Global phase diagram of D-wave superconductivity in the square-lattice <i>t-J</i> model.

Abstract

The Hubbard and closely related <i>t-J</i> 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 <i>t-J</i> model on a square lattice in the parameter regime relevant to cuprate superconductors. On large 8-leg cylinders, we demonstrate that the pure <i>t-J</i> model with only nearest-neighbor hoppings and superexchange interactions, for a wide range of doping ([Formula: see text]), hosts robust d-wave superconductivity possibly coexisting with weak unidirectional pair density wave. Furthermore, a small next nearest neighbor hopping [Formula: see text] 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 <i>t-J</i> model as a proper minimum model for the emergence of superconductivity in cuprate superconductors.