  We study a novel type of graphene-based superlattices formed owing to a
periodic modulation of the Fermi surface. Such a modulation is possible for
graphene deposited on a striped substrate made of materials with substantially
different values of the dc permittivity. Similar superlattices appear also in
graphene sheets applied over substrates with a periodic array of parallel
grooves. We suggest a model describing such superlattices. Using the
transfer-matrix technique, we determine the dispersion relation and calculate
the energy spectrum of these superlattices. We also analyze at a qualitative
level the current--voltage characteristics of the system under study.
