A multiscale low-energy continuum model for moiré phonons*

Multiscale continuum models have been widely applied to solving the electronic structure and understanding the lattice relaxation in twisted layered van der Waals heterostructures. However, a systematic study of the phonon properties of moiré materials is lacking due to the computational challenge of obtaining force fields accurately and the lack of periodicity. An accurate description of moiré phonons is critical to understanding the nature of observed superconductivity in moiré systems. In this work, we show that the same multiscale framework for electronic and mechanical properties can be used to study moiré phonons. We present a general continuum framework for low-energy moiré phonons in twisted bilayer heterostructures, based on the local configuration and first-principles density functional theory. Our model not only bypasses the need for a supercell approximation but is also computationally efficient while having the computational accuracy of first-principles calculations.