Three-dimensional nature of the band structure of ${\mathrm{ZrTe}}_{5}$ measured by high-momentum-resolution photoemission spectroscopy

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Three-dimensional nature of the band structure of ${ZrTe}_{5}$ measured by high-momentum-resolution photoemission spectroscopy

H. Xiong, J. A. Sobota, S.-L. Yang, H. Soifer, A. Gauthier, M.-H. Lu, Y.-Y. Lv, S.-H. Yao, D. Lu, M. Hashimoto, P. S. Kirchmann, Y.-F. Chen, and Z.-X. Shen

Phys. Rev. B 95, 195119 – Published 10 May 2017

Abstract

We have performed a systematic high-momentum-resolution photoemission study on ${ZrTe}_{5}$ using 6-eV photon energy. We have measured the band structure near the $Γ$ point, and quantified the gap between the conduction and valence band as $18 \leq Δ \leq 29$ meV. We have also observed photon-energy-dependent behavior attributed to final-state effects and the three-dimensional (3D) nature of the material's band structure. Our interpretation indicates the gap is intrinsic and reconciles discrepancies on the existence of a topological surface state reported by different studies. The existence of a gap suggests that ${ZrTe}_{5}$ is not a 3D strong topological insulator nor a 3D Dirac semimetal. Therefore, our experiment is consistent with ${ZrTe}_{5}$ being a 3D weak topological insulator.

Received 21 January 2017

DOI:https://doi.org/10.1103/PhysRevB.95.195119

Physics Subject Headings (PhySH)

Electronic structure Topological phases of matter

Photoemission spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

H. Xiong^1,2, J. A. Sobota^1,2,3, S.-L. Yang^1,2, H. Soifer², A. Gauthier^1,2, M.-H. Lu⁴, Y.-Y. Lv⁴, S.-H. Yao⁴, D. Lu⁵, M. Hashimoto⁵, P. S. Kirchmann², Y.-F. Chen^4,6, and Z.-X. Shen^1,2,*

¹Geballe Laboratory for Advanced Materials, Departments of Physics and Applied Physics, Stanford University, Stanford, California 94305, USA
²Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA
³Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
⁴National Laboratory of Solid State Microstructures, Department of Materials Science and Engineering, Nanjing University, Nanjing, Jiangsu 210093, China
⁵Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA
⁶Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, Jiangsu 210093, China

^*zxshen@stanford.edu

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Vol. 95, Iss. 19 — 15 May 2017

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Figure 1
(a–d) Band dispersion measured along the $k_{a}$ axis in momentum space; the cuts are taken at $k_{c} = 0, 0.03, 0.06, and 0.12 Å^{- 1}$ [red dashed lines in (e)]. (e–i) Constant energy contour mapping at different energy cuts: $E - E_{F} = 0, - 0.06, - 0.11, - 0.21, and - 0.31$ eV [red dashed lines in (a)]. These measurements were performed using 5.90-eV photon energy at 20 K.
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Figure 2
(a) The spectrum containing both CB and VB with a gap in between. (b–d) MDCs at corresponding binding energies in (a). (e) Within a $0.05 − Å^{- 1}$ momentum range, both CB and VB dispersions are extracted from MDC fitting (blue dots). We use two different models to fit the band structure. A simple linear extrapolation fitting gives a gap size of $18 \pm 2$ meV (green lines); another more complex model (see main text) gives a gap size of $29 \pm 7$ meV (red curves). These measurements were performed using 5.90-eV photon energy at 20 K.
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Figure 3
(a) There is a monotonic binding-energy shift when the temperature increases from 20 to 300 K. The band top is extrapolated (intersections of the dashed lines) and shifts from below to above $E_{F}$ . (b) The momentum-integrated energy distribution curve is used to extract the low-energy cutoff, which is then used to calculate the work function. (c) The energy of the VB top at different temperatures is plotted in blue squares; the work function at different temperatures is plotted in red circles. These measurements were performed using 6.02-eV photon energy. (d) The transport measurement shows the resistivity along the $a$ -axis peaks at 140 K, falling into the shaded region in (c).
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Figure 4
(a,b) Illustrations showing that photons with different energies photoemit electrons with different initial-state momenta along the $k_{b}$ axis. Both the initial- and final-state dispersions are plotted along $k_{b}$ . The bottom row shows that for each photon energy, instead of a single $k_{b}$ , a Lorentzian distribution centered at $k_{b 0}$ with width $σ$ contributes to the photoemission process. Due to the Bloch-like final state, even a small change of photon energy shifts $k_{b 0}$ by a significant portion of the Brillouin zone. (c) Band dispersion at different $k_{b}$ constructed to phenomenologically reproduce the experiment. (d,e) Simulated spectra with $σ = 0.3 π / b$ at $k_{b 0} = 0, π / 2 b$ , respectively. The parameters are chosen to reproduce the experiments. (f,g) ARPES spectra measured at $h ν = 5.90$ and 5.64 eV, respectively.
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Figure 5
(a–c) ARPES spectra measured using photon energies $h ν = 6.02, 5.90, and 5.78$ eV. (d–f) Spectra processed by the minimum gradient method [30], each corresponding to the red rectangular region in (a–c). The red dashed curves are guides to the eye following the intensity peaks, and the yellow arrow shows where the “momentum switching” occurs.
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Physical Review B

covering condensed matter and materials physics

Three-dimensional nature of the band structure of ${ZrTe}_{5}$ measured by high-momentum-resolution photoemission spectroscopy

H. Xiong, J. A. Sobota, S.-L. Yang, H. Soifer, A. Gauthier, M.-H. Lu, Y.-Y. Lv, S.-H. Yao, D. Lu, M. Hashimoto, P. S. Kirchmann, Y.-F. Chen, and Z.-X. Shen

Phys. Rev. B 95, 195119 – Published 10 May 2017

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Physical Review B

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Three-dimensional nature of the band structure of ZrTe5 measured by high-momentum-resolution photoemission spectroscopy

H. Xiong, J. A. Sobota, S.-L. Yang, H. Soifer, A. Gauthier, M.-H. Lu, Y.-Y. Lv, S.-H. Yao, D. Lu, M. Hashimoto, P. S. Kirchmann, Y.-F. Chen, and Z.-X. Shen

Phys. Rev. B 95, 195119 – Published 10 May 2017

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Three-dimensional nature of the band structure of ${ZrTe}_{5}$ measured by high-momentum-resolution photoemission spectroscopy