Revealing temperature evolution of the Dirac band in ${\mathrm{ZrTe}}_{5}$ via magnetoinfrared spectroscopy

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Revealing temperature evolution of the Dirac band in ${ZrTe}_{5}$ via magnetoinfrared spectroscopy

Yuxuan Jiang, Tianhao Zhao, Luojia Zhang, Qiang Chen, Haidong Zhou, Mykhaylo Ozerov, Dmitry Smirnov, and Zhigang Jiang

Phys. Rev. B 108, L041202 – Published 26 July 2023

Abstract

We report the temperature evolution of the Dirac band in semiconducting zirconium pentatelluride ( ${ZrTe}_{5}$ ) using magnetoinfrared spectroscopy. We find that the band gap is temperature independent at low temperatures and increases with temperature at elevated temperatures. Although such an observation seems to support a weak topological insulator phase at all temperatures and defy the previously reported topological phase transition (TPT) at an intermediate temperature in ${ZrTe}_{5}$ , we show that it is also possible to explain the observation by considering the effect of conduction-valence band mixing and band inversion with a strong topological insulator phase at low temperatures. Our work provides an alternative picture of the band gap evolution across TPT.

Received 26 January 2023
Accepted 13 July 2023

DOI:https://doi.org/10.1103/PhysRevB.108.L041202

Physics Subject Headings (PhySH)

Landau levels Topological insulators

Dirac semimetal

Fourier transform infrared spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yuxuan Jiang ^1,2,*, Tianhao Zhao³, Luojia Zhang³, Qiang Chen ⁴, Haidong Zhou⁴, Mykhaylo Ozerov⁵, Dmitry Smirnov⁵, and Zhigang Jiang ^3,†

¹School of Physics and Optoelectronics Engineering, Anhui University, Hefei 230601, China
²Center of Free Electron Laser and High Magnetic Field, Anhui University, Hefei 230601, China
³School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
⁴Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA
⁵National High Magnetic Field Laboratory, Tallahassee, Florida 32310, USA

^*yuxuan.jiang@ahu.edu.cn
^†zhigang.jiang@physics.gatech.edu

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Vol. 108, Iss. 4 — 15 July 2023

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Figure 1
(a) Crystal structure of ${ZrTe}_{5}$ in the $b − c$ plane. (b) Schematic illustration of a volume expansion induced TPT and the associated low-energy band structure around $Γ$ point. Here, $2 Δ$ is the band gap. The WTI phase is expected to have a normal band gap in the bulk, similar to that of NI. The red and blue colors denote the conduction and valence band characters in different energy bands. (c) Temperature dependence of the lattice constants along different crystallographic directions, determined by x-ray powder diffraction measurements. (d) Temperature-dependent resistance for the Te-flux grown ${ZrTe}_{5}$ . The curve is normalized to the resistance value at 300 K.
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Figure 2
(a) Magnetic field dependence of normalized magnetotransmission spectra, $T (B) / T (0 T)$ , of ${ZrTe}_{5}$ measured at 6 K from 1 T to 4.5 T. (b) Temperature-dependent magnetotransmission spectra, $T (B) / T (0 T)$ , of ${ZrTe}_{5}$ from 6 K to 175 K at 1.5 T. The integer index $n$ labels the interband LL transitions $L_{- n (- n - 1)} \to L_{n + 1 (n)}$ . The asterisk symbol ( $*$ ) indicates the second set of LL transitions, a hallmark of the STI phase in ${ZrTe}_{5}$ at low temperatures [36]. A CR mode emerges at elevated temperatures, which can be attributed to the $L_{- 1} \to L_{0^{-}}$ transition. (c) False color map of the temperature evolution of the normalized magnetotransmission spectra, $T (B) / T (0 T)$ , of ${ZrTe}_{5}$ measured at 3 T. The symbols and lines denote the CR (red symbol) and interband $n = 0$ (orange symbol) transition energies calculated from the band parameters extracted from the model fitting of the interband LL transitions. The corresponding raw spectra of (c) are shown in Fig. 6 in the Appendix. All measurements are performed with $B ∥ b$ axis. The spectra are offset vertically for clarity in (a) and (b).
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Figure 3
Magnetic field dependence of LL transitions at selected temperatures of (a) $T = 6$ K, (b) 105 K, and (c) 175 K. The black squares are the experimentally extracted transition energies, and the size of the squares is larger than the uncertainty of the transition energies. The solid lines are the best fits to the data using the massive Dirac fermion model (1). (d) Representative Landau fan diagram for $T = 175$ K. The LLs are labeled by the index $n = 0, 1, 2, . . .$ , and their corresponding LL transitions $L_{- n (- n - 1)} \to L_{n + 1 (n)}$ are color-coded consistent with those in (a)–(c). Due to the electron-hole symmetry at low fields, the $Δ n = \pm 1$ transitions degenerate.
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Figure 4
(a) Temperature dependence of the extracted Fermi velocities and band gaps. The error bars are determined from the LL transition energy uncertainties. (b and c) Schematic drawings of the band structure evolution as a function of temperature for two possible scenarios that can describe our experiment.
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Figure 5
Normalized magnetotransmission spectra measured from $B = 1$ T to 5 T with a step size of 0.5 T under a fixed temperature. The selected temperatures are (a) 40 K, (b) 85 K, (c) 130 K, and (d) 175 K. In each panel, the spectra are offset vertically for clarity.
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Figure 6
Temperature-dependent normalized magnetotransmission spectra measured from 20 K to 175 K at 3 T. The spectra are offset vertically for clarity.
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Physical Review B

covering condensed matter and materials physics

Revealing temperature evolution of the Dirac band in ${ZrTe}_{5}$ via magnetoinfrared spectroscopy

Yuxuan Jiang, Tianhao Zhao, Luojia Zhang, Qiang Chen, Haidong Zhou, Mykhaylo Ozerov, Dmitry Smirnov, and Zhigang Jiang

Phys. Rev. B 108, L041202 – Published 26 July 2023

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Physical Review B

covering condensed matter and materials physics

Revealing temperature evolution of the Dirac band in ZrTe5 via magnetoinfrared spectroscopy

Yuxuan Jiang, Tianhao Zhao, Luojia Zhang, Qiang Chen, Haidong Zhou, Mykhaylo Ozerov, Dmitry Smirnov, and Zhigang Jiang

Phys. Rev. B 108, L041202 – Published 26 July 2023

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Revealing temperature evolution of the Dirac band in ${ZrTe}_{5}$ via magnetoinfrared spectroscopy