Transfer learning electronic structure: millielectron-volt accuracy for sub-million-atom moiré semiconductor

The integration of density functional theory (DFT) with machine learning enables efficient ab initio electronic structure calculations for ultra-large systems. In this work, we develop a transfer learning framework tailored for long-wavelength moir ́e systems. To balance efficiency and accuracy, we adopt a two-step transfer learning strategy: (1) the model is pre-trained on a large dataset of computationally inexpensive non-twisted structures until convergence, and (2) the network is then fine-tuned using a small set of computationally expensive twisted structures. Applying this method to twisted MoTe2, the neural network model generates the resulting Hamiltonian for a 1000-atom system in 200 seconds, achieving a mean absolute error below 0.1 meV. To demonstrate O(N) scalability, we model nanoribbon systems with up to 0.25 million atoms (∼ 9 million orbitals), accu- rately capturing edge states consistent with predicted Chern numbers. This approach addresses the challenges of accuracy, efficiency, and scalability, offering a viable alternative to conventional DFT and enabling the exploration of electronic topology in large scale moir ́e systems towards simulating realistic device architectures.