  We present a theory for charge and heat transport parallel to the interfaces
of a multilayer (ML) in which the interfacing gives rise the redistribution of
the electronic charges. The ensuing electrical field couples self-consistently
to the itinerant electrons, so that the properties of the ML crucially depend
on an interplay between the on-site Coulomb forces and the long range
electrostatic forces. The ML is described by the Falicov-Kimball model and the
self-consistent solution is obtained by iterating simultaneously the DMFT and
the Poisson equations. This yields the reconstructed charge profile, the
electrical potential, the planar density of states, the transport function, and
the transport coefficients of the device.
  We find that a heterostructure built of two Mott-Hubbard insulators exhibits,
in a large temperature interval, a linear conductivity and a large
temperature-independent thermopower. The charge and energy currents are
confined to the central part of the ML. Our results indicate that correlated
multilayers have the potential for applications; by tuning the band shift and
the Coulomb correlation on the central planes, we can bring the chemical
potential in the immediate proximity of the Mott-Hubbard gap edge and optimize
the transport properties of the device. In such a heterostructure, a small gate
voltage can easily induce a MI transition. This switching does not involve the
diffusion of electrons over macroscopic distances and it is much faster than in
ordinary semiconductors. Furthermore, the right combination of strongly
correlated materials with small ZT can produce, theoretically at least, a
heterostructure with a large ZT.
