Statistical learning of engineered topological phases in the kagome superlattice of AV3Sb5

Recent experimental findings have reported the presence of unconventional charge orders in the enlarged (2 x 2) unit-cell of kagome metals AV(3)Sb(5) (A = K, Rb, Cs) and hinted towards specific topological signatures. Motivated by these discoveries, we investigate the types of topological phases that can be realized in such kagome superlattices. In this context, we employ a recently introduced statistical method capable of constructing topological models for any generic lattice. By analyzing large data sets generated from symmetry-guided distributions of randomized tight-binding parameters, and labeled with the corresponding topological index, we extract physically meaningful information. We illustrate the possible real-space manifestations of charge and bond modulations and associated flux patterns for different topological classes, and discuss their relation to present theoretical predictions and experimental signatures for the AV(3)Sb(5) family. Simultaneously, we predict higher-order topological phases that may be realized by appropriately manipulating the currently known systems.