  The effect of the Berry phase is included explicitly in the wavefunction
describing conduction electrons in a crystal composed of periodically arrayed
Jahn-Teller centers that have conically intersecting potential energy surfaces.
The Berry phase can make a drastic change in the band structure, leading
generally to the formation of an orbital-density-wave state. We discuss
implications of our theory and possible relations to the orbital ordering
observed in the manganese perovskites.
