  The interplay between ferroelectricity and band topology can give rise to a
wide range of both fundamental and applied research. Here, we map out the
emergence of nontrivial corner states in two-dimensional ferroelectrics, and
remarkably demonstrate that ferroelectricity and corner states are coupled
together by crystallographic symmetry to realize the electric control of
higher-order topology. Implemented by density functional theory, we identify a
series of experimentally synthesized two-dimensional ferroelectrics, such as
In$_2$Se$_3$, BN bilayers, and SnS, as realistic material candidates for the
proposed ferroelectric higher-order topological insulators. Our work not only
sheds new light on traditional ferroelectric materials but also opens an avenue
to bridge the higher-order topology and ferroelectricity that provides a
nonvolatile handle to manipulate the topology in next-generation electronic
devices.
