Machine-Learning Modeling of Elemental Ferroelectric Bismuth Monolayer.

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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 1.2meV 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.