Fragile topology in line-graph lattices*

The geometric properties of a lattice can have profound consequences on its band spectrum. For example, symmetry constraints and geometric frustration can give rise to topologicially nontrivial and dispersionless bands, respectively. Line-graph lattices are a perfect example of both of these features: their lowest energy bands are perfectly flat, and we have found and proved connections between their geometric properties and the presence or absence of fragile topology in their flat bands [1]. In this talk, I present these connections. This theoretical work will enable experimental studies of fragile topology in several types of line-graph lattices, most naturally suited to superconducting circuits.
[1] C. S. Chiu, D.-S. Ma, Z.-D. Song, B. A. Bernevig, and A. A. Houck. Fragile Topology in Line-Graph Lattices with 2, 3, or 4 Gapped Flat Bands. arXiv: 2010.11953 (2020).