Unraveling the 3D Atomic Structure of a Suspended Graphene/hBN van der Waals Heterostructure

Abstract

In this work we demonstrate that a free-standing van der Waals heterostructure, usually regarded as a flat object, can exhibit an intrinsic buckled atomic structure resulting from the interaction between two layers with a small lattice mismatch. We studied a freely suspended membrane of well-aligned graphene on a hexagonal boron nitride (hBN) monolayer by transmission electron microscopy (TEM) and scanning TEM (STEM). We developed a detection method in the STEM that is capable of recording the direction of the scattered electron beam and that is extremely sensitive to the local stacking of atoms. A comparison between experimental data and simulated models shows that the heterostructure effectively bends in the out-of-plane direction, producing an undulated structure having a periodicity that matches the moiré wavelength. We attribute this rippling to the interlayer interaction and also show how this affects the intralayer strain in each layer.

Double Moiré with a Twist: Supermoiré in Encapsulated Graphene

“…This was done through total energy minimization of the unit cell, with certain constraints. We used the Brenner potentials for the graphene layer, Tersoff potentials for the B-N interaction in the top hBN and the Morse potential developed in [26] for the inter-layer interactions. Simulations were performed within the "Large-scale atomic.molecular massively parallel simulator" (LAMMPS) software [27,28].…”

Composite super-moiré lattices in double-aligned graphene heterostructures

“…We used the bond-order Brenner potentials for the graphene layer, Tersoff potentials for the B-N interaction in the hBN layers and the Morse potential developed in Ref. (34) for the inter-layer interactions. The simulations are performed within the "large-scale atomic/molecular massively parallel simulator" (LAMMPS) (35,36) by considering a disk of radius 120nm.…”

Stacking in incommensurate graphene/hexagonal-boron-nitride heterostructures based on ab initio study of interlayer interaction

“…1a) is in qualitative agreement with the previous studies. 32,33,36,[38][39][40] Two types of maxima on the potential energy surface correspond to the AA and AB2 stackings ( Fig. 1b).…”

“…[19][20][21]33 In the case when the change in the bond lengths of the layers due to the interlayer interaction is neglected and the layers are completely aligned we can estimate that the period of the Moiré pattern is L 0 = a/δ = 14.2 nm, in agreement with the experimental measurements of ∼14 nm 19,20 51,52,[54][55][56][57][58]69 Nevertheless, since the characteristic interlayer interlayer interaction energy w int is comparable to the characteristic elastic energy w el , significant modulation of positions of atoms in the interacting layers is possible. Such a modulation has been previously observed in atomistic simulations 33,38,44 and calculations using continuum models. 28,31 However, the correction to the period of the Moiré pattern induced by the interlayer interaction has not been considered explicitly.…”