Prediction of the Hubbard U parameter from scanning tunneling microscopy images of moire systems using image recognition

Abstract

The atomistic Hubbard interaction U, representing the on-site Coulomb repulsion, serves as a pivotal parameter in theoretical models describing correlated systems, yet its precise experimental determination, especially in moire systems, remains challenging. Scanning Tunneling Microscopy (STM) provides real-space images of the local density of states (LDOS), offering rich data sets that reflect the unique electronic structure of the material. Here, we introduce a systematic methodology for extracting the Hubbard U parameter directly from these LDOS images through the application of machine learning (ML) in the case of twisted bilayer graphene in the flat-band regime. Accurate regression of U is achieved despite the extremely high visual similarity between FT-LDOS images corresponding to different interaction strengths. Subsequent data analysis further suggests a gradual interaction-dependent redistribution of spectral weight, with a possible crossover scale of order U/t ~ 1. To assess robustness beyond idealized simulations, we introduce physically motivated perturbations that emulate experimental STM imperfections and demonstrate that augmentation-based training substantially improves generalization to noisy and symmetry-broken FT-LDOS images.