Fig. 5: Automated structural analysis of twist-stacked vdW bilayers.
From: Auto-resolving the atomic structure at van der Waals interfaces using a generative model
a Schematics illustrating the training dataset acquisition for one twist angle θ. L represents the periodicity length of twist-stacked bilayer MoS2. ∆L represents the step size of the sliding window to collect image patches for one moiré pattern. La and Lb represent the horizontal and vertical coordinates of the initial position of the sliding window (red box). n and m are natural numbers. Scale bars: 0.5 nm. b Experimental ADF-STEM image of twist-stacked bilayer MoS2. Scale bar: 1 nm. Inset is the fast Fourier transform (FFT) of (b). c Infeasibility of uniquely assigning the twist angle of bilayer MoS2 by the FFT pattern. The intensity profile taken along the circle in the FFT of (b) displays similar intensities for 12 reflection spots (top panel), leading to two possible assignments of θ (lower panels). d Zoom-in view of the white-boxed region in (b) (top panel), atomic models of bilayer MoS2 with twist angles of 20° and 40° (middle panels), and the DRIT-generated images of 20°- and 40°-twisted MoS2 (bottom panels). Scale bars: 0.5 nm. e Intensity line profiles taken along the red, magenta, and blue circles in (d). f Artificially constructed large-area atomic model of bilayer MoS2 where the twist angles of the adjacent triangular areas switch between 9.8° (blue triangle) and 11.8° (yellow triangle). Insets show the magnified views of the atomic structures of twisted stackings with the twist angles of 9.8° and 11.8°. g DRIT-generated image based on the atomic model in the black-boxed region in (f). h FFT of the white-boxed region in (g). i FFT of (g). j θ mapping of (g) inferred by the ML model. Scale bars in (g) and (j): 5 nm. Scale bars in all FFT diagrams: 4 nm−1.
