Flat and Tunable Moiré Phonons in Twisted Transition-Metal Dichalcogenides.

Displacement fields are one of the main tuning knobs employed to engineer flat electronic band dispersions in twisted van der Waals multilayers. Here, we show that electric fields can also be used to tune the phonon dispersion of moiré superlattices formed by noncentrosymmetric materials, focusing on twisted transition metal dichalcogenide homobilayers. This effect arises from the intertwining between the local stacking configuration and the formation of polar domains within the moiré supercell. For small twist angles, increasing the electric field leads to a universal moiré phonon spectrum characterized by a substantially softened longitudinal acoustic phason mode and a flat optical phonon mode, both of which cause a significant enhancement in the vibrational density of states. The phasons also acquire a prominent chiral character, displaying a nonzero angular momentum spread across the Brillouin zone. We discuss how the tunability of the moiré phonon spectra may affect electronic properties, focusing on the recently discovered phenomenon of van der Waals ferroelectricity.