Origin of different piezoelectric responses in elemental Sb and Bi monolayers

Sb and Bi monolayers, as single-element ferroelectric materials with similar atomic structure, hold intrinsic piezoelectricity theoretically, which makes them highly promising for applications in functional nanodevices such as sensors and actuators. Here, using density functional theory 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 two dimensional ferroelectric materials and their potential applications in nanoelectronic devices.