2013/11/30 by Li Chen, Tahereh Mazaheri, Alexander Seidel +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Berry connection and curvature #Chern class #Class (philosophy) #Computer science #Curvature #Degenerate energy levels #Geometry #Lattice (music) #Mathematics #Physics #Pure mathematics #Quantum #Quantum many-body systems #Quantum mechanics #Topological Materials and Phenomena #Zero (linguistics) #cond-mat.str-el #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/1751-8113/47/15/152001
published as J. Phys. A: Math. Theor. 47 (2014) 152001 · Published Version. Some references and additional comments added
openalex publication_date 2014/03/31 · arxiv created 2014/04/11 · arxiv updated 2014/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate the possibility of exactly flat non-trivial Chern bands in tight binding models with local (strictly short-ranged) hopping parameters. We demonstrate that while any two of three criteria can be simultaneously realized (exactly flat band, non-zero Chern number, local hopping), it is not possible to simultaneously satisfy all three. Our theorem covers both the case of a single flat band, for which we give a rather elementary proof, as well as the case of multiple degenerate flat bands. In the latter case, our result is obtained as an application of K-theory. We also introduce a class of models on the Lieb lattice with nearest and next-nearest neighbor hopping parameters, which have an isolated exactly flat band of zero Chern number but, in general, non-zero Berry curvature.