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Moiré materials provide exciting platforms for studying the interplay of strong electronic correlation and large magnetic flux effects. We study the lightly doped Hofstadter-Hubbard model on a triangular lattice through the large-scale density matrix renormalization group and determinantal quantum Monte Carlo simulations. We find strong evidence for a robust chiral superconducting (SC) phase with dominant power-law pairing correlations and a quantized spin Chern number. The SC phase emerges at very weak interaction and grows stronger at intermediate interaction strengths ( $U$ ) for a wide range of hole doping. We also discuss the possible distinct nature of the normal state in different $U$ regimes. Our Letter provides theoretical insights into the emergence of topological superconductivity from doping topological Chern bands or magnetic-flux-induced chiral spin liquid states of Moiré materials. 

The Hubbard and closely relatedt-Jmodels are exciting platforms for unconventional superconductivity (SC). Through state-of-the-art density matrix renormalization group calculations using the grand canonical ensemble, we address open issues regarding the ground-state phase diagram of the extendedt-Jmodel on a square lattice in the parameter regime relevant to cuprate superconductors. On large 8-leg cylinders, we demonstrate that the puret-Jmodel with only nearest-neighbor hoppings and superexchange interactions, for a wide range of doping ( $\delta =0.1\mathrm{to}0.2$ ), hosts robust d-wave superconductivity possibly coexisting with weak unidirectional pair density wave. Furthermore, a small next nearest neighbor hopping $t_2$ suppresses pair and charge density waves, resulting in a uniform d-wave SC phase in both electron- and hole-doped cuprate model systems. Our work validates thet-Jmodel as a proper minimum model for the emergence of superconductivity in cuprate superconductors.