paper

Magic distances in twisted bilayer graphene

arXiv:2401.09884 · doi:10.1038/s41699-025-00616-7

Abstract

Twisted bilayer graphene exhibits isolated, relatively flat electronic bands near charge neutrality when the interlayer rotation is tuned to specific magic angles. These small misalignments, typically below 1.1°, result in long-period moiré patterns with anomalous electronic properties, posing severe challenges for accurate atomistic simulations due to the large supercell sizes required. Here, we introduce a framework to map arbitrarily stacked graphene bilayers, characterized by specific rotation angles corresponding to precise interplanar distances, onto an equivalence class represented by magic-angle twisted bilayer graphene. Using a continuum model, we derive the equivalence relation defining this class and extend its implementation to tight-binding approaches. We further explore the applicability of this mapping within density functional theory, demonstrating that the magic-angle physics can be efficiently studied using twisted bilayer graphene configurations with larger stacking angles and computationally manageable supercell sizes. This approach offers a pathway for ab initio investigations into unconventional topological phases and emergent excitations in the low-energy quasi-flat bands of twisted bilayer materials.

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