  Organic$-$inorganic hybrid Ruddlesden$-$Popper perovskites (HRPPs) have
gained much attention for optoelectronic applications due to their high
moisture resistance, good processibility under ambient conditions, and long
functional lifetimes. Recent success in isolating molecularly thin hybrid
perovskite nanosheets and their intriguing edge phenomena have raised the need
for understanding the role of edges and the properties that dictate their
fundamental behaviours. In this work, we perform a prototypical study on the
edge effects in ultrathin hybrid perovskites by considering monolayer
(BA)$_2$PbI$_4$ as a representative system. Based on first-principles
simulations of nanoribbon models, we show that in addition to significant
distortions of the octahedra network at the edges, strong edge stresses are
also present in the material. Structural instabilities that arise from the edge
stress could drive the relaxation process and dominate the morphological
response of edges in practice. A clear downward shift of the bands at the
narrower ribbons, as indicative of the edge effect, facilitates the separation
of photo-excited carriers (electrons move towards the edge and holes move
towards the interior part of the nanosheet). Moreover, the desorption energy of
the organic molecule can also be much lower at the free edges, making it easier
for functionalization and/or substitution events to take place. The findings
reported in this work elucidate the underlying mechanisms responsible for edge
states in HRPPs and will be important in guiding the rational design and
development of high-performance layer$-$edge devices.
