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.