Atom-by-atom imaging of moiré phasons with electron ptychography
Yichao Zhang, Ballal Ahammed, Sang Hyun Bae, Chia‐Hao Lee, Jeffrey Huang, M. Abir Hossain, Tawfiqur Rakib, Arend M. van der Zande, Elif Ertekin, Pinshane Y. Huang
Abstract
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 (WSe 2 ). 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.