Research ArticlePHYSICAL SCIENCE

Butterfly magnetoresistance, quasi-2D Dirac Fermi surface and topological phase transition in ZrSiS

See allHide authors and affiliations

Science Advances  16 Dec 2016:
Vol. 2, no. 12, e1601742
DOI: 10.1126/sciadv.1601742
  • Fig. 1 Calculated Fermi surface for ZrSiS.

    (A) Projection of the merged band Fermi surface for ZrSiS, looking down the kz axis. The sizes of two orbits easily identifiable from this projection (shown with dashed red and white lines, respectively) were extracted and found to be 2.24 × 10–2 and 4.52 × 10–2 Å–2, respectively. The orbit highlighted in red corresponds to the more tubular feature, whereas the orbit highlighted in white corresponds to the diamond feature. (B) Canted view of the total Fermi surface showcasing the different types of pockets. (C and D) Two-band deconvoluted Fermi surface. The tubular feature and diamond contributions to the merged Fermi surface come from different bands (each existing twice due to spin-orbit coupling). Because of the diamond shape (which comes from the bands creating the Dirac line node), ZrSiS may exhibit nesting effects at low temperatures.

  • Fig. 2 Transport measurements on ZrSiS.

    (A) Zero-field temperature dependence of the resistivity in ZrSiS. The inset shows the extraordinarily low residual resistivity of 48(4) nΩ⋅cm for a crystal with an RRR of ≈300. (B) Temperature dependence (9 T) of the resistivity in ZrSiS at various angles. The θ value is taken as the angle between the applied field and the current, which is applied along the a axis. The inset shows the Hall resistance (H perpendicular to I) as a function of temperature at various magnetic fields. Dashed vertical lines show the magnetic field dependence of the maximum RH. A p-n crossover is evident for the 3 and 4-T measurements at 30 and 39 K, respectively, before reaching a plateau at low temperatures.

  • Fig. 3 AMR of ZrSiS.

    (A) Polar plot illustrating the butterfly AMR effect, coming from a convolution of two- and fourfold symmetry dependencies, taken at different applied magnetic field strengths. The θ value is taken as the angle between the applied field and the current, which is applied along the a axis. (B) Standard plot of the AMR showcasing the field strength–dependent dip in the MR, beginning at 85°, maximizing by 90°, and ending by 95°. Additional minor oscillatory components, on top of the two- and fourfold symmetry, and peak splitting around 45°, which also exhibits field strength dependence, are also present.

  • Fig. 4 MR as a function of applied field at various angles in ZrSiS.

    (A) MR versus μ0H at various angles (full data in the Supplementary Materials) along with fits to MR = 1 + c1H + c2H2, where c1 and c2 are the relative weights given to the linear and quadratic terms of the equation. Solid, smooth lines are the fits, whereas oscillating lines are the data. (B) Extracted c1 and c2 dependencies from the full 9-T MR versus H curves taken at 0°, 10°, 20°, 30°, 35°, 40°, 45°, 50°, 55°, 60°, 70°, 80°, 85°, 87.5°, 90°, 92.5°, 95°, 100°, and 105°, where θ is taken as the angle between the applied field and the current, which is applied along the a axis. Solid squares and solid triangles are the extracted values for c1 and c2, respectively.

  • Fig. 5 Quantum oscillation analysis and extraction of the Berry phase in ZrSiS.

    (A) FFT at 90° of the SdH oscillations extracted after subtracting a polynomial background (see the Supplementary Materials). Fα, Fβ, and Fδ denote frequencies at 23, 243, and 130 T, respectively. Extra peaks resulting from F, F, F, and F are also visible along with three more unidentified frequencies at 154, 186, 426, and 487 T. The inset shows the LK fit used to determine the effective mass of the electrons for the 23-, 243-, and 130-T peaks. (B) Deconvoluted oscillations pertaining to the Fα. Dashed lines indicate the apparent decay of the period of the oscillation with decreasing field and showcase the temperature-dependent shift of the oscillation’s maxima, making the phase analysis of Fα extremely unreliable. (C) FFT from the extracted oscillations at many different angles of the applied field. Curved lines are guides to the eye to illustrate the peak splitting and shifting occurring as a function of the angle of the applied field. (D) Angular dependence of the Fβ peak. Here, the definition of θ was rotated 90° to allow for easier comparison with other materials; θ= 0 is H parallel to c. Red triangles are the expected values for a truly 2D pocket following the 1/cos(θ) law, inverted blue triangles are the measured values, and a deviation occurs by 20°. The inset shows a fit of the data to F/Bcos(a*θ). (E) Extracted total phase (γ − δ) of Fβ as a function of angle, obtained by fitting the LK formula to the deconvoluted Fβ’s SdH oscillations. See the Supplementary Materials for details.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/12/e1601742/DC1

    fig. S1. Powder x-ray diffraction pattern for ground single crystals of ZrSiS.

    fig. S2. AMR measured in other principal directions along with symmetry fitting.

    fig. S3. Extracted weights from AMR fitting.

    fig. S4. Quantitative quantum oscillation analysis using band pass filtration.

    fig. S5. Direct Lifshitz-Kosevich fitting compared with Landau Level fan diagram.

    References (4244)

  • Supplementary Materials

    This PDF file includes:

    • fig. S1. Powder x-ray diffraction pattern for ground single crystals of ZrSiS.
    • fig. S2. AMR measured in other principal directions along with symmetry fitting.
    • fig. S3. Extracted weights from AMR fitting.
    • fig. S4. Quantitative quantum oscillation analysis using band pass filtration.
    • fig. S5. Direct Lifshitz-Kosevich fitting compared with Landau Level fan diagram.
    • References (42–44)

    Download PDF

    Files in this Data Supplement:

Stay Connected to Science Advances

Navigate This Article