Fragile topology in line-graph lattices with two, three, or four gapped flat bands

TL;DR

This paper develops a formalism linking geometric properties of line-graph lattices to the presence of fragile topology in their flat bands, facilitating experimental exploration in superconducting circuits.

Contribution

It introduces a theoretical framework connecting lattice geometry with fragile topology in flat bands of line-graph lattices.

Findings

Identifies conditions for fragile topology in flat bands

Connects geometric frustration with topological properties

Enables experimental studies in superconducting circuits

Abstract

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 here we develop a formalism to connect some of their geometric properties with the presence or absence of fragile topology in their flat bands. This theoretical work will enable experimental studies of fragile topology in several types of line-graph lattices, most naturally suited to superconducting circuits.