Topological superconductivity with emergent vortex lattice in twisted semiconductors

The coexistence of superconductivity and fractional quantum anomalous Hall (FQAH) effect has recently been observed in twisted MoTe$_2$ and theoretically demonstrated in a model of repulsively interacting electrons under an emergent magnetic field arising from the layer pseudospin texture in moiré superlattice. Here, we show that this superconducting state is a chiral $f$-wave superconductor hosting an array of $double$ vortices, which are induced by the emergent magnetic field with $h/e$ flux quanta per moiré unit cell. This superconducting vortex lattice state is topological and features Chern number $-1/2$, giving rise to a half-integer thermal Hall conductance. Our theory provides a common mechanism and unified understanding of FQAH and topological superconductivity, with a rich phase diagram controlled by the spatial modulation of the emergent magnetic field.