Experimental evidence of hourglass fermion in the candidate nonsymmorphic topological insulator KHgSb

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Science Advances  05 May 2017:
Vol. 3, no. 5, e1602415
DOI: 10.1126/sciadv.1602415
  • Fig. 1 Hourglass fermions predicted in KHgSb with nonsymmorphic spatial symmetry.

    (A) Schematic surface state bands for materials with symmorphic and nonsymmorphic spatial symmetries. Panels (i) and (ii) present topologically trivial and nontrivial cases with symmorphic spatial symmetry, respectively. Panels (iii) and (iv) are the same as (i) and (ii), respectively, but with nonsymmorphic spatial symmetry showing hourglass-shaped surface band dispersion. (B) Crystal structure of double-layered KHgSb with space group P63/mmc (no. 194). The yellow plane indicates the glide mirror plane Embedded Image preserved on the (010) side surface. The arrows and coordinates indicate the operation of the glide reflection Embedded Image. (C) Three-dimensional (3D) bulk BZ of KHgSb as well as its projected (001) and (010) surface BZs. (D and E) Projections of calculated bulk and surface bands on the (001) and (010) surfaces of KHgSb, respectively. The calculations show hourglass-shaped surface bands along the glide-symmetric line Embedded Image on the (010) surface. The complex-conjugate Embedded Image eigenvalues are paired as ±i pairs at Embedded Image and +1 (or −1) pairs at Embedded Image. (F) Logarithmic plot of XRD data measured on the (001) plane of KHgSb single crystal. The peaks marked by stars are from the Sb flux. Inset: LEED pattern shows the hexagonal structure of the (001) surface. arb.u., arbitrary units. (G) Core-level photoemission spectrum showing characteristic peaks of K 3p, Hg 5d, and Sb 4d core levels.

  • Fig. 2 Electronic structure on the KHgSb (001) surface.

    (A) 3D intensity plot of ARPES spectra showing the electronic structure of valence bands in the kx-ky plane. (B) ARPES intensity plot along Embedded Image after in situ K doping, showing the bottom of the conduction bands. (C) ARPES intensity plot showing band dispersions along Embedded Image on the pristine (001) surface. The dashed curves represent the calculated bulk bands at kz = 0. Because generalized gradient approximation (GGA) calculations usually underestimate the bandgap of semiconductors, we rigidly shifted the calculated conduction bands upward to have a 0.46-eV bandgap, which is the value determined experimentally in (B). For clarity, the chemical potential of the calculated band structure is chosen to have the best match with the measured valence band dispersions. (D) Corresponding curvature intensity plot of (C).

  • Fig. 3 Band dispersions along Embedded Image on the KHgSb (010) surface.

    (A) ARPES intensity plot at EF recorded along Embedded Image by varying the photon energy from 20 to 100 eV on the (010) surface, which maps the kx-ky plane at kz = 0 of the 3D bulk BZ. The overlaid hexagons indicate the BZ structure in the kx-ky plane. (B and C) Band dispersions along cuts 1 and 2 indicated in (A), recorded with photon energy hv = 22 and 56 eV, respectively. The solid curves represent the calculated bulk bands along Γ − M. Note that the chemical potential on the (010) surface is slightly different from that on the (001) surface, most likely because of different surface chemistry effects. (D) Band dispersions along kx at different ky positions recorded with different photon energies from 22 to 56 eV. The dashed curve indicates the dispersion of one representative bulk band along Γ − KM. (E) Calculated bulk bands along Γ − KM. The red curves indicate the calculated bulk bands that correspond to the experimental band dispersion indicated in (D). (F) Near-EF band dispersions along kx at different ky positions recorded with different photon energies from 56 to 78 eV, showing a Dirac-like surface state band along Embedded Image. The momentum locations are indicated in (A).

  • Fig. 4 Electronic structure of surface states on the KHgSb (010) surface.

    (A to C) Calculated surface band dispersions along Embedded Image, Embedded Image, and Embedded Image, respectively. (D) 3D sketch of the band structure of hourglass fermions along high-symmetry lines. (E and G) ARPES intensity plots showing band dispersions along Embedded Image and Embedded Image, respectively. (F and H) Corresponding curvature intensity plots of momentum distribution curves of (E) and (G), respectively. (I and J) ARPES intensity plot and corresponding curvature intensity plot along Embedded Image, respectively. (K) FS intensity map recorded at hv = 70 eV. (L) Summary of the experimental results recorded on the (001) and (010) surfaces. Top: Curvature intensity plot of the band dispersions along Embedded Image on the (001) surface. Bottom: Surface band structure along Embedded Image on the (010) surface. The symbols represent the extracted bands from the experimental data in (E) to (J). Middle: 3D bulk BZ of KHgSb and its projected (001) and (010) surface BZs.

Supplementary Materials

  • Supplementary Materials

    This PDF file includes:

    • Crystal structure of KHgSb determined from powder XRD data
    • fig. S1. Refinements of powder XRD data of KHgSb.
    • fig. S2. Band inversion confirmed by HSE06.
    • References (29, 30)

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