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The mechanism of the unconventional topological superconductivity (TSC)remains a long-standing issue. We investigate the quantum phase diagram of theextended $t$-$J$-$J_{\chi}$ model including spin chiral interactions ontriangular lattice based on the state-of-the-art density matrix renormalizationgroup simulations. We identify distinct classes of superconducting phasescharacterized by nonzero topological Chern numbers $C=1$ and $2$, and a nematicd-wave superconducting phase with a zero Chern number. The TSC states are shownto emerge from doping either a magnetic insulator or chiral spin liquid, whichopens new opportunities for experimental discovery. In addition, we furtherclassify the $C=2$ class of TSC phases into an isotropic and a nematic TSCphases, and present evidence of continuous quantum phase transitions from thenematic TSC phase to both isotropic TSC and nematic d-wave phases. Theseresults provide new insight into the mechanism of TSC with an emphasis on therole played by hole dynamics, which changes spin background and drives atopological phase transition at a hole doping level around $3\%$ upon doping amagnetic insulator to enable the emergence of the TSC.

Topological chiral and nematic superconductivity by doping Mott insulators on triangular lattice