We study the prerequisites for realizing superconductivity in doped triangular-lattice Mott insulators by considering three distinct parent spin backgrounds, i.e., ${120}^{\circ }$ antiferromagnets, quantum spin liquid, and stripy antiferromagnets, and all possible sign combinations $({\tau }_1,{\tau }_2)$ of nearest-neighbor hopping and next-nearest-neighbor hopping $(t_1,t_2)$. Based on density matrix renormalization group calculations, we find that, with finite $t_2$ and specific sign combinations $({\tau }_1,{\tau }_2)$, the quasi-long-range superconductivity order can always be achieved, regardless of the nature of the parent spin backgrounds. Besides specific hopping signs $({\tau }_1,{\tau }_2)$, these superconductivity phases in triangular lattices are commonly characterized by short-ranged spin correlations and two charges per stripe. In the robust superconductivity phase realized at larger $t_2/t_1$, flipping the signs ${\tau }_2$ and ${\tau }_1$ gives rise to the stripe phase without strong pairing and a pseudogaplike phase without Cooper-pair phase coherence, respectively. Interestingly, the roles of the two hopping signs are switched at smaller $t_2/t_1$. Moreover, different sign combinations $({\tau }_1,{\tau }_2)$ would stabilize distinct phases including superconductivity, charge density waves, spin density waves, and pseudogaplike phases accordingly. Our findings suggest the important role of charge kinetic energy in realizing superconductivity in doped triangular-lattice Mott insulators.

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• Pairing mechanisms
• Superconductivity
• Mott insulators
• Strongly correlated systems
• Density matrix renormalization group