Abstract

A Feynman path-integral type of treatment is developed to determine under which conditions the energy of a bipolaron is lower than the energy of two polarons. A detailed analytical and numerical study of the Fröhlich bipolaron is presented, resulting in a phase diagram for the stability of the bipolaron in terms of the electron–phonon coupling strength α and the strength U of the Coulomb repulsion. The stability region for two- and three-dimensional bipolarons is examined for several materials.

It is shown that the bipolaron binds more easily in 2D than in 3D and that its radius is only a few ångström units. Alexandrov, Bratkovsky and Mott have recently stressed the importance of this confinement, as derived by the present authors, for high-Tc superconductivity. We analyze as an example the occurence of bipolarons in La2CuO4. First results on optical absorption of bipolarons are also presented.

Bednorz and Müller's discovery of the high-temperature superconductors stimulated both experimental and theoretical efforts to determine the mechanism responsible for superconductivity in these new materials. Bipolarons (dielectric and spin) have been invoked as possible ‘Cooper pairs’ at the basis of high-Tc superconductivity (Alexandrov, Bratkovsky and Mott [1]).

Bipolarons (large and small) had been studied before [2, 5–10] also in the context of superconductivity [3]. Emin proposed Bose–Einstein condensation of large two-dimensional bipolarons as a possible mechanism responsible for superconductivity in these materials.

In the present paper a path-integral study of large bipolarons is presented in two and three dimensions. Conditions will be discussed under which bipolarons can exist in the copper oxides. Some experimental difficulties in determining material parameters, e.g. the band mass, are also discussed.