Self-consistent theory of $2\times 2$ pair density waves in kagome superconductors

Pair density wave (PDW) is an intriguing quantum matter proposed in the frontier of condensed matter physics. However, the existence of PDW in microscopic models has been rare. In this work, we obtain, by Ginzburg-Landau arguments and self-consistent mean field theory, novel $2a_0\times 2a_0$ PDW on the kagome lattice arising from attractive on-bond pairing interactions and the distinct Bloch wave functions near the p-type van Hove singularity. The PDW state carrying three independent wave-vectors, the so-called 3Q PDW, is nodeless and falls into two topological classes characterized by the Chern number $C=0$ or $C=\pm 2$. The chiral ($C=\pm 2$) PDW state presents a rare case of interaction driven topological quantum state without the requirement of spin-orbit coupling. Finally, we analyze the stabilities and properties of these PDWs intertwining with charge orders, and discuss the relevance of our minimal model to recent experimental observations in kagome superconductors. Our theory not only elucidates the driving force of the chiral PDW, but also predicts strongly anisotropic superconducting gap structure in the momentum space and quantized transverse thermal conductivity that can be tested in future experiments.