Research ArticlePHYSICS

Realization of flat band with possible nontrivial topology in electronic Kagome lattice

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Science Advances  16 Nov 2018:
Vol. 4, no. 11, eaau4511
DOI: 10.1126/sciadv.aau4511
  • Fig. 1 Kagome lattice imaged by STM.

    (A) Schematic diagram of destructive quantum interference inducing an FB in the Kagome lattice. Three different sites (A, B, and C) are marked with three different colors (blue, white, and red, respectively). The A and C sites have the same wave amplitude, but the A site is antiphase with the C site. Considering only the NN hopping, the possibility of an electron escaping the hexagon is determined by overlapping two hopping vectors, hopping from A to B and from C to B. Because the A and C sites have the same amplitude and the same sign, the two hopping wave vectors will have the same amplitude and opposite signs, as shown in the schematic drawings. Thus, these two vectors will cancel each other out and lead to zero possibility of an electron hopping from the hexagon to the B site, which means that the electrons are localized in the hexagons in the Kagome lattice. In momentum space, the localized electron states mean infinite effective mass and that the energy band is flat. (B) STM topographical image (image size, 50 nm × 50 nm; sample bias Vs = 2.7 V; tunneling current It = 100 pA) of multilayer silicene (about five layers estimated from the deposition flux) grown on the Ag(111) substrate. (C) STM topographical image (5 nm × 5 nm, Vs = 1 V, It = 100 pA), giving an enlarged view of the lower right black rectangle in (B) in the Kagome area, with a Kagome lattice constant of 1.7 nm. (D) STM topographical image (5 nm × 5 nm, Vs = −0.8 V, It = 100 pA), giving an enlarged view of the upper left black rectangle in (B). It shows a honeycomb lattice with a lattice constant of 0.64 nm, which is ascribed to the Embedded Image phase of silicene.

  • Fig. 2 Electronic structure of the Kagome area.

    (A) STS spectrum (Vs = 2 V, It = 100 pA) from the Kagome area shows two distinctive peaks: an intensive peak at 1.32 V (FB peak) and a broad peak (BP) centered around 1.7 V. The valley position corresponds to the energy of Kagome edge state (ES). The inset figure shows the STS spectrum from −1.5 to 1 V (Vs = 1 V, It = 100 pA). Two vHs peaks are resolved at −1.2 and 0.75 V. (B) Fitting results for the intensive peak and the broad peak. The broad peak is fitted by Lorentzian functions. The two peak components are centered at 1.60 and 1.73 V. (C) STM image of large-scale Kagome lattice (20 nm × 20 nm, Vs = 1 V, It = 100 pA). (D and E) DOS mappings of the region enclosed by the black square in (C) at the FB (6 nm × 6 nm, Vs = 1.32 V, It = 100 pA) and broad peak (6 nm × 6 nm, Vs = 1.7 V, It = 100 pA) energies. (F) Structural model of an interlayer twisted silicene multilayer. Two kinds of AA stacking sites are marked by red and black plates, respectively. The red plates are larger than the black plates because of the influence of the larger area of AA stacking sites of unbuckled atoms. The regions not affected have been marked by blue circles. (G and H) DFT simulation images of LDOS for the FB at around 1.30 V and broad band at around 1.50 V, respectively. The Star of David is a guide to the eye.

  • Fig. 3 DFT simulation of electronic Kagome lattice.

    (A) Band structure for a Kagome lattice unit cell made of three Si atoms (left). The right part shows the DOS. Inset of the left panel displays an artificial Kagome lattice with Si atoms (left) and projected pz bands with one FB and one Dirac cone (right). (B to E) Experimental dI/dV maps for the Kagome region with different sample bias: (B) 1.25 V, (C) 1.30 V, (D) 1.35 V, and (E) 1.70 V. (F to I) Spatial distribution and 2D mapping of the Kagome bands (F to H) and higher band (I) in the band structure (4 × 4 repeated cell). The black Star of David and red rhombus are used as guides to the eye.

  • Fig. 4 Electronic structure of Kagome area.

    (A) Large-area image of the Kagome lattice surrounded by Embedded Image silicene (R3 area) (50 nm × 50 nm, Vs = 3 V, It = 100 pA). The boundary between them is marked by the black solid line. The red solid line shows the height profile along the white dashed line. The step height is the thickness of one layer of silicene. (B) DOS mapping simultaneously obtained at 1.45 V, which is the corresponding edge state energy. The position of the edge state is highlighted by the white arrow. (C) Topographical image (10 nm × 10 nm, Vs = 1 V, It = 100 pA) of the border region between the Kagome lattice (upper left) and Embedded Image silicene (lower right), which is enclosed by the red square in (B). The Kagome lattice is constructed from three different sites, which are marked by blue, white, and red circles, respectively. The Kagome edge is marked by the black dashed line connecting the white circles. The terrace edge is marked by the white dotted line. (D and E) DOS mapping of the FB energy (10 nm × 10 nm, Vs = 1.33 V, It = 100 pA) reveals the Kagome pattern on the left of these images. The Star of David is a guide to the eye. (E) DOS mapping of the edge state energy (10 nm × 10 nm, Vs = 1.45 V, It = 100 pA) shows higher DOS along the dashed line in (C). (F) Dangling bonds are revealed by DOS mapping (10 nm × 10 nm, Vs = 1.5 V, It = 100 pA).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/11/eaau4511/DC1

    Fig. S1. Multiple superstructures of silicene on the Ag(111) substrate.

    Fig. S2. A 1 × 1 honeycomb structure of Formula silicene.

    Fig. S3. Composite moiré pattern for twisted Formula silicene multilayers.

    Fig. S4. Kagome lattice formed by composite moiré pattern.

    Fig. S5. Comparing twisted multilayer silicene model with STM images.

    Fig. S6. High-resolution image of Kagome area shows faint height-modulated Formula silicene structure.

    Fig. S7. Kagome lattice on second layer of silicene.

    Fig. S8. Ideal STM tunnel junction between tip and twisted Formula silicene multilayer.

    Fig. S9. DOS maps in the broad-band bias range.

    Fig. S10. Coulomb pseudo-gap.

    Fig. S11. Edge state at boundary between Kagome lattice and Formula silicene.

    Fig. S12. Edge state located between FB and broad band.

    Fig. S13. Absence of FB in imperfect Kagome lattice.

    Fig. S14. Spectral distribution in the broken region of the Kagome lattice.

    Fig. S15. Electronic structure of Kagome area.

    Fig. S16. DFT simulation of artificial Kagome lattice.

    Fig. S17. Hexagonal 2D mapping of the local electron density.

    Fig. S18. DFT simulation of twisted bilayer silicene.

    References (3942)

  • Supplementary Materials

    This PDF file includes:

    • Fig. S1. Multiple superstructures of silicene on the Ag(111) substrate.
    • Fig. S2. A 1 × 1 honeycomb structure of 3×3 silicene.
    • Fig. S3. Composite moiré pattern for twisted 3×3 silicene multilayers.
    • Fig. S4. Kagome lattice formed by composite moiré pattern.
    • Fig. S5. Comparing twisted multilayer silicene model with STM images.
    • Fig. S6. High-resolution image of Kagome area shows faint height-modulated 3×3 silicene structure.
    • Fig. S7. Kagome lattice on second layer of silicene.
    • Fig. S8. Ideal STM tunnel junction between tip and twisted 3×3 silicene multilayer.
    • Fig. S9. DOS maps in the broad-band bias range.
    • Fig. S10. Coulomb pseudo-gap.
    • Fig. S11. Edge state at boundary between Kagome lattice and 3×3 silicene.
    • Fig. S12. Edge state located between FB and broad band.
    • Fig. S13. Absence of FB in imperfect Kagome lattice.
    • Fig. S14. Spectral distribution in the broken region of the Kagome lattice.
    • Fig. S15. Electronic structure of Kagome area.
    • Fig. S16. DFT simulation of artificial Kagome lattice.
    • Fig. S17. Hexagonal 2D mapping of the local electron density.
    • Fig. S18. DFT simulation of twisted bilayer silicene.
    • References (3942)

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