No-go theorem for topological insulators and high-throughput identification of Chern insulators

Article

关键词: WANNIER FUNCTIONS;    BAND REPRESENTATIONS;    ENERGY-BANDS;    SYMMETRY;    POLARIZATION;    CLASSIFICATION;    STATES;    BLOCH;   

DOI  :  10.1103/PhysRevB.98.184305

来源: SCIE

【 摘 要 】

For any symmorphic magnetic space group G, we prove that topological band insulators (with vanishing first Chern numbers) cannot have a ground state composed of a single, energetically isolated band. This no-go statement means that such topological insulators cannot be realized in tight-binding models with a single, filled, low-energy band. An implication is that the minimal dimension of the tight-binding Hamiltonian (at each wave vector) is four, if the topological insulator is stable, i.e., the filled bands remain topological upon addition of nontopological bands. Otherwise, if the topological insulator is unstable, the minimal dimension is three. In addition to our no-go statement, we present a surefire recipe to model Chern insulators and unstable topological insulators, by energetically splitting elementary band representations; this recipe, combined with recently constructed Bilbao tables on band representations, can be systematized for high-throughput identification of magnetic and time-reversal-invariant topological materials. All stated results follow from our theorem which applies to any single, isolated energy band of a G-symmetric Schrodinger-type or tight-binding Hamiltonian: for such bands, being topologically trivial (in the category of complex vector bundles) is equivalent to being a band representation of G.

【 授权许可】

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