  For graphene to be utilized in the digital electronics industry the challenge
is to create bandgaps of order 1eV as simply as possible. The most successful
methods for the creation of gaps in graphene are (a) confining the electrons in
nanoribbons, which is technically difficult or (b) placing a potential
difference across bilayer graphene, which is limited to gaps of around 300meV
for reasonably sized electric fields. Here we propose that electronic band gaps
can be created without applying an external electric field, by using the
electron-phonon interaction formed when bilayer graphene is sandwiched between
highly polarisable ionic materials. We derive and solve self-consistent
equations, finding that a large gap can be formed for intermediate
electron-phonon coupling. The gap originates from the amplification of an
intrinsic Coulomb interaction due to the proximity of carbon atoms in
neighbouring planes.
