Universal Symmetries in Twisted Moir\'e Materials

Two-dimensional multi-layer materials with an induced moir\'e pattern, either due to strain or relative twist between layers, provide a versatile platform for exploring strongly correlated and topological electronic phenomena. While these systems offer unprecedented tunability, their theoretical description remains challenging due to their complex atomic structures and large unit cells. A notable example is twisted bilayer graphene, where even the relevant symmetry group remains unsettled despite its critical role in constructing effective theories. Here, we focus on twisted bilayer graphene and use a combination of analytical methods, molecular dynamics simulations, and first-principles calculations to show that twisted atomic configurations with distinct microscopic symmetries converge to a universal interlayer structure that governs the low-energy physics. This emergent universality provides a robust foundation for symmetry-respecting models and offers insight into the role of commensurability in real twisted moir\'e systems.