Valence transition theory of the pressure-induced dimensionality crossover in superconducting Sr14-xCaxCu24O41

One of the strongest justifications for the continued search for superconductivity within the single-band Hubbard Hamiltonian originates from the apparent success of single-band ladder-based theories in predicting the occurrence of superconductivity in the cuprate coupled-ladder compound Sr14-xCaxCu24O41. Recent theoretical works have, however, shown the complete absence of quasi-long-range superconducting correlations within the hole-doped multiband ladder Hamiltonian including realistic Coulomb repulsion between holes on oxygen sites and oxygen-oxygen hole hopping. Experimentally, superconductivity in Sr14-xCaxCu24O41 occurs only under pressure and is preceded by dramatic transition from one to two dimensions that remains not understood. We show that understanding the dimensional crossover requires adopting a valence transition model within which there occurs transition in Cu-ion ionicity from +2 to +1, with transfer of holes from Cu to O ions [S. Mazumdar, Phys. Rev. B 98, 205153 (2018)]. The driving force behind the valence transition is the closed-shell electron configuration of Cu1+, a feature shared by cations of all oxides with a negative charge-transfer gap. We make a falsifiable experimental prediction for Sr14-xCaxCu24O41 and discuss the implications of our results for layered two-dimensional cuprates.