Inter-Polaron Interaction and Bipolaron Formation. I

The system of two electrons coupling with phonon fields is studied with the use of the path integral method. In particular, the condition of the formation of a bipolaron and its physical properties are investigated in detail. The deformation potential interaction with acoustic phonons (the coupling constant S ac ) and the Fröhlich interaction with optical phonons ( S op ) act to help the bipolaron formation against the direct Coulomb repulsion which prevents it. Usually, S ac plays a dominant role. With ε ∞ / ε 0 ≪1 and the optical phonon energy not so large compared with the electron band width, however, the bipolaron can be formed at large values of S op even when S ac =0. The bipolaron always has an enormous effective mass; thus it is practically localized. The mean distance between two electrons in the bipolaron is usually of the order of the interatomic distance.

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