Topological superconductivity from Abelian fractional Chern insulators

Abstract

Can a Laughlin anyon fluid become a topological superconductor? We answer this question for a $ν=1/3$ fractional Chern insulator (FCI) using a $U(3)$ infrared parton theory. Three charge-$e/3$ 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 $c_-=3/2$, and a strong-pairing anyon superconductor with $c_-=3$. The same framework organizes a nearby $σ_{xy}=0$ charge density wave (CDW) state. At commensurate filling, the normal state and the $c_-=3$ and $c_-=3/2$ 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 $c_-=3/2$ topological superconductor. The FCI, reentrant CDW, and chiral superconductivity are unified in the $U(3)$ parton theory.