Pair breaking in semiclassical singlet small-bipolaron hopping

The Holstein-Hubbard model is used to study high-temperature (T>T-phonon/3) hopping transport when it is energetically favorable for carriers to pair as singlet small bipolarons. The semiclassical rates for one-electron transfers involving small polarons are found to be much greater than those that only involve small bipolarons. In particular, the most rapid one-electron-transfer processes have a small-polaron hopping to a vacant site and one of a small bipolaron's two carriers jumping onto the site of an adjacent small polaron. As a result, even when most carriers form small bipolarons rather than small polarons, one-electron transfers involving small polarons always dominate the de conductivity. The energy to thermally generate small polarons from small bipolarons thus contributes to the conductivity's activation energy. This pair-breaking energy also manifests itself in a thermally activated contribution to the system's paramagnetic susceptibility. In addition, the carriers' Seebeck coefficient garners a contribution with a temperature dependence that is characterized by the pair-breaking energy.