Absence of Luther-Emery superconducting phase in the three-band model for cuprate ladders

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