Graph machine learning framework for depicting wavefunction on interface

Abstract The wavefunction, as the basic hypothesis of quantum mechanics, describes the motion of particles and plays a pivotal role in determining physical properties at the atomic scale. However, its conventional acquisition method, such as density functional theory (DFT), requires a considerable amount of calculation, which brings numerous problems to wide application. Here, we propose an algorithmic framework based on graph neural network (GNN) to machine-learn the wavefunction of electrons. This framework primarily generates atomic features containing information about chemical environment and geometric structure and subsequently constructs a scalable distribution map. For the first time, the visualization of wavefunction of interface is realized by machine learning (ML) methods, bypassing complex calculation and obscure comprehension. In this way, we vividly illustrate quantum mechanics, which can inspire theoretical exploration. As an intriguing case to verify the ability of our method, a novel quantum confinement phenomenon on interfaces based on graphene nanoribbon (GNR) is uncovered. We believe that the versatility of this framework paves the way for swiftly linking quantum physics and atom-level structures.