  It is widely accepted that phonon-mediated high-temperature superconductivity
is impossible at ambient pressure, because of the very large effective masses
of polarons/bipolarons at strong electron-phonon coupling. Here we challenge
this belief by showing that strongly bound yet very light bipolarons appear for
strong Peierls/Su-Schrieffer-Heeger interaction. These bipolarons also exhibit
many other unconventional properties, e.g. at strong coupling there are two
low-energy bipolaron bands that are stable against strong on-site Hubbard
repulsion. Using numerical simulations and analytical arguments, we show that
these properties result from the specific form of the phonon-mediated
interaction, which is of "pair-hopping" instead of regular density-density
type. This unusual effective interaction is bound to have non-trivial
consequences for the superconducting state expected to arise at finite carrier
concentrations, and should favor a large critical temperature.
