Research ArticleCONDENSED MATTER PHYSICS

Magnetizing topological surface states of Bi2Se3 with a CrI3 monolayer

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Science Advances  31 May 2019:
Vol. 5, no. 5, eaaw1874
DOI: 10.1126/sciadv.aaw1874
  • Fig. 1 Atomic structure and charge difference in CrI3/BS/CrI3.

    (A) Side view of the most stable CrI3/BS/CrI3. The green, red, pink, and blue balls are for I, Cr, Se, and Bi atoms, respectively. Dashed lines show the alignments between atoms in CrI3 and BS layers; d0 denotes the optimized vdW gap. (B) Real-space distribution of the charge difference Δρ = ρtotal − ρBS − ρCrI3 and (C) planar-averaged spin density Δσ = ρ − ρ in the interfacial region of the CrI3/6QL-BS/CrI3 heterostructure.

  • Fig. 2 Band structures of CrI3/BS/CrI3.

    DFT-calculated band structures of (A) CrI3/4QL-BS/CrI3, (B) CrI3/5QL-BS/CrI3, and (C) CrI3/6QL-BS/CrI3. Insets in (A), (B), and (C) are the fine band structures around the Fermi level. Colors in the main panels indicate the weights of bands from BS (blue) and CrI3 (yellow). Colors in insets indicate the spin projections.

  • Fig. 3 Topological properties of CrI3/BS/CrI3.

    (A) Chiral edge state of the Chern insulator CrI3/5QL-BS/CrI3 ribbon. (B) Dependence of Chern numbers and gaps of CrI3/BS/CrI3 on the number (N) of QLs of BS. The inset shows the dependence of bandgaps of CrI3/6QL-BS/CrI3 on the CrI3-BS interlayer distance d. d0 is the optimized interfacial distance. (C) and (D) show the fitting parameters Δ and M in different CrI3/BS/CrI3 heterostructures, respectively. The horizontal dashed line in (B) shows the position of 3.5 meV.

  • Fig. 4 Effect of Vp on the topological properties of CrI3/6QL-BS/CrI3.

    (A) to (C) show band evolutions with Vp increasing from 0 to 5.0 meV. (D) Berry curvatures of occupied bands around the Γ point for Vp = 0 (A, top) and Vp = 5.0 meV (C, bottom). The large positive Berry curvatures in the bottom panel are highlighted by black circles. (E) Dependence of Chern numbers and gaps on Vp Δ=3.1 meV and M = 1.4 meV are adopted in these calculations.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/5/eaaw1874/DC1

    Table S1. Magnetic moment, bandgap, magnetocrystalline anisotropy energy, and Heisenberg exchange interactions J1 and J2.

    Table S2. Parameters of the effective four-band model (see Eq. 1 in the main text) are used to fit the DFT-calculated band of CrI3/BS/CrI3.

    Table S3. Analysis of band inversions and the Chern number CN with respect to parameters Δ, M, and B.

    Fig. S1. DFT + SOC + U–calculated band structure of the CrI3 ML with pristine and stretched lattice constants.

    Fig. S2. Top views of the three highly symmetric alignments between CrI3 and BS in CrI3/BS/CrI3 heterostructures.

    Fig. S3. Dependence of the binding energies and the vdW gaps of CrI3/BS/CrI3 on the number (N) of QL of BS.

    Fig. S4. Topological properties of CrI3/4QL-BS/CrI3.

    Fig. S5. Topological properties of CrI3/5QL-BS/CrI3.

    Fig. S6. DFT-calculated (black lines) and fitted band structures (red dashed lines) of CrI3/BS/CrI3 based on the effective four-band model (see Eq. 1 in the main text).

    Fig. S7. Effect of U on the topological properties of CrI3/BS/CrI3.

  • Supplementary Materials

    This PDF file includes:

    • Table S1. Magnetic moment, bandgap, magnetocrystalline anisotropy energy, and Heisenberg exchange interactions J1 and J2.
    • Table S2. Parameters of the effective four-band model (see Eq. 1 in the main text) are used to fit the DFT-calculated band of CrI3/BS/CrI3.
    • Table S3. Analysis of band inversions and the Chern number CN with respect to parameters Δ, M, and B.
    • Fig. S1. DFT + SOC + U–calculated band structure of the CrI3 ML with pristine and stretched lattice constants.
    • Fig. S2. Top views of the three highly symmetric alignments between CrI3 and BS in CrI3/BS/CrI3 heterostructures.
    • Fig. S3. Dependence of the binding energies and the vdW gaps of CrI3/BS/CrI3 on the number (N) of QL of BS.
    • Fig. S4. Topological properties of CrI3/4QL-BS/CrI3.
    • Fig. S5. Topological properties of CrI3/5QL-BS/CrI3.
    • Fig. S6. DFT-calculated (black lines) and fitted band structures (red dashed lines) of CrI3/BS/CrI3 based on the effective four-band model (see Eq. 1 in the main text).
    • Fig. S7. Effect of U on the topological properties of CrI3/BS/CrI3.

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