Superconductivity in doped triangular Mott insulators: the roles of parent spin backgrounds and charge kinetic energy

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 $t_2\mathrm{/}{t}_1$, flipping the signs ${\tau }_2$ and ${\tau }_1$ gives rise to the stripe phase without strong pairing and pseudogap-like phase without Cooper-pair phase coherence, respectively. Interestingly, the roles of the two hopping signs are switched at smaller $t_2\mathrm{/}{t}_1$. Moreover, different sign combinations $({\tau }_1,{\tau }_2)$ would stabilize distinct phases including superconductivity, charge density waves, spin density waves, and pseudogap-like phases accordingly. Our findings suggest the important role of charge kinetic energy in realizing superconductivity in doped triangular-lattice Mott insulators.