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Unravelling competing orders emergent in doped Mott insulators and theirinterplay with unconventional superconductivity is one of the major challengesin condensed matter physics. To explore possible superconductivity state in thedoped Mott insulator, we study a square-lattice $t$-$J$ model with both thenearest and next-nearest-neighbor electron hoppings and spin Heisenberginteractions. By using the state-of-the-art density matrix renormalizationgroup simulations with imposing charge $U(1)$ and spin $SU(2)$ symmetries onthe large-scale six-leg cylinders, we establish a quantum phase diagramincluding three phases: a stripe charge density wave phase, a superconductingphase without static charge order, and a superconducting phase coexistent witha weak charge stripe order. Crucially, we demonstrate that the superconductingphase has a power-law pairing correlation decaying much slower than the chargedensity and spin correlations, which is a quasi-1D descendant of the uniformd-wave superconductor in two dimensions. These findings reveal that enhancedcharge and spin fluctuations with optimal doping is able to produce robustd-wave superconductivity in doped Mott insulators, providing a foundation forconnecting theories of superconductivity to models of strongly correlatedsystems.

Robust d-wave superconductivity in the square-lattice $t$-$J$ model