Transfer learning electronic structure: millielectron volt accuracy for sub-million-atom moir\'e semiconductor

TL;DR

This paper introduces a transfer learning framework that combines DFT and machine learning to accurately and efficiently model electronic structures of large moiré systems with sub-meV precision, enabling scalable simulations of realistic devices.

Contribution

The authors develop a two-step transfer learning approach that achieves high accuracy and scalability for large moiré systems, surpassing traditional computational methods.

Findings

Achieves <0.1 meV MAE in 200 seconds for 1000-atom systems.

Models up to 0.25 million atoms with $O(N)$ scalability.

Captures edge states and topological properties accurately.

Abstract

The integration of density functional theory (DFT) with machine learning enables efficient \textit{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 MoTe$_2$, 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 ($\sim9$ million orbitals), accurately 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.