Global Phase Diagram of D-wave Superconductivity in the Square-Lattice $t\text{-}J$ Model

Abstract

The Hubbard and closely related $t\text{-}J$ models are exciting platforms for unconventional superconductivity (SC). Through state-of-the-art density matrix renormalization group calculations using the grand canonical ensemble, we address open issues regarding the ground-state phase diagram of the extended $t\text{-}J$ model on a square lattice in the parameter regime relevant to cuprate superconductors. On large 8-leg cylinders, we demonstrate that the pure $t\text{-}J$ model with only nearest-neighbor hoppings and superexchange interactions, for a wide range of doping ($\delta =0.1-0.2$), hosts robust d-wave superconductivity possibly coexisting with weak unidirectional pair density wave. Furthermore, a small next nearest neighbor hopping $t_2$ suppresses pair and charge density waves, resulting in a uniform d-wave SC phase in both electron- and hole-doped cuprate model systems. Our work validates the $t\text{-}J$ model as a proper minimum model for the emergence of superconductivity in cuprate superconductors.

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