The tight-binding (TB) method is an ideal candidate for determining electronic and transport properties for a large-scale system. It describes the system as real-space Hamiltonian matrices expressed on a manageable number of parameters, leading to substantially lower computational costs than the ab-initio methods. Since the whole system is defined by the parameterization scheme, the choice of the TB parameters decides the reliability of the TB calculations. The typical empirical TB method uses the TB parameters directly from the existing parameter sets, which hardly reproduces the desired electronic structures quantitatively without specific optimizations. It is thus not suitable for quantitative studies like the transport property calculations. The ab-initio TB method derives the TB parameters from the ab-initio results through the transformation of basis functions, which achieves much higher numerical accuracy. However, it assumes prior knowledge of the basis and may encompass truncation error. Here, a machine learning method for TB Hamiltonian parameterization is proposed, within which a neural network (NN) is introduced with its neurons acting as the TB matrix elements. This method can construct the empirical TB model that reproduces the given ab-initio energy bands with predefined accuracy, which provides a fast and convenient way for TB model construction and gives insights into machine learning applications in physical problems.

An investigation of the transport and optical properties of buckled bismuthene with different adsorbed gas molecules.

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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.

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