Abstract: In the limit of strong electron-phonon coupling, we use either a Pekar-type or an oscillator wave function for the center-of-mass coordinate and either a Coulomb or an oscillator wave function for the relative coordinate, and are able to reproduce all the results from the literature for the large-bipolaron binding energy. Lower bounds are constructed for the critical ratio eta(c) of dielectric constants below which bipolarons can exist. It is found that, in the strong-coupling limit, the stability region for bipolaron formation is much larger in two dimensions (2D) than in 3D. We introduce a model that combines the averaging of the relative coordinate over the asymptotically best wave function with a path-integral treatment of the center-of-mass motion. The stability region for bipolaron formation is increased compared with the full path-integral treatment at large values of the coupling constant alpha. The critical values are alpha(c) almost-equal-to 9.3 in 3D and alpha(c) almost-equal-to 4.5 in 2D. Phase diagrams for the presented models are also obtained in both 2D and 3D.

Abstract: In the present paper, the theory of the large bipolaron is reviewed and the possibility of bipolaron formation in the high-T(c) superconductors is indicated. Operator and path-integral formulations of the large bipolaron problem are compared. In the strong-coupling limit, the effect of non-optimal upper-bounds to the single-polaron groundstate energy is emphasized. The fact that the interaction with multiple phonon branches enhances the electron-phonon interaction and might result in a larger stability region for bipolaron formation is indicated. Experimental values for the static and high-frequency dielectric constants are used to discuss the relevance of bipolaron formation as a pair-forming mechanism in the high-T(c) superconductors.