Research ArticleCONDENSED MATTER PHYSICS

Topological materials discovery by large-order symmetry indicators

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Science Advances  08 Mar 2019:
Vol. 5, no. 3, eaau8725
DOI: 10.1126/sciadv.aau8725
  • Fig. 1 Electronic band plots of TCIs.

    (A) Electronic band plot of TCI Pt3Ge within SG140. (B) Electronic band plot of TCI graphite within SG194.

  • Fig. 2 Electronic band plots of TCIs.

    (A) Electronic band plot of PbPt3 within SG221. (B) Electronic band plot of Au4Ti within SG87.

  • Fig. 3 Electronic band plot of TCI Ti2Sn within SG194.
  • Fig. 4 Electronic band plots of Dirac semimetals.

    (A) AgCsF3 within SG140 owns Dirac points pinned down at P and N points. (B) AgAsBa within SG194 has a Dirac point lying in the high-symmetry line ΓA. The Dirac point is protected by C6v, and the band crossing arises from two twofold degenerate bands with different irreps (Δ7 and Δ9).

  • Table 1 Topological crystalline (TC) insulating materials for SGs87,140, and 221.

    These SGs all own the same strong SI factor group, ℤ8, but with different other weak SI factor groups. The numbers in the parenthesis following the name of material are the nonvanishing SI in the corresponding XBS. The SI is obtained by qiCi mod Ci, where ai has a common factor larger than 1, which corresponds to the subscript of the factor groups of XBS. The blue color denotes the materials carefully discussed in this work.

    SGXBSMaterial (SI)
    872 × ℤ8Au4Ti (10), Hf5Te4 (11)
    1402 × ℤ8Pt3Ge (04), SiTa2 (11)
    2214 × ℤ8AlX (X = Sc, Y) (03)
    XB6 (X = Ca, Sr, Ba) (03)
    BeTi (03), CaPd (20), CsPbBr3 (23)
    CsGeBr3 (23), CsSnI3 (23)
    Ca3PbO (22), XPt3 (X = Pb, Sn) (34)
  • Table 2 TC insulating materials for SGs191 and 194.

    These SGs all own the same strong SI factor group, ℤ12, but with different other weak SI factor groups. The numbers in the parenthesis following the name of material are the nonvanishing SI in the corresponding XBS. The SI is obtained by qiCi mod Ci, where ai has a common factor larger than 1, which corresponds to the subscript of the factor groups of XBS. The blue color denotes the materials carefully discussed in this work.

    SGXBSMaterial (SI)
    1916 × ℤ12XB2 (X = Mg, Ca) (52), SrB2 (15), Ti (33)
    19412AlLi (4), AlC2Ta3 (1), Ca2NI (3)
    Graphite (4), Na2CdSn (4)
    MgPo (1), SiSr2 (1)
    Ti2Sn (6)

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/3/eaau8725/DC1

    Section S1. First-principles calculated parities

    Section S2. S4 invariant materials

    Section S3. Details of calculating mirror Chern numbers by first-principles method

    Section S4. Details of the TB model and the glide/mirror-protected surface states

    Section S5. AI basis vectors

    Section S6. Materials statistics

    Table S1. Ab initio calculated parities.

    Table S2. Ab initio calculated κ4 for body-centered lattice.

    Table S3. Ab initio calculated κ4 for primitive lattice.

    Table S4. AI basis vectors in this work for SGs 87, 140, and 221.

    Table S5. AI basis vectors in this work for SGs 191 and 194.

    Fig. S1. TB fitting of Pt3Ge and its surface states.

    Fig. S2. TB fitting of graphite and its surface states.

    Fig. S3. Materials statistics.

    Source code

  • Supplementary Materials

    The PDF file includes:

    • Section S1. First-principles calculated parities
    • Section S2. S4 invariant materials
    • Section S3. Details of calculating mirror Chern numbers by first-principles method
    • Section S4. Details of the TB model and the glide/mirror-protected surface states
    • Section S5. AI basis vectors
    • Section S6. Materials statistics
    • Table S1. Ab initio calculated parities.
    • Table S2. Ab initio calculated κ4 for body-centered lattice.
    • Table S3. Ab initio calculated κ4 for primitive lattice.
    • Table S4. AI basis vectors in this work for SGs 87, 140, and 221.
    • Table S5. AI basis vectors in this work for SGs 191 and 194.
    • Fig. S1. TB fitting of Pt3Ge and its surface states.
    • Fig. S2. TB fitting of graphite and its surface states.
    • Fig. S3. Materials statistics.

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    Other Supplementary Material for this manuscript includes the following:

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