  The study of the electronic properties of charged defects is crucial for our
understanding of various electrical properties of materials. However, the high
computational cost of density functional theory (DFT) hinders the research on
large defect models. In this study, we present an E(3) equivariant graph neural
network framework (HamGNN-Q), which can predict the tight-binding Hamiltonian
matrices for various defect types with different charges using only one set of
network parameters. By incorporating features of background charge into the
element representation, HamGNN-Q enables a direct mapping from structure and
background charge to the electronic Hamiltonian matrix of charged defect
systems without DFT calculation. We demonstrate the model's high precision and
transferability through testing on GaAs systems with various charged defect
configurations. Our approach provides a practical solution for accelerating
charged defect electronic structure calculations and advancing the design of
materials with tailored electronic properties.
