Topological superconductivity from Abelian fractional Chern insulators

Can a Laughlin anyon fluid become a topological superconductor? We answer this question for a $\nu =1\mathrm{/}3$ fractional Chern insulator (FCI) using a $U(3)$ infrared parton theory. Three charge-$e\mathrm{/}3$ constituents form the electron, while three constituent pairs form a gauge-invariant charge-$2e$ Cooper pair. The resulting superconductors share an ordinary charge-$2e$ sector but differ in their neutral color response, giving an SC${}^{\ast }$ with the parent Laughlin $U(1{)}_3$ order, a chiral topological superconductor with $c_{-}=3\mathrm{/}2$, and a strong-pairing anyon superconductor with $c_{-}=3$. The same framework organizes a nearby ${\sigma }_{xy}=0$ charge density wave (CDW) state. At commensurate filling, the normal state and the $c_{-}=3$ and $c_{-}=3\mathrm{/}2$ superconducting descendants are naturally tied to a period-three density order background, while the SC${}^{\ast }$ branch can preserve microscopic translations. Away from commensuration, a chargon metal can pair into the same $c_{-}=3\mathrm{/}2$ topological superconductor. The FCI, reentrant CDW, and chiral superconductivity are unified in the $U(3)$ parton theory.