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Twisted graphene layers produce a moir\'e pattern (MP) structure with apredetermined wavelength for given twist angle. However, predicting themembrane corrugation amplitude for any angle other than pure AB-stacked orAA-stacked graphene is impossible using first-principles density functionaltheory (DFT) due to the large supercell. Here, within elasticity theory wedefine the MP structure as the minimum energy configuration, thereby leavingthe height amplitude as the only unknown parameter. The latter is determinedfrom DFT calculations for AB and AA stacked bilayer graphene in order toeliminate all fitting parameters. Excellent agreement with scanning tunnelingmicroscopy (STM) results across multiple substrates is reported as function oftwist angle.

physical review. b, condensed matter and materials physics

Membrane amplitude and triaxial stress in twisted bilayer graphene  deciphered using first-principles directed elasticity theory and scanning  tunneling microscopy