  Most of the proposed models of high-temperature superconductivity (HTSC) are
based on the short-range electron-electron correlations or/and on a short-range
electron-phonon interaction. However, in the cuprates the screening is poor due
to a low carrier density, layered crystal structure, and high ionicity of the
lattice. We develop further the bipolaron model of HTSC, which explicitly takes
into account the long-range origin of all interactions. The long-range
electron-phonon (Froehlich) interaction binds carriers into real space pairs
(small bipolarons) with surprisingly low mass but sufficient binding energy,
while the long-range Coulomb repulsion keeps them from forming larger clusters.
The model has explained many key features of cuprates. Here it is shown that
real-space pairing takes place in many cuprates at variance with some
(incorrect) criteria of the BCS-BEC crossover.

Superconductivity;Strongly Correlated Electrons