  Size-driven transition of an antiferroelectric into a polar ferroelectric or
ferrielectric state is a strongly debated issue from both experimental and
theoretical perspectives. While critical thickness limits for such transitions
have been explored, a bottom-up approach in the ultrathin limit considering few
atomic layers could provide insight into the mechanism of stabilization of the
polar phases over the antipolar phase seen in bulk PbZrO$_3$. Here, we use
first-principles density functional theory to predict the stability of polar
phases in Pt/PbZrO$_3$/Pt nanocapacitors. In a few atomic layer thick slabs of
PbZrO$_3$ sandwiched between Pt electrodes, we find that the polar phase
originating from the well established R3c phase of bulk PbZrO$_3$ is
energetically favorable over the antipolar phase originating from the Pbam
phase of bulk PbZrO$_3$. The famous triple-well potential of antiferroelectric
PbZrO$_3$ is modified in the nanocapacitor limit in such a way as to swap the
positions of the global and local minima, stabilizing the polar phase relative
to the antipolar one. The size effect is decomposed into the contributions from
dimensionality reduction, surface charge screening, and interfacial relaxation,
which reveals that it is the creation of well-compensated interfaces that
stabilizes the polar phases over the antipolar ones in nanoscale PbZrO$_3$.
