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

Abstract

Twisted graphene layers produce a moiré 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.

arXiv commentto appear in Phys. Rev. B

References in corpus (20)

• The electronic properties of graphene
• Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils
• Van der Waals heterostructures
• Graphene bilayer with a twist: electronic structure
• Substrate-induced bandgap in graphene on hexagonal boron nitride
• Emergence of Superlattice Dirac Points in Graphene on Hexagonal Boron Nitride
• Unravelling the intrinsic and robust nature of van Hove singularities in twisted bilayer graphene
• Generic Miniband Structure of Graphene on a Hexagonal Substrate
• The nature and strength of inter-layer binding in graphite
• Electronic properties of graphene: a perspective from scanning tunneling microscopy and magneto-transport
• Precisely aligned graphene grown on hexagonal boron nitride by catalyst free chemical vapor deposition
• Chiral Tunnelling in Twisted Graphene Bilayer
• Electronic Properties of Twisted Trilayer Graphene
• Graphene on boron-nitride: Moiré pattern in the van der Waals energy
• Nano-engineered non-uniform strain in graphene
• Strain engineered graphene using a nanostructured substrate: I Deformations
• Electronic structure of graphene hexagonal flake subjected to triaxial stress
• Strain engineered graphene using a nanostructured substrate: II Pseudo-magnetic fields
• The Coexistence of van Hove Singularities and Superlattice Dirac Points in a Slightly Twisted Graphene Bilayer
• Competing scanning tunneling microscope tip-interlayer interactions for twisted multilayer graphene on the a-plane SiC surface

Cited by in corpus (9)

• Complete steric exclusion of ions and proton transport through confined monolayer water
• Relaxation of moiré patterns for slightly misaligned identical lattices: graphene on graphite
• Structure of twisted and buckled bilayer graphene
• MoS2: a Choice Substrate for Accessing and Tuning the Electronic Properties of Graphene
• High-$T_{\text{C}}$ Superconductivity Originating from Interlayer Coulomb Coupling in Gate-Charged Twisted Bilayer Graphene Moir$\acute{e}$ Superlattices
• Origin of the vortex displacement field in twisted bilayer graphene
• Exceptional magic angles in non-Hermitian twisted bilayer graphene
• Ab initio study of angle-resolved electron reflection spectroscopy of few-layer graphene
• Magic distances in twisted bilayer graphene