Neural network Hamiltonian: development of tight-binding-based Hamiltonian generation simulator for crystal structure

Abstract

The thesis demonstrates the method to obtain the Hamiltonian based on tight-binding (TB) for a crystal structure using an artificial neural network (ANN). We propose the Tight-Binding Parameter Extraction Package (TBPGP) to extract the TB parameters for the crystal structure obtained through density functional theory (DFT) simulation and Tight-Binding Parameter Neural Network (TBPNN) to learn the TB parameters for the strained structure with an ANN. TBPGP can reproduce the band structure more accurately than the existing TB method using the Naval research laboratory tight-binding (NRL-TB) method. As a result, for black phosphorus and silicon dioxide, TBPGP generated NRL-TB parameters that reproduce band energy with a difference of 30 meV or less from the DFT band energy. On the other hand, TBPNN can generate NRL-TB parameters accurately and quickly using multilayer perceptrons, deep neural networks, and convolutional neural networks. As a result, TBPNN obtained NRL-TB parameters which implement band structure with a difference of 50 meV or less from the DFT band structure within 0.01 second for the strained black phosphorus structure.