Why twisting angles are diverse in graphene Moiré patterns?

Abstract

The interlayer energy of the twisting bilayer graphene is investigated by the molecular mechanics method using both the registry-dependent potential and the Lennard-Jones potential. Both potentials show that the interlayer energy is independent of the twisting angle θ, except in the two boundary regions θ ≈ 0 or 60 • , where the interlayer energy is proportional to the square of the twisting arc length. The calculation results are successfully interpreted by a single atom model. An important information from our findings is that, from the energy point of view, there is no preference for the twisting angle in the experimental bilayer graphene samples, which actually explains the diverse twisting angles in the experiment.

A Gaussian treatment for the friction issue of Lennard-Jones potential in layered materials: Application to friction between graphene, MoS2, and black phosphorus

“…25 This weak frictional energy can also be analyzed from a geometrical point of view. 26 The intrinsic lattice mismatch leads to a Moiré pattern, resulting in a large unit cell for the heterostructure. The Moiré pattern varies during the frictional motion of the heterostructure.…”

A journey toward the heaven of chemical fidelity of intermolecular force fields

“…While KC potential underestimates the energy barriers, Lebedeva's modification traces the DFT‐D curve precisely. The modified potential has been used to model the thermal properties of few‐layer graphene and twisted Moiré patterns of graphene 173,174 . According to Jiang et al ., the change in interlayer interaction energy with twist angle is negligible unless near the boundary regions.…”

“…The modified potential has been used to model the thermal properties of few-layer graphene and twisted Moiré patterns of graphene. 173,174 According to Jiang et al, the change in interlayer interaction energy with twist angle is negligible unless near the boundary regions. This theoretical result could explain the presence of diverse twist angles in experimental samples.…”

“…This theoretical result could explain the presence of diverse twist angles in experimental samples. 174 Hod and co-workers, in 2014, developed a new potential for describing the interlayer interactions, which can be fitted to high-level first-principles calculations. 175 Hod's interlayer potential (H-ILP) incorporates an attractive component taken from the Tkatchenko-Scheffler (TS) dispersion correction, 176 and for computational ease, they brought in a simplified formulation for repulsion based on the KC potential.…”

“…According to Jiang et al ., the change in interlayer interaction energy with twist angle is negligible unless near the boundary regions. This theoretical result could explain the presence of diverse twist angles in experimental samples 174 …”