by poor screening of high-frequency optical phonons and they are more appropriately described by the finite-range Fröhlich EPI. The unscreened Fröhlich EPI provides relatively light lattice polarons and combined with the Coulomb repulsion also “superlight” but yet small (intersite) bipolarons. In contrast with the crawler motion of on-site bipolarons, the intersite-bipolaron tunnelling is a crab-like, so that the effective mass scales linearly with the polaron mass. Such bipolarons are several orders of magnitude lighter than small bipolarons in HHM [@ale5]. Here I review a few analytical [@ale5; @alekor2] and more recent Quantum Monte-Carlo (QMC) [@jim2; @jim3] studies of CFM which have found superlight bipolarons in a wide parameter range with achievable phonon frequencies and couplings. They could have a superconducting transition in excess of room temperature.

Coulomb-Fröhlich model
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Any realistic theory of doped narrow-band ionic insulators should include both the finite-range Coulomb repulsion and the strong finite-range EPI. From a theoretical standpoint, the inclusion of the finite-range Coulomb repulsion is critical in ensuring that the carriers would not form clusters. The Coulomb repulsion, $V_{c}$, makes the clusters unstable and lattice bipolarons *more mobile*.

To illustrate the point let us consider a generic multi-polaron “Coulomb-Fröhlich” model (CFM) on a lattice, 