Abstract

Two-polaron states on a square lattice are studied in the presence of on-site repulsion U and inter-site attraction V. In the limit of infinite U the exact critical value Vcr for bipolaron formation is obtained as a function of the attraction radius R. The results are compared with the continuum limit of the same model. It is shown that if R≃(2–3) lattice constants then Vcr is of the order of the characteristic phonon frequency in the high-temperature superconductors.

The temperature-dependence of the upper critical field [1,2], the resistivity and Seebeck coefficient [3], and the universal correlation between the critical temperature and the hole content [4] in the p-type oxide superconductors unambiguously support the validity of the local pair conception for these compounds at low doping 0.06≤n≤0.12. Phonons are the most natural candidates for the bosonic field whose interaction with the carriers (polarons) results in the effective interpolaron attraction. However, there are several arguments against the phonon pairing mechanism. One of them is that the phonon-mediated attraction between polarons is much weaker than the shortrange Coulomb repulsion, hence creation of local pairs is inhibited. The typical estimates for the on-site copper, copper–oxygen, and inter-site copper Coulomb potentials are Udd≃10 eV, Upd≃1 eV and U′dd≃Q.l eV correspondingly [5, 6]. Since the typical phonon frequency ω is of the order of 0.1 eV or less, ω » U/dd, Upd and ω≃U′dd and therefore the existence of the local pair in which the polarons are localized on the same lattice site or on the nearest neighbours is impossible.