Chiral $p$-Wave Superconductivity Proximate to a Fractional Chern Insulator and a Topological Charge Density Wave in a Moiré Chern Band

We study a spin-polarized moiré Chern band of twisted MoTe$_2$ with short-range repulsion, finding superconductivity proximate to a fractional Chern insulator at filling $ν=2/3$ and a topological charge density wave at $ν=3/4$. Exact diagonalization reveals pair binding over $0.7\lesssimν\lesssim0.77$, consistent with experiment, along with finite superfluid stiffness, chiral $p$-wave pairing correlations, and adiabatic connectivity to an attractive model. At weak repulsion, Kohn-Luttinger theory supports a Fermi-surface instability with the same pairing symmetry. The superconducting state has a Bogoliubov-de Gennes Chern number $C_{\mathrm{BdG}}=-1$, opposite to the normal-state Chern number at $ν=1$. Our results reveal interplay among superconductivity, fractional topology, and charge order.