  The stability of a high-symmetry $P4mm$ polar phase in seventeen short-period
ferroelectric perovskite superlattices with polar discontinuity is studied from
first principles within the density-functional theory. It is shown that in most
superlattices this phase exhibits either the ferroelectric instability or the
antiferrodistortive one, or both of them. For each superlattice, the
ground-state structure, the structure of possible metastable phases, the
spontaneous polarization, and piezoelectric properties are calculated. The
properties of superlattices with the polar discontinuity are compared with
those of superlattices with broken symmetry and of ordinary superlattices,
which have no the polar discontinuity. It is shown that high piezoelectric
coefficients (up to 150--270 pC/N) in some superlattices with the polar
discontinuity are due to the appearance of strong lattice distortions, whose
symmetry follows that of a low-lying polar phonon mode of the ground-state
structure, under the influence of external strain.
