Superconductivity in zigzag CuO chains

Superconductivity has recently been discovered in ${\mathrm{Pr}}_{2}{\mathrm{Ba}}_{4}{\mathrm{Cu}}_{7}{\mathrm{O}}_{15\ensuremath{-}\ensuremath{\delta}}$ with a maximum ${T}_{c}$ of about $15\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Since the CuO planes in this material are believed to be insulating, it has been proposed that the superconductivity occurs in the double (or zigzag) CuO chain layer. On phenomenological grounds, we propose a theoretical interpretation of the experimental results in terms of a phase for the zigzag chain, labeled by ${\mathrm{C}}_{1}{\mathrm{S}}_{3∕2}$. This phase has a gap in the relative charge mode and a partial gap in the relative spin mode. It has gapless uniform charge and spin excitations and can have a divergent superconducting susceptibility, even for repulsive interactions. A microscopic model for the zigzag CuO chain is proposed, and on the basis of density matrix renormalization group and bosonization studies, we adduce evidence that supports our proposal.