  Two-dimensional (2D) ferroelectricity has attracted extensive attention since
its discovery in the monolayers of van der Waals materials. Here we show that
2D ferroelectricity induced by octahedral rotation distortion is widely present
in the perovskite bilayer system through first-principles calculations. The
perovskite tolerance factor plays a crucial role in the lattice dynamics and
ground-state structure of the perovskite monolayers and bilayers, thus
providing an important indicator for screening this hybrid improper
ferroelectricity. Generally, the ferroelectric switching via an orthorhombic
twin state has the lowest energy barrier. Epitaxial strain can effectively tune
the ferroelectric polarization and ferroelectric switching by changing the
amplitude of octahedral rotation and tilt distortion. The increasing
compressive strain causes a polar to nonpolar phase transition by suppressing
the tilt distortion. The cooperative effect of octahedral distortion at the
interface with the substrate can reduce the energy barrier of the reversing
rotation mode and can even change the lowest-energy ferroelectric switching
path.
