Machine learning of the Γ-point gap and flat bands of twisted bilayer graphene at arbitrary angles

The novel electronic properties of bilayer graphene can be fine-tuned via twisting, which may induce flat bands around the Fermi level with nontrivial topology. In general, the band structure of such twisted bilayer graphene (TBG) can be theoretically obtained by using first-principles calculations, tight-binding method, or continuum model, which are either computationally demanding or parameters dependent. In this work, by using the sure independence screening sparsifying operator method, we propose a physically interpretable three-dimensional (3D) descriptor which can be utilized to readily obtain the Γ-point gap of TBG at arbitrary twist angles and different interlayer spacings. The strong predictive power of the descriptor is demonstrated by a high Pearson coefficient of 99% for both the training and testing data. To go further, we adopt the neural network algorithm to accurately probe the flat bands of TBG at various twist angles, which can accelerate the study of strong correlation physics associated with such a fundamental characteristic, especially for those systems with a larger number of atoms in the unit cell.