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

TL;DR

This study combines elasticity theory and first-principles calculations to accurately predict membrane corrugation amplitudes in twisted bilayer graphene, validated by STM experiments across various substrates.

Contribution

It introduces a parameter-free method to determine membrane amplitude in twisted bilayer graphene using elasticity theory and DFT, extending predictions beyond pure stacking configurations.

Findings

Excellent agreement with STM measurements across multiple substrates.

Method accurately predicts membrane amplitude for various twist angles.

Eliminates fitting parameters by combining elasticity theory with DFT.

Abstract

Twisted graphene layers produce a moir\'e pattern (MP) structure with a predetermined wavelength for 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 (STM) results across multiple substrates is reported as function of twist angle.