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A lightly doped single-band Hubbard model on a two leg ladder exhibits aLuther-Emery phase, while the three-band Hubbard ladder behaves as a Luttingerliquid upon hole doping. In order to understand this discrepancy, we present asystematic density-matrix renormalization group study of the three-band Hubbardmodel on two-leg cylinders with further-neighbor particle hoppings. Theinclusion of the longer-range hopping is motivated by the studies of thesingle-band Hubbard model in which the further-neighbor hopping terms aresuggested to be crucial for the unconventional superconductivity. When thelonger-range hopping parameters are small, the ground state is a Luttingerliquid having mutually commensurate superconducting, charge and spin densitywave correlations. Increasing the longer-range hopping drives a transition intoa Luther-Emery phase with quasi-long ranged superconducting and charge ordersbut short-ranged spin-spin correlations. By down-folding the three-band Hubbardmodel into an effective $t$-$t'$-$J$-$J'$ model, we find that in theLuther-Emery phase, both the nearest and second neighbor kinetic energies areenhanced due to an effective increase of copper-oxygen hybridization.Amplifying inter-cell oxygen orbital hopping mirrors the benefits of reducingthe charge transfer energy, causing doped holes to favor oxygen orbitals andstrengthening superconducting pairing.

Recovery of a Luther-Emery phase in the three-band Hubbard model with longer-range hopping