Unraveling the Topological Phase of ${\mathrm{ZrTe}}_5$ via Magnetoinfrared Spectroscopy

For materials near the phase boundary between weak and strong topological insulators (TIs), their band topology depends on the band alignment, with the inverted (normal) band corresponding to the strong (weak) TI phase. Here, taking the anisotropic transition-metal pentatelluride ${\mathrm{ZrTe}}_5$ as an example, we show that the band inversion manifests itself as a second extremum (band gap) in the layer stacking direction, which can be probed experimentally via magnetoinfrared spectroscopy. Specifically, we find that the band anisotropy of ${\mathrm{ZrTe}}_5$ features a slow dispersion in the layer stacking direction, along with an additional set of optical transitions from a band gap next to the Brillouin zone center. Our work identifies ${\mathrm{ZrTe}}_5$ as a strong TI at liquid helium temperature and provides a new perspective in determining band inversion in layered topological materials.

Figure 1

(a) Schematic view of ${\mathrm{ZrTe}}_5$ unit cell. (b)–(d) Normalized magneto-IR spectra of ${\mathrm{ZrTe}}_5$ with the magnetic field applied along three principal crystal axes. To optimize the signal [35], the spectra with $B\parallel a$ axis (b) and $B\parallel c$ axis (c) are measured in Voigt reflection, while those with $B\parallel b$ axis (d) are measured in Faraday transmission. In (b)–(d), the interband LL transitions $L_{-n(-n-1)}\to L_{n+1(n)}$ are recognized as spectral peaks and labeled with integer $n=0,1,2,\dots$. All measurements are performed at liquid helium temperature ($T=4.2\mathrm{K}$), and the spectra are offset vertically for clarity.

Figure 2

(a)–(c) Magnetic field dependence of the extracted LL transition energies from Figs. 1 for $B\parallel a$ axis (a), $B\parallel c$ axis (b), and $B\parallel b$ axis (c), with the symbol size indicating the upper bound of errors in energy positions. The dash lines are best fits to the data using Eq. (2). When splitting occurs, the fit goes through the average energy of the two branches. The interband LL transitions $L_{-n(-n-1)}\to L_{n+1(n)}$ are labeled by integer $n=0,1,2,\dots$, consistent with that in Figs. 1. (d) Representative Landau fan diagram for the case of $B\parallel a$ axis. The red and blue lines correspond to the $s=\pm 1$ LLs, respectively.

Figure 3

(a),(b) Zero-field band structures of ${\mathrm{ZrTe}}_5$, calculated in the STI (a) and WTI (b) phases with different $v_{Fb}$. The PB component is kept the same in the calculation but with a positive (negative) sign for the STI (WTI) phase. For STI, two band extrema occur at $\mathrm{\Gamma }$ (red arrow) and $\zeta$ (black arrow) points when $v_{Fb}$ is sufficiently small. (c) Normalized magnetotransmission spectrum, $-T(B)/T(0\mathrm{T})$, of ${\mathrm{ZrTe}}_5$ measured at $B=0.4\mathrm{T}$ and $B\parallel b$ axis. The up triangles label the energy positions of the LL transitions from $\zeta$ (black) and $\mathrm{\Gamma }$ (red) points. (d),(e) Best fits to the magnetic field dependence of the LL transitions from $\mathrm{\Gamma }$ (d) and $\zeta$ (e) points using the simple massive Dirac fermion model of Eq. (1). The symbol size indicates the upper bound of errors in energy positions.