Chiral Phonons in Moir\'e Superlattices

We discover chiral phonons at the lowest-energy bands in moir\'e superlattices. The moir\'e chiral phonons we uncover are the collective excitations of the stacking domains. Their origin is uniquely attributed to the stacking configurations whose interlayer binding energy breaks the $C_{2z}$ symmetry on the moir\'e length scale. Within elastic theory, we use a general symmetry analysis to provide a complete classification of van der Waals heterostructures in respect to hosting moir\'e chiral phonons and show the calculation for twisted MoS$_2$ as an example. We present a low-energy effective model to qualitatively understand the moir\'e chiral phonons and show that it captures the essential physics remarkably well. Our result potentially opens up new possibilities in phononic twistronics as the moir\'e chiral phonons have high tunability, moir\'e scale wavelengths, excitation energies in only a few meV, and can possibly be mechanically excited.