Crossover from large to small bipolarons

A variational procedure is developed to study the properties of the bipolaron in the Fröhlich model including explicitly the electron band structure and taking into account the long-range repulsive electron-electron interaction. Adopting two different ansatze for the longitudinal optical phonon distribution function, the large-bipolaron and small-bipolaron limits are obtained. The evolution of the bipolaron ground state as a function of the electron-phonon coupling constant and of the bare-electronic bandwidth is discussed and the bipolaron phase diagram is presented. A clear crossover from the large-bipolaron to the small-bipolaron regime takes place