Designing Topological High-Order Van Hove Singularities: Twisted Bilayer Kagom\'e

The interplay of high-order Van Hove singularities and topology plays a central role in determining the nature of the electronic correlations governing the phase of a system with unique signatures characterising their presence. Layered van der Waals heterostuctures are ideal systems for band engineering through the use of twisting and proximity effects. Here, we use symmetry to demonstrate how twisted Kagom\'e bilayers can host topological high-order Van Hove singularities. We study a commensurate system with a large twist angle and demonstrate how the initial choice of high-symmetry stacking order can greatly influence the electronic structure and topology of the system. We, furthermore, study the sublattice interference in the system. Our results illustrate the rich energy landscape of twisted Kagom\'e bilayers and unveil large Chern numbers (of order 10), establishing twisted bilayer Kagom\'e as a natural playground for probing the mixing of strong correlations and topology.