Tunability of moiré phonons in twisted TMD homobilayers

Moiré structures are incommensurate at general twist angles. Among the collective vibrations of the moiré pattern (moiré phonons), two acoustic branches (phasons) appear, as the elastic free energy becomes degenerate with respect to global, relative translations of the layers. We show that in twisted TMD homobilayers, external out-of-plane electric fields soften the phasons dispersion and change the symmetries of the energy landscape. The origin of this effect is found in the formation of local polar domains tied to the local stacking order, ultimately due to the presence of two atomic species. The symmetry of the relaxation pattern evolves from a triangular towards a honeycomb lattice for increasing voltage. In the presence of the electric field, the moiré phonons acquire nonzero angular momentum, which can be measured with different optical probes. Importantly, some optical modes and one of the acoustic branches become flat at experimentally realizable fields, enhancing the vibrational density of states. As a consequence, the effective electron-phonon coupling should become larger in the material. Electronic scattering mediated by phasons contributes to the resistivity and might explain the unusual transport behavior in moiré systems, which has been previously attributed to a strange-metal phase.