Thermodynamic-Limit Evidence for Chiral Superconductivity Induced by Doping Chiral Topological Phases

The emergence of chiral superconductivity from strongly correlated Mott regimes in purely repulsive, genuinely two-dimensional fermionic systems poses a key challenge, particularly when topology and superconducting long-range order must be treated on equal footing. Here we provide direct thermodynamic-limit evidence for chiral superconductivity in the triangular Hofstadter-Hubbard model relevant to moir\'e materials. This is achieved by advancing a simplex tensor-network formulation that simultaneously captures superconducting long-range order and chiral topological order in interacting fermionic systems with intrinsic charge fluctuations. We show that a chiral spin liquid occupies a broad intermediate-$U$ regime, forming a robust undoped parent state. Upon hole doping, we identify a uniform chiral superconducting phase in the infinite system, diagnosed directly by a finite complex pairing order parameter and chiral entanglement spectrum. The superconducting phase exhibits an almost universal phase winding across a wide interaction-doping region, together with a distinct pocket of opposite winding near the Mott criticality. These results establish thermodynamic-limit chiral superconductivity emerging from doped chiral topological states, revealing richer winding competition near the Mott transition point of the undoped system while preserving a common chiral topological character throughout the superconducting region.