Interplay of Higher-Order van Hove Singularities and Band Topology in Kagome Systems

In 2D materials, van Hove Singularities (VHS) for the density of states usually correspond to saddle points on the energy bands in the momentum space. The Higher-order VHS (HOVHS) is a new classification of VHS that corresponds to a higher-order saddle point, where a power law describes the density of states. Here, we investigate the Kagome lattice using the tight-binding model and produced a set of phase diagrams demonstrating HOVHS emergence for the high-symmetry points in the Brillouin zone. We also discuss the onset of these HOVHS in topological Chern bands in the kagome lattice.