Small-bipolaron formation

Using the scaling arguments of Emin and Holstein, we examine the formation of small bipolarons by coupling of electrons to acoustic phonons. We find that for sufficiently small Coulomb interactions, the bipolaron forms at 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.