon mode in ${\mathrm{ZrTe}}_5$ [18].

Figure 2

(a)–(e) False-color plots of the first field-derivative of relative magnetoreflectivity, $d/dB[R_B/R_0]$, measured at the temperature of $T=5,60,80,100$ and 120 K. (f)–(j) The extracted positions of resonances at a given magnetic field and temperature. The solid lines represent the fits of interband inter-LL transitions for the data collected below 1 T. The dashed lines represent extrapolations of these fits to higher magnetic fields and energies. Dotted horizontal lines show energies of the three most pronounced phonon modes (at 6, 11, and 23 meV) observed in Refs. [18, 19]. (k) The extracted energy band gap of ${\mathrm{ZrTe}}_5$ as a function of temperature. (l) The experimentally determined temperature dependence of the effective velocity parameter. (m) The resistance anomaly in the explored ${\mathrm{ZrTe}}_5$ sample, with the maximum of $R_S\left(T\right)$ around $T_p\approx 75\mathrm{K}$. The blue dots show the sample resistance during the first cooldown, the red circles before each run of the magneto-optical measurements at a given $T$. The temperature corresponding to the maximum in resistivity is marked by the vertical dashed lines in (k)–(m).