Twisted graphene layers produce a moiré pattern (MP) structure with a predetermined wavelength for a given twist angle. However, predicting the membrane corrugation amplitude for any angle other than pure AB-stacked or AA-stacked graphene is impossible using first-principles density functional theory (DFT) due to the large supercell. Here, within elasticity theory, we define the MP structure as the minimum-energy configuration, thereby leaving the height amplitude as the only unknown parameter. The latter is determined from DFT calculations for AB- and AA-stacked bilayer graphene in order to eliminate all fitting parameters. Excellent agreement with scanning tunneling microscopy results across multiple substrates is reported as a function of twist angle.

• Received 28 April 2014
• Revised 3 July 2014

DOI:https://doi.org/10.1103/PhysRevB.90.064101