Pair density wave and superconductivity in doped three band Hubbard model with second-neighbor electron hopping

We study the ground state properties of the lightly hole-doped three-band Hubbard model on a two-leg cylinder using density matrix renormalization group. By including the second-neighbor hopping terms t_dd between Cu orbitals and t_pp' between oxygen orbitals, we have observed a rich ground state phase diagram with intertwined orders including pair-density-wave (PDW), d-wave superconductivity (SC), charge density wave (CDW) and spin density wave (SDW) orderes. The superconducting pair-field correlations in both the PDW and d-wave SC phases are dominant between the neighboring Cu orbitals with d-wave pairing symmetry. By tuning the sign and magnitude of t_dd and t_pp' , the relative charge density between Cu and oxygen orbitals is reshuffled, and the relative strength of superconducting correlations between PDW and d-wave SC states is also changed. The connection and comparison between the single-band and three-band Hubbard model are also discussed.