Statistical learning of engineered topological phases in the kagome superlattice of AV${}_3$Sb${}_5$

Abstract

Recent experimental findings have reported the presence of unconventional charge orders in the enlarged ($2\times 2$) 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 new higher-order topological phases that may be realized by appropriately manipulating the currently known systems.

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• Origin of $\pi$-shifted three-dimensional charge density waves in kagome metal AV${}_3$Sb${}_5$
• Detecting topological phases in the square-octagon lattice with statistical methods
• Inter-Layer Correlation of Loop Current Charge Density Wave on the Bilayer Kagomé Lattice
• Charge-density waves in kagome-lattice extended Hubbard models at the van Hove filling