  Correlated-electron theories of superconductivity in layered cuprates often
start from the premise of a gapped spin-liquid phase proximate to the
superconducting state. This assumption is justified based on analytical and
numerical demonstrations of a superconducting Luther-Emery phase in the doped
2-leg one-band Hubbard ladder, and the perceived analogy between coupled
ladders and the two dimensional CuO2 layer. We demonstrate from accurate
density matrix renormalization group studies the absence of the superconducting
Luther-Emery phase in the doped 2-leg three-band ladder consisting of both
copper and oxygen, even as the spin gap is large in the undoped three-band
ladder. For realistic oxygen-oxygen hopping and Hubbard repulsion on the oxygen
atoms, density-density rather than pairing correlations are dominant at long
range. This result is equally valid whether or not the oxygens outside the
ladder proper, over and above the rung and leg oxygens, are included in the
computation. These results demonstrate the critical importance of oxygen
orbitals, and raise disturbing questions about the applicability of many of the
existing correlated-electron theories of superconductivity.
