  The stability of high-symmetry $P4mm$ polar phase in eleven ferroelectric
perovskite superlattices with the polar discontinuity is studied from first
principles. In most superlattices, this phase exhibits either the ferroelectric
or the antiferrodistortive instability, or both of them. The structure of the
ground state and, for a number of systems, also of metastable phases in these
superlattices is found. The spontaneous polarization and piezoelectric
properties of superlattices are calculated. The appearance of high
piezoelectric coefficients (up to 150-270 pC/N) in some superlattices is
associated with the strain-induced local rearrangement of certain atomic groups
in the primitive cell.
