Research ArticlePHYSICS

Tunable Weyl and Dirac states in the nonsymmorphic compound CeSbTe

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Science Advances  23 Feb 2018:
Vol. 4, no. 2, eaar2317
DOI: 10.1126/sciadv.aar2317
  • Fig. 1 Refined neutron diffraction data taken at 5 K.

    Small impurity peaks were excluded from the refinement. The upper inset shows a scanning electron microscopy image of a typical crystal of CeSbTe, and the lower inset shows a drawing of the crystal structure of CeSbTe, where the nonsymmorphic symmetry elements are highlighted. arbs, arbitrary units; Obs, observed; Calc, calculated.

  • Fig. 2 Comparison of measured and calculated electronic structure of CeSbTe.

    (A) Calculated bulk band structure plotted along ΓMΓ (blue) in comparison to ZAZ (green). Along this path, the band structure is relatively 2D. All crossings at M are forced by nonsymmorphic symmetry. (B) Dispersion along ΓMΓ measured with ARPES. Except for the energy scaling, the measured band structure is in agreement with the calculations. The 4f states are highlighted in blue on the right side and with dashed lines on the left side. (C) Measured data overlaid with extracted maximal intensity data shown as red circles. The observed crossings at M are numerated. (D) Surface band structure calculation with surface-derived bands shown in red. The crossings at M are numerated analogous to the measured data.

  • Fig. 3 Magnetic properties of CeSbTe.

    (A) Temperature-dependent magnetic susceptibility; different colored lines represent different applied field strengths (Hc). (B) Field-dependent magnetic susceptibility; different colors represent different temperatures. Below TN, a field direction–dependent magnetic transition is observed that is reached at lower field strengths for Hc, but the saturation moment is reached faster with Hc. (C) Specific heat of CeSbTe. The magnetic transition is clearly visible at 2.7 K. The inset shows the behavior with different applied field strengths. (D) Refinement of neutron diffraction data taken at 1.5 K, below the magnetic transition. The lower panel shows the pure magnetic diffraction pattern, which was obtained by subtracting the 5-K data from the 1.5-K data. The region below the nuclear Bragg reflection was excluded from the refinement because of the irregular background caused by small changes in the cell parameters between the two temperatures. Arrows point to the main magnetic Bragg peak, indicating the doubling of the unit cell. emu, electromagnetic unit; f.u., formula unit.

  • Fig. 4 Magnetic phase diagram of CeSbTe.

    Three different regions can be observed within a low field limit. The magnetic structures of the different phases are shown in the respective regions. Different colors indicate different samples and different symbols indicate different measurement techniques.

  • Fig. 5 Band structure of CeSbTe.

    (A) Calculated paramagnetic band structure including SOC. The green and orange boxes highlight the nonsymmorphic Dirac and the tilted Dirac crossing, respectively. (B) Symmetry groups of the different accessible phases (for drawings of the respective magnetic structures, see fig. S13). (C) Detailed plots of the region around the X point and how different types of magnetic order affect the electronic structure. (D) Detailed plots of the region along ΓZ and the effect of magnetic order.

  • Fig. 6 Band structure of the AFM phase of CeSbTe plotted for lower energies to highlight the degeneracies at the A point.

    Two crossing points are highlighted, with the lower one showing a true eightfold degeneracy.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/2/eaar2317/DC1

    Supplementary Text

    fig. S1. Electron diffraction on CeSbTe.

    fig. S2. Analysis of neutron powder diffraction data.

    fig. S3. Refinement of the pure magnetic Bragg peaks, obtained by subtraction of the 5-K data from the 1.5-K data with respect to the two possible different magnetic structures.

    fig. S4. Energy dispersions of CeSbTe along high-symmetry lines.

    fig. S5. Additional ARPES measurements on CeSbTe.

    fig. S6. Additional magnetic susceptibility and specific heat data.

    fig. S7. Accessible magnetic subgroups discussed in this paper.

    table S1. Crystallographic data and details of data collection for single-crystal x-ray and low-temperature neutron diffraction.

    table S2. Position coordinates and thermal displacement parameters for paramagnetic (top) and AFM (bottom) CeSbTe.

    table S3. Possible dimensions of the irreducible representations at each TRIM and along certain high-symmetry lines of different phases of CeSbTe.

  • Supplementary Materials

    This PDF file includes:

    • Supplementary Text
    • fig. S1. Electron diffraction on CeSbTe.
    • fig. S2. Analysis of neutron powder diffraction data.
    • fig. S3. Refinement of the pure magnetic Bragg peaks, obtained by subtraction of the 5-K data from the 1.5-K data with respect to the two possible different magnetic structures.
    • fig. S4. Energy dispersions of CeSbTe along high-symmetry lines.
    • fig. S5. Additional ARPES measurements on CeSbTe.
    • fig. S6. Additional magnetic susceptibility and specific heat data.
    • fig. S7. Accessible magnetic subgroups discussed in this paper.
    • table S1. Crystallographic data and details of data collection for single-crystal xray and low-temperature neutron diffraction.
    • table S2. Position coordinates and thermal displacement parameters for paramagnetic (top) and AFM (bottom) CeSbTe.
    • table S3. Possible dimensions of the irreducible representations at each TRIM and along certain high-symmetry lines of different phases of CeSbTe.

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