Kagome superconductors from Pomeranchuk fluctuations in charge density wave metals

Motivated by the recent experiments on the kagome metals $A\text{V}_3\text{Sb}_5$ with $A=\text{K}, \text{Rb}, \text{Cs}$, which see onset of charge density wave (CDW) order at $\sim$ $100$ K and superconductivity at $\sim$ $1$ K, we explore the onset of superconductivity, taking the perspective that it descends from a parent CDW state. In particular, we propose that the pairing comes from the Pomeranchuk fluctuations of the reconstructed Fermi surface in the CDW phase. This scenario naturally explains the large separation of energy scale from the parent CDW. Remarkably, the phase diagram hosts the double-dome superconductivity near two reconstructed Van Hove singularities. These singularities occur at the Lifshitz transition and the quantum critical point of the parent CDW. The first dome is occupied by the $d_{xy}$-wave nematic spin-singlet superconductivity. Meanwhile, the $(s+d_{x^2-y^2})$-wave nematic spin-singlet superconductivity develops in the second dome. Our work sheds light on an unconventional pairing mechanism with strong evidences in the kagome metals $A\text{V}_3\text{Sb}_5$.