Chiral superconductivity near a fractional Chern insulator

Abstract: 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 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 moire potential. Large-scale density-matrix renormalization group (DMRG) calculations show that, as the FCI gap closes, two nearly degenerate phases emerge before a metallic state forms. A chiral $f+if$ superconductor and a commensurate $\sqrt{3} \times \sqrt{3}$ charge-density wave (CDW) differ in energy by less than $1\%$, reproducing the distinct superconducting and re-entrant integer quantum Hall (RIQH) phases experimentally observed near the FCI regime. The superconducting dome remains robust against realistic Coulomb screening, light doping, and variations in 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.