Sublattice Interference promotes Pair Density Wave in Kagome Metals*

We show that at the p-type van Hove filling in a Kagome lattice, the sublattice interference provides the microscopic basis for the formation of a pair density wave state at intermediate coupling strength. We first show that the sublattice interference allows for a simple identification of lattice interactions on band fermions. And from analyzing how  the interactions are renormailized when the energy scale is lowered, we find that the Hubbard repulsion U becomes weaker, while other interactions such as nearest neighbor density repulsion V, on-bond exchange interaction J₀ and bond pair hopping J₁ can be significantly enhanced. Next, using mean field analysis, we find that both V and J₁ can be attractive at finite momentum, and, if strong enough, can give rise to the pair density wave order. In cases when J₀ becomes large, bond charge order may also arise. We argue that this establishes the microscopic foundation for pair density waves in Kagome metals.