A lightly doped single-band Hubbard model on a two leg ladder exhibits a
Luther-Emery phase, while the three-band Hubbard ladder behaves as a Luttinger
liquid upon hole doping. In order to understand this discrepancy, we present a
systematic density-matrix renormalization group study of the three-band Hubbard
model on two-leg cylinders with further-neighbor particle hoppings. The
inclusion of the longer-range hopping is motivated by the studies of the
single-band Hubbard model in which the further-neighbor hopping terms are
suggested to be crucial for the unconventional superconductivity. When the
longer-range hopping parameters are small, the ground state is a Luttinger
liquid having mutually commensurate superconducting, charge and spin density
wave correlations. Increasing the longer-range hopping drives a transition into
a Luther-Emery phase with quasi-long ranged superconducting and charge orders
but short-ranged spin-spin correlations. By down-folding the three-band Hubbard
model into an effective t-t′-J-J′ model, we find that in the
Luther-Emery phase, both the nearest and second neighbor kinetic energies are
enhanced due to an effective increase of copper-oxygen hybridization.
Amplifying inter-cell oxygen orbital hopping mirrors the benefits of reducing
the charge transfer energy, causing doped holes to favor oxygen orbitals and
strengthening superconducting pairing