Landau-level spectroscopy of massive Dirac fermions in single-crystalline ${\mathrm{ZrTe}}_5$ thin flakes

We report infrared magnetospectroscopy studies on thin crystals of an emerging Dirac material ${\mathrm{ZrTe}}_5$ near the intrinsic limit. The observed structure of the Landau-level transitions and zero-field infrared absorption indicate a two-dimensional Dirac-like electronic structure, similar to that in graphene but with a small relativistic mass corresponding to a 9.4-meV energy gap. Measurements with circularly polarized light reveal a significant electron-hole asymmetry, which leads to splitting of the Landau-level transitions at high magnetic fields. Our model, based on the Bernevig-Hughes-Zhang effective Hamiltonian, quantitatively explains all observed transitions, determining the values of the Fermi velocity, Dirac mass (or gap), electron-hole asymmetry, and electron and hole $g$ factors.

Figure 1

(a) Schematic view of ${\mathrm{ZrTe}}_5$ unit cell along the $a$ axis. The layer stacking direction is along the $b$ axis. (b) Extinction spectrum, $1-T/T_{\text{tape}}$, of ${\mathrm{ZrTe}}_5$/tape composite measured at $B=0$ T and $T=25$ K. The fast oscillations originate from the Fabry-Pérot interference. The gray stripes cover the opaque regions due to tape absorption. (c) Normalized transmission spectrum, $T\left(B\right)/T(B=0)$, measured at $B=2$ T and $T=4.2$ K. The black and blue curves correspond to the far-IR and the mid-IR spectrum, respectively. The red dashed lines mark the expected energies of $L_{-n(-n-1)}\to L_{n+1\left(n\right)}$ transitions for massless Dirac fermions. (d) Extracted LL transition energy from (c) as a function of LL index $n$. The red line shows the best fit to the data using Eq. (1).

Figure 2

(a) Normalized transmission spectra, $T\left(B\right)/T(B=0\text{T})$, of ${\mathrm{ZrTe}}_5$/tape composite measured at selected magnetic fields. The down triangles ($▾$) label the splitting of low-lying LL transitions, while the star symbols ($☆$) point to $B$-independent spectral features originating from the normalization process. (b) Zoom-in view of the fourfold splitting of the $L_{-1(-2)}\to L_{2\left(1\right)}$ transition taken at $B=8$ T and 10 T. In all panels, the spectra are offset vertically for clarity, and the gray stripes cover the opaque regions due to tape absorption.

Figure 3

Normalized transmission, $T\left(B\right)/T(B=6\text{T})$, through ${\mathrm{ZrTe}}_5$/tape composite as a function of magnetic field with unpolarized (black) and circularly polarized (red and green) incident IR light of 117 meV. The negative magnetic field sweep (green) is flipped to the positive side for ease of comparison. The fourfold splitting of the $L_{-1(-2)}\to L_{2\left(1\right)}$ transition is labeled by down triangles ($▾$) on the unpolarized data, which is offset vertically for clarity.

Figure 4

Fourfold splitting of the (a) $L_{0(-1)}\to L_{1\left(0\right)}$ and (b) $L_{-1(-2)}\to L_{2\left(1\right)}$ transitions as a function of magnetic field. Symbols represent the extracted transition energies from both the broad-band measurements at constant magnetic field and the QCL-based measurements at constant photon energy [20]. The color-coded lines show best fits to the data using Eqs. (2) and (3). The corresponding transitions are illustrated in the insets with the same color code. The solid and dashed lines denote the spin-conserved strong transitions and the spin-flipped weak transitions, respectively.