  Two-dimensional materials that exhibit spontaneous electric polarization are
of notable interest for functional materials. However, despite many
two-dimensional polar materials are predicted in theory, the number of
experimentally confirmed two-dimensional ferroelectrics are still far less than
bulk ferroelectrics. We provide strong evidence that the Pmn2$_1$ phase of
arsenic chalcogenides As$_2$X$_3$ (X=S, Se, and Te), which include the recently
isolated monolayer orpiment, are intrinsic ferroelectrics and demonstrate
strong in-plane piezoelectricity. We found the calculated energy barriers for
collectively reversing the electric polarization or moving a 180$^\circ$ domain
wall are reasonable compared to previously reported ferroelectrics. We propose
a high-symmetry structure (with Pmmn space group) transforms into the
ferroelectric Pmn2$_1$ phase by a soft B$_{2u}$ phonon mode. By studying other
soft modes of the high-symmetry Pmmn structure, we identify several
undiscovered metastable polymorphs, including a polar phase (with a P2$_1$
space group) with sizable piezoelectricity.
