Research ArticleCONDENSED MATTER PHYSICS

Resolving the topological classification of bismuth with topological defects

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Science Advances  01 Nov 2019:
Vol. 5, no. 11, eaax6996
DOI: 10.1126/sciadv.aax6996
  • Fig. 1 Surface and edge spectrum of Bi(111).

    (A) Schematic illustration of an SD in a lattice. (B) Bulk Brillouin zone (BZ) of rhombohedral Bi and its (111) surface–projected 2D BZ and zigzag edge–projected 1D BZ, with all TRIM points indicated. (C) Bulk band structure of Bi obtained from ab initio calculations using the modified Becke-Johnson (MBJ) exchange potential and generalized gradient approximation shown by the solid and dashed lines, respectively. Inset shows the band structure around the energy gap (5 meV) at L calculated with MBJ. (D) Large-scale STM topography of a Bi terrace with crystallographic step edges. Inset shows atomically resolved image overlaid with Bi bilayer crystal structure. (E) dI/dV spectroscopy given in arbitrary units (au) as measured at a point on the surface far away from impurities. (F) dI/dV map measured normal to the step edge (marked with a black arrow) along the gray dotted line in (D) showing the modulated LDOS and the 1D topological edge mode (marked by curly brackets). (G) Fourier transform of (F) showing the energy dispersion of scattering wave vectors along Γ¯M¯ and the corresponding calculated spin-selective scattering probability (SSP). (H) Calculated zigzag edge–projected LDOS showing 1D edge states dispersing along ΓM (see fig. S4).

  • Fig. 2 Topographic and spectroscopic mapping of an SD.

    (A) Topographic image of a clean (111) surface consisting of an SD (solid black arrow) with a single Bi bilayer long Burger’s vector. (B) Topographic line cut along the black dotted line shown in (A). (C) Spectroscopic map measured along the dotted line in (A) showing QPI pattern for the 2D surface states and a nearly unhindered edge mode on the atomically corrugated step edge terminating at the SD. (D and E) dI/dV line cuts along the black dashed lines shown in (C). The shadowed regions in (B) to (D) correspond to the segment where the STM tip images the atomic vacancy states and the segment at which it descends from the top to the bottom terraces where the tunneling matrix element from tip to sample may change.

  • Fig. 3 Imaging the localization of the edge mode in the vicinity of the SD.

    (A) Topographic image of the region around an SD. (B to D) Spatially resolved differential conductance map in the vicinity of the SD. The increased LDOS on the step edge and the SD shown in (C) and (D) correspond to a segment of the 1D edge mode. The black dashed line represents the position of the line cut shown in Fig. 2C.

  • Fig. 4 Strain analysis in the vicinity of the SD and modeling.

    (A) Phase and (B) magnitude of the shear strain field around an SD calculated from the gradient of the topography in Fig. 3A, showing its azimuthal radially decaying profile. The amount of strain within the dashed line in (B) is sufficient to invert the band ordering around the L energy gap and to induce a topological phase. (C) Radial cuts along different directions from the SD of the strain magnitude. Inset shows the (001) direction of the Burger’s vector piercing the ABC stacked Bi bilayers. (D) Ab initio calculation of the band structure evolution around the L gap under uniform strain. A topological phase transition occurs at about 3.5% strain.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/11/eaax6996/DC1

    Section S1. Effect of substrate magnetic order on Bi

    Section S2. dI/dV mapping of the SD

    Section S3. Edge states of Bi nanoribbon

    Section S4. Model of shear strain

    Fig. S1. Effect of the magnetic order of the GdPtBi substrate on Bi.

    Fig. S2. QPI of 2D surface states from SD.

    Fig. S3. Direct visualization of the topological edge mode localized on the SD.

    Fig. S4. The model used to simulate Bi step edge.

    Fig. S5. Effect of shear strain on the electronic properties of Bi.

    Reference (62)

  • Supplementary Materials

    This PDF file includes:

    • Section S1. Effect of substrate magnetic order on Bi
    • Section S2. dI/dV mapping of the SD
    • Section S3. Edge states of Bi nanoribbon
    • Section S4. Model of shear strain
    • Fig. S1. Effect of the magnetic order of the GdPtBi substrate on Bi.
    • Fig. S2. QPI of 2D surface states from SD.
    • Fig. S3. Direct visualization of the topological edge mode localized on the SD.
    • Fig. S4. The model used to simulate Bi step edge.
    • Fig. S5. Effect of shear strain on the electronic properties of Bi.
    • Reference (62)

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