Spin-Orbit-Induced Topological Flat Bands in Line and Split Graphs of Bipartite Lattices.

Topological flat bands, such as the band in twisted bilayer graphene, are becoming a promising platform to study topics such as correlation physics, superconductivity, and transport. In this work, we introduce a generic approach to construct two-dimensional (2D) topological quasi-flat bands from line graphs and split graphs of bipartite lattices. The flat band in these lattices connects to the dispersive bands through a degenerate state at some momentum. We find that, with spin-orbit coupling (SOC), the flat band becomes quasi-flat and gapped from the dispersive bands. We find that (i) if the flat band (without SOC) has inversion or C₂ symmetry and is non-degenerate, then the resulting quasi-flat band must be topologically nontrivial, and (ii) if the flat band (without SOC) is degenerate, then there exists an SOC potential such that the resulting quasi-flat band is topologically nontrivial. This generic mechanism serves as a paradigm for finding topological quasi-flat bands in 2D crystalline materials and meta-materials.

Ref: D.-S. Ma, Y. Xu, C. S. Chiu, N. Regnault, A. A. Houck, Z. Song, and B. A. Bernevig, Spin-Orbit-Induced Topological Flat Bands in Line and Split Graphs of Bipartite Lattices, arXiv:2008.08231v2 (2020)