  For heterostructures of ultrathin, strongly correlated copper-oxide films and
dielectric perovskite layers, we predict inhomogeneous electronic interface
states. Our study is based on an extended Hubbard model for the cuprate film.
The interface is implemented by a coupling to the electron and phonon degrees
of freedom of the dielectric oxide layer. We find that electronic ordering in
the film is associated with a strongly inhomogeneous polaron effect. We propose
to consider the interfacial tuning as a powerful mechanism to control the
charge ordering in correlated electronic systems.
