Abstract text (incl. figure legends and references)

Since the discovery of superconductivity in twisted bilayer graphene at a so-called magic angle [1], there has been an increasing interest in twisted bilayers of two-dimensional materials. Various interesting electronic and optical phenomena have been shown or predicted for these materials [2], and the pronounced moiré patterns occurring at certain twist angles [3,4] have led to the materials also being referred to as "moiré materials". Furthermore, it has been shown that for low twist angles (typically <2°), the moiré structure may deviate from the static lattice by forming large domains of differently stacked layers [5].

Here, we elucidate the difference in the low-loss EELS data between single-, bilayer, and twisted bilayer tungsten diselenide at both high and low twist angles. For the latter, we analyze the local variations in the low-loss EELS data in conjunction with high-resolution (S)TEM imaging in order to correlate effects of local strains originating from domain formation.

We use mechanically exfoliated WSe₂ samples deposited on SiO₂ wafers, with a second layer stacked on top using a PMMA film. These are subsequently transferred to TEM grids using the KOH assisted method.

For high-resolution TEM imaging, we use the Cc/Cs-corrected SALVE TEM operated at 80 kV in order to minimize beam damage. For high-resolution STEM-EELS spectral imaging, we use the aberration-corrected and monochromated NION HERMES STEM instrument operated at an acceleration voltage of 60 kV.

Exciton peaks are fitted with Lorentzian functions on a linear background, which was adapted from the paradigm presented in [6].

We have developed a framework for analyzing exciton peak shifts of twisted bilayer TMD samples in low -loss EELS with high lateral resolution in order to match these shifts to features observed in the high-resolution TEM and STEM images. Care needs to be taken to avoid strong contamination, as we found that the exciton peaks vanish in the center of a trapped contamination bubble.

In the case of a boundary between a single layer and a twisted bilayer of WSe₂ at a twist angle of 8.7° (figure 1), investigation in high-resolution (S)TEM shows an atomically sharp, but jagged interface. When analyzing the scanning EELS data, we observe a reduction in the energy of the exciton peaks when crossing the boundary between the single layer and the bilayer region. Furthermore, comparing the maps of peak positions of the A and D excitons, respectively, we observe a broader transition area between the single- and bilayer for the former. We attribute this behavior to stronger delocalization at lower energies.

In the next step, we correlate high-resolution (S)TEM images with mapped peak shifts originating from strain due to lattice reconstruction at low twist angles.

Figure 1: 60 kV HAADF STEM image (a) and map of peak positions of A and D excitons (b and c, respectively), showing a broader transition area in the case of the A exciton.

[1] Cao et al. Nature 556 (2018), 43–50

[2] Tran et al. Nature 567 (2019), 71–75

[3] Shallcross et al. Phys. Rev. B 81 (2010), 165105

[4] Campos-Delgado et al. Small 9 (2013), 3247-3251

[5] Weston et al. Nat. Nanotechnol. 15 (2020), 592–597

[6] Hong et al. Phys. Rev. Lett. 124 (2020), 087401