Torsional Periodic Lattice Distortion in Twisted Bilayer Graphene

Periodic lattice distortions (PLD) are at the heart of correlated electronic behaviors such as superconductivity [1], metal-insulator transitions [2], and charge density waves (CDW) [3]. PLDs are typically intrinsic to a crystal [3, 4], Fermi-surface driven [5], accompanied by a CDW, and have periodicity spanning a few unit cells (~1–2nm). Recently, extrinsic van der Waals (vdW) driven superlattices with tunable periodicity (up to a few 100nm) were discovered in twisted bilayer graphene (tBLG) [6]. tBLG has been spotlighted for extraordinary correlated electron behaviors at the so-called “magic” angle (1.1°) [7]. Therefore, a full atomistic structural understanding is key to harnessing the exotic properties of tBLG. Here, we provide an analytic description of tBLG superlattices at and near the magic angle using a torsional PLD and report the torsional PLD amplitude of 7.8 ± 0.6 pm and 6.1 ± 0.4 pm for twist angle (θ) of 1.1° and 1.2°.