Graph representation-based machine learning framework for predicting electronic band structures of quantum-confined nanostructures

Abstract

The application of machine learning (ML) to electronic structure theory enables electronic property prediction with ab initio accuracy. However, most previous ML models predict one or several properties of intrinsic materials. The prediction of electronic band structure, which embeds all the main electronic information, has yet to be deeply studied. This is a challenging task due to the highly variable inputs and outputs; the input materials may have different sizes and compositions, and the output band structures may have varying band numbers and k-point samplings. This task becomes even more difficult when quantum-confined nanostructures are considered, whose band structures are sensitive to the confinements applied. This paper presents an ML framework for predicting band structures of quantum-confined nanostructures from their geometries. Our framework introduces a graph convolutional network applicable to materials with varying compositions and geometries to extract their atoms’ local environment information. A learnable real-space Hamiltonian construction process then enables the utilization of the information to predict the electronic structure at any arbitrary k-point; the theoretical foundations introduced in this process help to capture and incorporate minor changes in quantum confinements into band structures, and endow the framework with the ability of few-shot learning. Taking an example of graphene nanoribbons, typical quantum-confined nanostructures, we show how the framework is constructed and its excellent performance on band structure prediction with a tiny data set. Our framework may not only provide a rapid yet reliable method for electronic structure determination but also enlighten the applications of graph representation to ML in related fields.