Van Hove charge density waves on hexagonal lattices: Haldane-model phase diagram, higher-order topology, and kagome superconductors

I show that the charge density waves can realize a host of unconventional phenomena at the Van Hove singularity on the hexagonal lattices, including the triangular, honeycomb, and kagome lattices. Under the interplay of real and imaginary orders, a Haldane-model phase diagram arises from the 3Q complex orders at three nesting momenta. The Chern insulators explain transparently the recent experiments on the kagome metals AV₃Sb₅ with A = K, Rb, Cs. Meanwhile, the 3Q charge bond orders can realize the higher-order topological insulators, where in-gap corner states arise and manifest fractional corner charges. I further propose that the superconductivity can develop from the reconstructed Pomeranchuk fluctuations in the parent charge density waves, which acquires strong evidences in the kagome metals AV₃Sb₅. Our theoretical model unprecedently explains the double-dome superconductivity under pressure, which is attributed to two reconstructed Van Hove singularities. More intriguing phenomena are expected for future explorations.