The Valence Transition model for the pressure-induced 1D-to-2D dimensionality crossover in Sr(14-x)Ca(x)Cu(24)O(41).*

We investigate theoretically the pressure-induced 1D-to-2D dimensionality crossover [1] in (Sr,Ca)[14]Cu[24]O[41] using DMRG for coupled multiband ladders containing both Cu and O. We report numerical results for two coupled ladders of 8 and 12 Cu-O-Cu rungs, using realistic hopping and Hubbard interaction parameters. Dimensionality effects are measured through computations of intra and interladder O-O bond orders (charge-transfers). The ratio of intra-versus interladder bond orders is very large for realistic parameters and carrier densities, in agreement with the experimentally observed one-dimensional behavior under ambient pressure [1]. We show that neither the assumption of increasing inter-ladder hopping nor carrier density can explain the dimensionality crossover. We then show that the recently proposed valence transition model [2], within which there occurs a discrete jump in Cu(2+)-to-Cu(1+) ionicity, leading to negative charge-transfer gap and a very large concomitant increase in the number of charge carriers on the O-sites, aptly explains the dimensionality crossover. We argue that a similar valence transition explains the very large doping-induced carrier densities in hole-[3] and electron-doped layered cuprates [4].