Machine-Learning Modeling of Elemental Ferroelectric Bismuth Monolayer

The bismuth monolayer has recently been experimentally identified as a novel platform for the investigation of two-dimensional single-element ferroelectric system. Here, we model the potential energy surface of a bismuth monolayer by employing a message-passing neural network and achieve an error smaller than 1.2 meV per atom. Empowered by the high accuracy and fast prediction of the machine learning model, we have embarked on in-depth and large-scale atomistic simulations. These explorations are tailored to understand the temperature-dependent phase transitions, with an emphasis on the difference between free-standing monolayers and those constrained by a substrate. Furthermore, with the large system used in the simulations, we are also able to observe ferroelectric domains within these systems and shed light on their intrinsic lattice thermal conductivity.