Berryonic Matter in the Cuprates

A novel form of Jahn-Teller (JT) effect in the cuprates can be reinterpreted as a conventional JT effect on a lattice with a larger unit cell. There is a triplet of instabilities, parametrized by a pseudospin, consisting of a form of the low-temperature tetragonal phase, a charge density wave phase, and a flux phase (orbital antiferromagnet). On a single 4-Cu plaquette, the problem is of E x (b_1+b_2) form. For a special choice of parameters, the model supports a dynamic JT effect, but is classically chaotic. The connection of this phase with Berryonic matter is discussed.