Multi-dome superconductivity in charge density wave kagome metals

Motivated by the recent experiments on the kagome metals $A\text{V}_3\text{Sb}_5$ with $A=\text{K}$, $\text{Rb}$, and $\text{Cs}$, which see the charge density wave (CDW) at $\sim$ $100$ K and the superconductivity at $\sim$ $1$ K, we explore the onset of the superconductivity, taking the perspective that it descends from a parent CDW. We argue that viewing the superconductivity as a weak-coupling instability of a reconstructed (by the CDW) Fermi surface naturally explains the experimentally observed 'multi-dome' non-monotonic dependence on pressure, with the 'peaks' in the superconducting critical temperature being associated to the Van Hove singularities of the reconstructed Fermi surface. This 'parent-child relationship' also naturally explains the large separation of energy scales between the superconductivity and the CDW. We discuss different possible pairing mechanisms, and speculate that the CDW/reconstructed Pomeranchuk fluctuations may mediate the pairing interaction.Comment: 9 pages, 4 figures. v2: Reorganization with additional supportive results from extensive numerical computatio