Superconducting stripes in the hole-doped three-band Hubbard model

We study the ground state properties of the hole-doped three-band Hubbard (Emery) model, describing the copper-oxygen planes of the cuprates, using large-scale 2D tensor network calculations. Our simulations reveal a period 4 stripe state with spin and weak charge order over an extended doping range beyond $\delta \sim 0.12$ and stripes with larger periods at smaller doping. The period 4 stripe exhibits coexisting $d$-wave superconductivity in the doping range $0.15\lesssim \delta <0.25$, while at smaller doping around $\delta \sim 1\mathrm{/}8$ we find a strong competition between superconducting and non-superconducting stripes, including also pair density-wave states with alternating sign structure on neighboring stripes, suggesting that the fate of superconductivity around 1/8 doping may be sensitive on the model parameters.