Research ArticleCONDENSED MATTER PHYSICS

Selective trapping of hexagonally warped topological surface states in a triangular quantum corral

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Science Advances  17 May 2019:
Vol. 5, no. 5, eaaw3988
DOI: 10.1126/sciadv.aaw3988
  • Fig. 1 Surface topography of the 0.9 BL Bi film on Bi2Te3 films.

    (A) Typical equilateral triangular Bi2Te3 vacancy island surrounded by Bi BLs (brighter regions) (42 nm × 42 nm, tunneling condition: 0.5 V, 0.1 nA). The Bi BL was grown on the Bi2Te3 film by MBE. The thickness of the Bi2Te3 film is 15 quintuple layers. The atomic resolution image in the white square shows the defect-free Te-terminated Bi2Te3 (16 nm × 16 nm, −0.4 V, 0.4 nA). Γ¯M¯ and Γ¯K¯ in the momentum space are shown to indicate their alignment with the TQC edges. (B) Typical dI/dV spectra taken near the TQC center in (A) (upper curve) and on pristine Bi2Te3 (lower curve). The curves are vertically offset for clarity. a.u., arbitrary units.

  • Fig. 2 Quasi-bound states in a TQC (L = 35 nm).

    Spatial dI/dV maps of TQC in Fig. 1A (42 nm × 42 nm) at different energies (−300, −275, −250, −225, −200, −175, −150, −125, −100, −75, 75, and 100 meV) (see fig. S2 for more images at other energies). The dashed triangles are guides for the eye, indicating the position of triangular barriers. The inset in each image is the simulated pattern of a certain index, which matches the interference pattern best. In this simulation, the spinor part of the wave function is omitted, which may only affect the overall intensity and does not contribute to the spatial variation of the pattern.

  • Fig. 3 Scattering process of possible quasi-bound surface states in Bi2Te3 in a TQC.

    (A) Schematic diagram of the scattering process of surface states inside the TQC. The thick (red) arrow indicates where the spatially dependent dI/dV spectra in Fig. 4 were taken. (B and C) Scattering process shown on the energy-dependent CECs of TSS with a strong warping effect. The dashed lines in (B) indicate the possible scattering vectors between wave vectors k1 to k6. q1, q2, and q3 denote three inequivalent reflections. kti and kvi are the wave vectors close to the tip and valley positions on the warped CECs, respectively. At high energies, the CECs are labeled with a spin texture exclusively for TSS with a strong warping term. Note that because of the warping effect, the spin-momentum helicity deviates from those at low energies, acquiring an out-of-plane spin component in the valley positions, as indicated by the crosses and dots in (C). The arrows with different lengths show the in-plane spin components with different magnitudes.

  • Fig. 4 Spatially dependent energy levels inside the TQC (L = 35 nm) and the derived spectrum of trapped TSS.

    (A) Bias and spatially dependent dI/dV spectra along the line in Fig. 3A (tunneling condition: 0.2 V, 0.2 nA). The dashed line indicates the center position of the TQC. The sidebar indicates the energy regions as described in the main text having different trapping behaviors. (B) Blow-up maps from −300 to 100 meV. The red arrows indicate the localized states near the barriers. (C) Schematic of the band structure of Bi2Te3 thin films. The two short lines indicate the states (2, 1) and (3, 1) (see fig. S6 for details of the green dashed region). (D) Spectrum (Enm, knm) of trapped TSS, where knm=3L4πknm. The half-filled squares [states (n ≥ 16, 1)] are obtained by counting the nodes in the dI/dV maps shown in fig. S2. The red solid and dashed lines are the linear fitting to the states (n ≥ 6, 1) (filled squares) and the states (n, m ≥ 2) (hollow squares), respectively. The equal-spaced short lines between −400 and − 240 meV indicate the peak positions in the dI/dV spectrum coming from the bulk valence subbands of the Bi2Te3 film. The dashed vertical lines indicate the positions of kn1, where n ranges from 2 to 6. The gray regions in (C) and (D) denote the forbidden region for the trapping of TSS.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/5/eaaw3988/DC1

    Fig. S1. Band structure of Bi/Bi2Te3 on (111) surface.

    Fig. S2. Successive dI/dV maps of the TQC (35 nm) at energies with an interval of 25 meV.

    Fig. S3. dI/dV spectra on TQCs of different sizes.

    Fig. S4. dI/dV maps on a smaller TQC (17 nm).

    Fig. S5. dI/dV spectra of Fig. 4A in the line plot form.

    Fig. S6. A zoom-in view of the schematic band structure in Fig. 4C.

    Fig. S7. Section profiles of patterns at 50, 75, and 100 meV along the lines indicated in fig. S2.

    Fig. S8. A particular situation adopted to give a rough estimation of the trapped states’ lifetime in which the path of the electron in a TQC roughly follows a regular pattern.

  • Supplementary Materials

    This PDF file includes:

    • Fig. S1. Band structure of Bi/Bi2Te3 on (111) surface.
    • Fig. S2. Successive dI/dV maps of the TQC (35 nm) at energies with an interval of 25 meV.
    • Fig. S3. dI/dV spectra on TQCs of different sizes.
    • Fig. S4. dI/dV maps on a smaller TQC (17 nm).
    • Fig. S5. dI/dV spectra of Fig. 4A in the line plot form.
    • Fig. S6. A zoom-in view of the schematic band structure in Fig. 4C.
    • Fig. S7. Section profiles of patterns at 50, 75, and 100 meV along the lines indicated in fig. S2.
    • Fig. S8. A particular situation adopted to give a rough estimation of the trapped states’ lifetime in which the path of the electron in a TQC roughly follows a regular pattern.

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