Symmetry-enforced double Weyl points, multiband quantum geometry, and singular flat bands of doping-induced states at the Fermi level

Moritz M. Hirschmann; Johannes Mitscherling

doi:10.1103/PhysRevMaterials.8.014201

paper

Symmetry-enforced double Weyl points, multiband quantum geometry, and singular flat bands of doping-induced states at the Fermi level

arXiv:2308.03751 · doi:10.1103/PhysRevMaterials.8.014201

Abstract

Two common difficulties in the design of topological quantum materials are that the desired features lie too far from the Fermi level and are spread over a too-large energy range. Doping-induced states at the Fermi level provide a solution, where nontrivial topological properties are enforced by the doping-reduced symmetry. To show this, we consider a regular placement of dopants in a lattice of space group (SG) 176 ( $P 6_{3} / m$ ), which reduces the symmetry to SG 143 ( $P 3$ ). Our two- and four-band models feature double Weyl points, Chern bands, Van Hove singularities, nontrivial multiband quantum geometry due to mixed orbital character, and singular flat bands. We relate these features to density-functional theory (DFT) calculations for dopant and vacancy bands of lead apatite Pb $_{10} ($ PO $_{4})_{6}$ O and Pb $_{10} ($ PO $_{4})_{6} ($ OH $)_{2}$ , the van der Waals ferromagnet Cr $_{2}$ Ge $_{2}$ Te $_{6}$ , the semiconductor SiC, and the 2D dichalcogenide MoS $_{2}$ .

arXiv comment14 pages, 5 figures, updated to peer-review version, typo in Eq. (7) and in equation below corrected

Symmetry-enforced double Weyl points, multiband quantum geometry, and singular flat bands of doping-induced states at the Fermi level

Abstract

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