  The recent discovery of novel charge density wave (CDW) and pair density wave
(PDW) in kagom\'e lattice superconductors $A$V$_3$Sb$_5$ ($A=$ K, Rb, Cs) hints
at unexpected time-reversal symmetry breaking correlated and topological states
whose physical origin and broader implications are not understood. Here, we
make conceptual advances toward a mechanism behind the striking observations
and new predictions for novel macroscopic phase coherent quantum states. We
show that the metallic CDW state with circulating loop currents is a doped
orbital Chern insulator near van Hove filling. The emergent Chern Fermi pockets
(CFPs) carry concentrated Berry curvature and orbital magnetic moment. We find
that the pairing of electrons on the CFPs leads to a superconducting state with
an emergent vortex-antivortex lattice and the formation of a complex
triple-\textbf{Q} PDW. A plethora of correlated and topological states emerge,
including a never-before-encountered chiral topological PDW superconductor, a
loop-current pseudogap phase, and vestigial charge-4$e$ and charge-6$e$
superconductivity in staged melting of the vortex-antivortex lattice and
hexatic liquid crystal. Our findings reveal previously unknown nature of the
superconducting state of a current-carrying Chern metal, with broad
implications for correlated and topological materials.
