Torsional Periodic Lattice Distortion in Twisted Bilayer Graphene

Periodic lattice distortions (PLD) are at the heart of correlated electronic behavior such as superconductivity, metal-insulator transitions, and charge density waves. PLDs are typically intrinsic to a crystal, Fermi-surface driven, accompanied by a CDW, and have periodicity spanning a few unit cells (~1–2nm). Recently, extrinsic van der Waals driven superlattices with tunable periodicity (up to a few 100nm) was discovered in twisted bilayer graphene (tBLG). tBLG has been spotlighted for extraordinary correlated electron behaviors at the so-called "magic" angle (1.1°). The structure of tBLG is a complex moiré material where relaxation between layers acts to minimize high energy AA regions and maximize low energy AB. Here, we provide an atomic 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 of 1.1° and 1.2°. The PLD amplitude was quantified by matching experimental and simulated diffraction intensities. The atomic rearrangement is remarkably well described with a single coefficient in a single harmonic torsional PLD that can be extracted from a single experimental diffraction pattern.