3D stacking of Kagome layers: interplay between symmetry, spin-orbit coupling, and topology

2D Kagome structure, with its pattern of corner-sharing triangles, is getting growing attention due to many interesting features related to frustrated magnetism, topology, and superconductivity, etc.. When stacked together to form 3D bulk structures, these Kagome layers can host new terms in their tight-binding Hamiltonians due to the broken symmetries. In this work, we screen out all possible crystallographic space groups that can host "perfect" Kagome layers and list all possible Kagome stackings. Through a group theoretical analysis, we build tight-binding models for each case, and study how the band structures and topological properties are influenced by different terms. Real-material examples are also included with the help of first-principle calculations (DFT).