Accurate force field of two-dimensional ferroelectrics from deep learning

The discovery of two-dimensional (2D) ferroelectrics with switchable out-of-plane polarization such as monolayer $\alpha$-In$_2$Se$_3$ offers a new avenue for ultrathin high-density ferroelectric-based nanoelectronics such as ferroelectric field effect transistors and memristors. The functionality of ferroelectrics depends critically on the dynamics of polarization switching in response to an external electric/stress field. Unlike the switching dynamics in bulk ferroelectrics that have been extensively studied, the mechanisms and dynamics of polarization switching in 2D remain largely unexplored. Molecular dynamics (MD) using classical force fields is a reliable and efficient method for large-scale simulations of dynamical processes with atomic resolution. Here we developed a deep neural network-based force field of monolayer In$_2$Se$_3$ using a concurrent learning procedure that efficiently updates the first-principles-based training database. The model potential has accuracy comparable with density functional theory (DFT), capable of predicting a range of thermodynamic properties of In$_2$Se$_3$ polymorphs and lattice dynamics of ferroelectric In$_2$Se$_3$. Pertinent to the switching dynamics, the model potential also reproduces the DFT kinetic pathways of polarization reversal and 180$^\circ$ domain wall motions. Moreover, isobaric-isothermal ensemble MD simulations predict a temperature-driven $\alpha \rightarrow \beta$ phase transition at the single-layer limit, as revealed by both local atomic displacement and Steinhardt's bond orientational order parameter $Q_4$. Our work paves the way for further research on the dynamics of ferroelectric $\alpha$-In$_2$Se$_3$ and related systems.