We variationally determine the conditions for the formation of large singlet bipolarons within the adiabatic approximation. We find that, in two- and three-dimensional electronic systems with only a short-range electron-lattice interaction, the only bipolarons are small bipolarons. Furthermore, with only the long-range (Fröhlich) electron-lattice interaction characteristic of an ionic solid, we find the classical result that bipolarons will not form. However, with the presence of both short- and long-range components of the electron-lattice interaction, we find a novel domain within which large bipolarons can be formed. In particular, an exceptionally large ratio of the static to high-frequency dielectric constants, ${\epsilon }_0$ and ${\epsilon }_{\infty }$, respectively, is critical to the formation of large singlet bipolarons. The remaining conditions for the formation of large singlet bipolarons are much less stringent for electronic systems of two dimensions than for those of three dimensions. Therefore, with the high-temperature superconductors having ${\epsilon }_0$≫${\epsilon }_{\infty }$, the notion that their charge carriers are singlet large bipolarons is a real possibility. Estimating the transition temperature for bipolaronic superconductivity as the temperature of the Bose-Einstein condensation, transition temperatures of the order of those found in the high-temperature superconductors are reasonably obtained. Furthermore, if, as envisioned in the ${\mathrm{CuO}}_2$-based materials, the mass of the large bipolaron is dominated by the short-range interaction of the carrier occupying oxygen sites with the surrounding (relatively heavy) cations, there is only a slight dependence of the transition temperature on isotopic substitutions for the solid’s oxygen atoms. Finally, the transition temperature increases linearly with the thickness of the disk-shaped bipolaron (the number of contiguous ${\mathrm{CuO}}_2$ sheets) until a limiting value is achieved when the bipolaron’s shape approaches three dimensionality. These findings are consistent with the general features of the high-temperature superconducting materials.

• Received 16 November 1988

DOI:https://doi.org/10.1103/PhysRevB.39.6575