Deep learning tight-binding approach for large-scale electronic simulations at finite temperatures with $ab$ $initio$ accuracy

Simulating electronic behavior in materials and devices with realistic large system sizes remains a formidable task within the $ab$ $initio$ framework due to its computational intensity. Here we show DeePTB, an efficient deep learning-based tight-binding approach with $ab$ $initio$ accuracy to address this issue. By training on structural data and corresponding $ab$ $initio$ eigenvalues, the DeePTB model can efficiently predict tight-binding Hamiltonians for unseen structures, enabling efficient simulations of large-size systems under external perturbations such as finite temperatures and strain. This capability is vital for semiconductor band gap engineering and materials design. When combined with molecular dynamics, DeePTB facilitates efficient and accurate finite-temperature simulations of both atomic and electronic behavior simultaneously. This is demonstrated by computing the temperature-dependent electronic properties of a gallium phosphide system with $10^6$ atoms. The availability of DeePTB bridges the gap between accuracy and scalability in electronic simulations, potentially advancing materials science and related fields by enabling large-scale electronic structure calculations.