Research ArticleCONDENSED MATTER PHYSICS

Discovery of log-periodic oscillations in ultraquantum topological materials

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Science Advances  02 Nov 2018:
Vol. 4, no. 11, eaau5096
DOI: 10.1126/sciadv.aau5096
  • Fig. 1 Characterization of high-quality ZrTe5 crystal.

    (A) HAADF STEM image of a typical ZrTe5 sample. The inset shows the atomic resolution. (B) RT characteristic of ZrTe5. Inset shows the schematic for electrical transport measurements. (C) Hall traces of s1 versus B at selected temperatures from 2 to 300 K. (D) Temperature dependence of the estimated mobility and carrier density of the carriers in ZrTe5 by analyzing the Hall data with a two-carrier model.

  • Fig. 2 Log-periodic MR oscillations in ZrTe5.

    (A) Resistivity of s6 versus B at low temperatures in a static perpendicular magnetic field. The inset shows the second derivative result of MR data at 2 K. (B) MR behavior of s6 in an ultrahigh magnetic field up to 58 T at 4.2 K. Dotted lines serve as guides to the eye. (C) Extracted MR oscillations in ZrTe5 samples (s6, s7, and s9) at 4.2 K. (D) FFT results for the log-periodic oscillation data in the form of ΔR versus log(B/B′) with B′ = 1 T.

  • Fig. 3 Log-periodic MR oscillations at different temperatures.

    (A) MR behavior of s6 at relatively low temperatures. (B) MR behavior of s6 at relatively high temperatures. (C) MR oscillations in s6 after subtracting a smooth background from the raw data. Dotted lines serve as guides to the eye. (D) FFT results for the MR oscillations at different temperatures in the form of ΔR versus log(B/B′) with B′ = 1 T.

  • Fig. 4 DSI in ultraquantum ZrTe5.

    (A) Index plot for the log-periodic oscillations. (B) Schematic of the two-body quasi-bound states composed of a Dirac-type massless hole and charged center via Coulomb attraction. (C) Normalized binding energy of the quasi-bound states under the magnetic field. E0 and L0 denote the cutoff scale. (D) Quantitative fitting (black curves) of the log-periodic oscillations in ZrTe5. arb.u., arbitrary units. (E) Temperature dependence of the normalized amplitude of the oscillation peak n = 1. The fitting (orange curve) of the oscillation data (blue points) indicates a disappearance temperature Td consistent with the experimental results.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/11/eaau5096/DC1

    Table S1. A brief review of the results of ZrTe5.

    Table S2. A summary of the energy-dispersive spectroscopy results on our ZrTe5 crystals.

    Table S3. Fitting parameters of log-periodic oscillations in different samples.

    Table S4. Fitting parameters of log-periodic oscillations in s6 at different temperatures.

    Fig. S1. Hall analysis in a two-carrier model.

    Fig. S2. Background produced by smoothing the raw MR data.

    Fig. S3. Log-periodic MR oscillations in s2 and s10.

    Fig. S4. MR oscillations periodic in logB and not in B or 1/B.

    Fig. S5. Strong anisotropy of the bulk ZrTe5.

    Fig. S6. Theoretical fitting of the experimental results.

    Supplementary discussions on other physical mechanisms

    Supplementary notes on theoretical details

    References (4457)

  • Supplementary Materials

    This PDF file includes:

    • Table S1. A brief review of the results of ZrTe5.
    • Table S2. A summary of the energy-dispersive spectroscopy results on our ZrTe5 crystals.
    • Table S3. Fitting parameters of log-periodic oscillations in different samples.
    • Table S4. Fitting parameters of log-periodic oscillations in s6 at different temperatures.
    • Fig. S1. Hall analysis in a two-carrier model.
    • Fig. S2. Background produced by smoothing the raw MR data.
    • Fig. S3. Log-periodic MR oscillations in s2 and s10.
    • Fig. S4. MR oscillations periodic in logB and not in B or 1/B.
    • Fig. S5. Strong anisotropy of the bulk ZrTe5.
    • Fig. S6. Theoretical fitting of the experimental results.
    • Supplementary discussions on other physical mechanisms
    • Supplementary notes on theoretical details
    • References (4457)

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