  We show that in crystals where light ions are symmetrically intercalated
between heavy ions, the electron-phonon coupling for carriers located at the
light sites cannot be described by a Holstein model. We introduce the
double-well electron-phonon coupling model to describe the most interesting
parameter regime in such systems, and study it in the single carrier limit
using the momentum average approximation. For sufficiently strong coupling, a
small polaron with a robust phonon cloud appears at low energies. While some of
its properties are similar to those of a Holstein polaron, we highlight some
crucial differences. These prove that the physics of the double-well
electron-phonon coupling model cannot be reproduced with a linear Holstein
model.
