Tunable Ferroelectric Topological Defects on 2D Topological Surfaces: Complex Strain Engineering Skyrmion-Like Polar Structures in 2D Materials

Polar topological structures in ferroelectric materials have attracted significant interest due to their fascinating physical properties and promising applications in high-density, nonvolatile memories. Currently, most polar topological patterns are only observed in the bulky perovskite superlattices. In this work, a discovery of tunable ferroelectric polar topological structures is reported, designed, and achieved using topological strain engineering in two-dimensional (2D) PbX (X = S, Se, and Te) materials via integrating first-principles calculations, machine learning molecular dynamics simulations, and continuum modeling. First-principles calculations discover the strain-induced reversible ferroelectric phase transition with diverse polarization directions strongly correlated to the straining conditions. Taking advantage of the mechanical flexibility of 2D PbX, using molecular dynamics (MD) simulations, it is successfully demonstrated that the complex strain fields of 2D topological surfaces under mechanical indentation can generate unique skyrmion-like polar topological vortex patterns. Further continuum simulations for experimentally accessible larger-scale 2D topological surfaces uncover multiple skyrmion-like structures (i.e., vortex, anti-vortex, and flux-closure) and transition between them by adopting/designing different types of mechanical loadings (such as out-of-plane indention and air blowing). Topological surfaces with various designable reversible polar topological structures can be tailored by complex straining flexible 2D materials, which provides excellent opportunities for next-generation nanoelectronics and sensor devices.