Flux Phase as a Dynamic Jahn-Teller Phase: Berryonic Matter in the Cuprates?

There is considerable evidence for some form of charge ordering on the hole-doped stripes in the cuprates, mainly associated with the low-temperature tetragonal phase, but with some evidence for either charge density waves or a flux phase, which is a form of dynamic charge-density wave. These three states form a pseudospin triplet, demonstrating a close connection with the E X e dynamic Jahn-Teller effect, suggesting that the cuprates constitute a form of Berryonic matter. This in turn suggests a new model for the dynamic Jahn-Teller effect as a form of flux phase. A simple model of the Cu-O bond stretching phonons allows an estimate of electron-phonon coupling for these modes, explaining why the half breathing mode softens so much more than the full oxygen breathing mode. The anomalous properties of $O^{2-}$ provide a coupling (correlated hopping) which acts to stabilize density wave phases.