Emergent Topological Chiral Superconductivity in a Triangular-Lattice $t$-$J$ Model

Topological superconductivity (TSC) is a highly sought-after superconducting state hosting topological order and Majorana excitations. In this work, we explore the mechanism to the TSC in the doped Mott insulators with time-reversal symmetry (TRS). Through large-scale density matrix renormalization group study of an extended triangular-lattice $t$-$J$ model on the $6$- and $8$-leg cylinders, we identify a $d+id$-wave chiral TSC phase with spontaneous TRS breaking, which is characterized by a Chern number $C=2$ and quasi-long-range superconducting order. We map out the quantum phase diagram with tuning the next-nearest-neighbor (NNN) electron hopping and spin interaction. In the weaker NNN-coupling regime, a charge stripe phase coexisting with strong spin fluctuations and fluctuating superconductivity is revealed. The TSC emerges in the intermediate-coupling regime, which has a transition to a $d$-wave superconducting phase at larger NNN couplings. The emergence of the TSC is driven by geometrical frustrations and hole dynamics, which suppress spin correlation and charge order, leading to a topological quantum phase transition.