Flat bands with fragile topology through superlattice engineering on single-layer graphene

'Magic'-angle twisted bilayer graphene has received a lot of interest due to its flat bands with potentially non-trivial topology that lead to intricate correlated phases. A spectrum with flat bands, however, does not require a twist between multiple sheets of van der Waals materials, but rather can be realized with the application of an appropriate periodic potential. Here, we propose the imposition of a tailored periodic potential onto a single graphene layer through local perturbations that could be created via lithography or adatom manipulation, which also results in an energy spectrum featuring flat bands. Our first-principle calculations for an appropriate decoration of graphene with adatoms indeed show the presence of flat bands in the spectrum. Furthermore, we reveal the topological nature of the flat bands through a symmetry-indicator analysis. This non-trivial topology manifests itself in corner-localized states with a filling anomaly as we show using a tight-binding model. Our proposal of a single decorated graphene sheet provides a new versatile route to study correlated phases in topologically non-trivial, flat band structures.