Chiral superconductivity near a fractional Chern insulator

Superconductivity arising from fully spin-polarized, repulsively interacting electrons can host intrinsically chiral Cooper pairs and Majorana zero modes, yet no concrete microscopic route to such a state has been established. Motivated by recent observations in twisted homobilayer MoTe$_2$ and rhombohedral pentalayer graphene, where fractional Chern insulators (FCIs) appear adjacent to spin-valley-polarized superconductors, we investigate a minimal model: spinless electrons in the lowest Landau level subject to a tunable periodic potential. Large-scale density-matrix renormalization group (DMRG) calculations reveal that, as the FCI gap closes, two nearly degenerate phases emerge before the system turns metallic: a chiral $f$-wave superconductor and a $\sqrt{3} \times \sqrt{3}$ charge-density wave (CDW) whose energies differ by less than $1\%$. These two competing states mirror the superconducting and re-entrant integer quantum Hall (RIQH) phases observed experimentally near the FCI regime. The superconducting dome survives realistic Coulomb interaction, light doping, and various lattice geometry. Melting the FCI therefore provides a new mechanism for realizing spin-polarized chiral superconductivity and RIQH order. We predict that twisted MoTe$_2$ at larger twist angles will develop a superconducting dome even at filling $\nu = 2/3$, and suppressing this superconductivity with a magnetic field should drive the system into an RIQH state.