Moiré structures in twisted bilayer graphene studied by transmission electron microscopy

Abstract

We investigate imaging of moiré structures in free-standing twisted bilayer graphene (TBG) carried out by transmission electron microscopy (TEM) in diffraction and in-line Gabor holography modes.Electron diffraction patterns of TBG acquired at typical TEM electron energies of 80 -300 keV exhibit the diffraction peaks caused by diffraction on individual layers. However, diffraction peaks at the scattering angles related to the periodicity of the moiré structure have not been observed in such diffraction patterns. We show that diffraction on moiré structure can create intense diffraction peaks if the energy of the probing electrons is very low, in the range of a few tens of eV.Experimental diffraction patterns of TBG acquired with low-energy electrons of 236 eV exhibiting peaks attributed to the moiré structure periodicity are shown. In holography mode, the intensity of the wave transmitted through the sample and measured in the far-field can be enhanced or decreased depending on the atomic arrangement, as for example AA or AB stacking. Thus, a decrease of intensity in the far-field must not necessarily be associated with some absorption inside the sample but can simply be a result of a particular atomic arrangement. We believe that our findings can be important for exploiting graphene as a support in electron imaging.

Convergent beam electron diffraction of multilayer Van der Waals structures

“…Recently, diffraction peaks due to the moiré structure were observed in diffraction patterns acquired with low-energy electrons of 236 eV [20], where the interaction parameter  is relatively large, 0.02   1/VÅ.…”

Holography and Coherent Diffraction Imaging with Low-(30–250 eV) and High-(80–300 keV) Energy Electrons: History, Principles, and Recent Trends

“…where ψ 0 r , which describes convergent (−) or divergent (+) spherical waves. For a stationary scattering wave, we can choose G → r = G + → r , and can rewrite the solution to the Schrödinger equation Equation (9) as follows:…”

“…CDI with low-energy electrons has been demonstrated by Fink et al in a dedicated low-energy electron microscope equipped with a microlens [120] to collimate the electron beam, as shown in Figure 26a. Low-energy electron diffraction patterns of individual macromolecules, such as carbon nanotubes [121,122] and graphene [9,123], were acquired. Diffraction patterns of individual stretched single-walled carbon nanotubes (SWCNTs) were acquired with 186 eV electrons at a resolution of 1.5 nm, as reported in reference [121], these results are shown in Figure 26b-d. Diffraction patterns of bundles of individual carbon nanotubes acquired with 145 eV electrons and reconstructed using a holographic CDI (HCDI) approach at a resolution of 0.7 nm were reported in reference [122], these are shown in Figure 26e-h.…”

“…To ensure an undisturbed reference wave, the sample needs to be placed onto an equipotential surface, for example graphene [92,93], in in-line low-energy electron holography. On the other hand, their high sensitivity to local potentials makes low-energy electrons the perfect type of radiation for studying 2D materials such as graphene and van der Waals structures [9,74,94,132]. Moreover, low-energy electrons can be employed for mapping unoccupied band structure of freestanding 2D materials, such as graphene by angle-resolved low-energy electron transmission measurements realized in in-line holography mode [133].…”

Bilayer Graphene: From Stacking Order to Growth Mechanisms

“…That means one can regulate TBG between insulators and superconductors . In addition, more different angles of TBG can be created and more physical phenomena could be explored in a single device . Therefore, the precise preparation of bilayer graphene with controlled stacking order is highly desired for various applications.…”