  Sb and Bi monolayers, as single-elemental ferroelectric materials with
similar atomic structure, hold intrinsic piezoelectricity theoretically, which
makes them highly promising for applications in functional nano-devices such as
sensors and actuators. Here, using first-principles calculations, we
systematically explore the piezoelectric response of Sb and Bi monolayers. Our
findings reveal that Sb exhibits a negative piezoelectric response, whereas Bi
displays a positive one. This discrepancy is attributed to the dominant role of
different atomic internal distortions (internal-strain terms) in response to
applied strain. Further electron-density distribution analysis reveals that the
atomic bonding in Sb tends to be covalent, while the atomic bonding in Bi leans
more towards ionic. Compared to the Sb monolayer, the Bi monolayer is
distinguished by its more pronounced lone-pair orbitals electrons and
associated larger Born effective charges. The Coulomb repulsions between
lone-pair orbitals electrons and the chemical bonds lead to the Bi monolayer
possessing more prominent atomic folds and, consequently, more significant
atomic distortion in the z-direction under strain. These differences result in
a considerable difference in internal-strain terms, ultimately leading to the
reversed piezoelectric response between Sb and Bi monolayers. The present work
provides valuable insights into the piezoelectric mechanism of 2D ferroelectric
materials and their potential applications in nano-electronic devices.
