Theory and Efficient Prediction of Electrostatic Superlattice Potential for Moiré Materials

Two-dimensional (2D) moiré materials with long-wavelength superlattice potential modulations have emerged as a versatile platform for exploring correlated and topological quantum phenomena. Theoretical studies have highlighted the crucial role of the electrostatic superlattice potential (ESP) in governing these quantum phases. However, identifying specific 2D materials to achieve these quantum physics remain challenging due to the lack of efficient predictive methods for the ESP.

In this work, we develop a novel non-empirical and computationally efficient approach to predict the ESP accurately for twisted 2D moiré materials. By comparing with the ESP from large-scale density functional theory (DFT) calculations, we show that our method can predict the ESP for twisted bilayer hBN spatially and accurately but with significantly reduced computational cost. Significantly, our approach successfully demonstrates the ESP sign change at small twist angles, a feature linked to the sign change of Chern numbers of moiré bands, and an effect not captured by existing analytical models. Furthermore, our approach enables exploration of various factors for the ESP, providing a deeper physical insight into moiré electrostatics. This new method provides a powerful tool to predict the ESP landscapes for large-scale 2D moiré materials, which can be used to accelerate the discovery and design of 2D materials hosting novel correlated and topological quantum states.