Valence Transition Theory of the Pressure-Induced Dimensionality Crossover in Superconducting Sr{14-x}Ca{x}Cu{24}O{41}

Pressure-driven superconductivity in Sr{14-x}Ca{x}Cu{24}O{41} (SCCO), containing weakly-coupled Cu2O3 ladders, is preceded by dramatic dimensional crossover from one to two dimension that has never been understood, The ``average resistivity'' immediately prior to superconducting transition corresponds to the universal 2D resistivity h/4e^2, confirming further the 2D character of the superconducting transition. Very recent theoretical work has also shown that the quasi-long range superconducting correlations found in the two-leg single-band Hubbard ladder are absent within the multiband Hubbard ladder Hamiltonian. Taken together, these results indicate serious deficiencies of the standard theoretical approaches to superconductivity in SCCO. We present DMRG computations of coupled Cu2O3 ladders within the multiband Hubbard Hamiltonian that clearly demonstrate that the dimensionality crossover is not due to pressure-induced hole transfer from the CuO2 chains to the Cu2O3 ladders, as had been assumed previously. We further show that the dimensional crossover can only be understood within a valence transition theory, within which there occurs a pressure-driven transition in Cu-ion ionicity from +2 to +1, with transfer of holes from Cu to O-ions. Following the valence transition, the system consists of a two-dimensional strongly correlated 1/4-filled oxygen sublattice. We discuss the implications of our results for hole- and electron-doped layered cuprates.