Atom-by-atom imaging of moiré phasons with electron ptychography.

Twisted two-dimensional materials exhibit distinctive vibrational modes called moiré phonons, which arise from the moiré superlattice. Here, we demonstrate atom-by-atom imaging of phasons, an ultrasoft class of moiré phonons in twisted bilayer tungsten diselenide (WSe2). Using ultrahigh-resolution (<15 picometers) electron ptychography, we imaged the size and shape of each atom to extract time-averaged vibrational amplitudes as a function of twist angle and position. We observed several signature properties of moiré phasons, such as increased vibrational amplitudes at solitons and AA-stacked regions. By correlating experiments with molecular dynamics simulations and lattice dynamics calculations, we show that phasons dominate the thermal vibrations in low-angle twisted bilayers. These results represent a powerful route to image thermal vibrations at atomic resolution, unlocking experimental studies of a thus far hidden branch of moiré phonon physics. Editor's summary: The collective vibrations of a low-twist-angle moiré superlattice of tungsten diselenide were imaged with high-resolution electron ptychography. The rotationally aligned regions in these superlattices are separated by networks of stacking faults that can host ultrasoft shear modes, or phasons, with frequencies less than one wavenumber that are inaccessible using conventional vibrational spectroscopy. Imaging by Zhang et al. at a resolution of under 15 picometers revealed that these spatially localized, anisotropic vibrations dominated the thermal vibrations (see the Perspective by Susi). —Phil Szuromi [ABSTRACT FROM AUTHOR]