We examine the formation of small bipolarons in disordered systems by combining the scaling arguments of Emin and Holstein for polarons with the scaling theory of localization. For extended states away from the mobility edge, we find that for a sufficiently small Coulomb interaction the bipolaron forms at a lower electron-phonon coupling constant than the polaron and is of lower energy than two polarons when these become stable. For larger Coulomb interactions, there can be a range of for which only the polaron is stable and above that a range for which the bipolaron is the lower-energy form. As we approach the mobility edge, the extended states tend to collapse into localized polarons or bipolarons, and the region of the stability diagram corresponding to extended states shrinks and eventually disappears as the mobility edge is reached.
All Science Journal Classification (ASJC) codes
- Condensed Matter Physics