Binding Energies, Effective Masses and Screenings Effects of Fröhlich Bipolarons

The bipolaron ground state binding energy and the effective masses are calculated self-consistently in a scheme where the electron-phonon interaction is described by the Fröhlich interaction. We explicitly use the total linear momentum conservation and both two-and three-dimensional systems are considered. We review results for binding energies and show that the bipolaron effective mass increases with the electron-phonon coupling constant α more rapidly than two free polaron masses. As expected, the increase is greater in two than in three dimensions. We estimate the screening effects due to an electronic or hole density n in a range of values such that n R 2 b ≪ 1 (here R b is the bipolaron radius). We find that the bipolaron binding energy decreases with n and eventually becomes positive indicating the existence of a metastable bipolaron state. Finally we discuss the possible connections between our results and high T c superconductivity.