Low-energy moiré phonons in twisted bilayer heterostructures*

We develop a continuum model for low-energy phonon modes in moiré bilayers based on force fields computed from first-principles Density Functional Theory (DFT) in local stacking configurations. Applied directly, DFT calculations of moiré phonons are intractable, and while empirical continuum models are efficient, they are crude and ignore important details. The model we propose is based on first-principles DFT while remaining efficient to compute. We show that the low-energy phonon modes sensitively depend on the twist angle, which dictates the interlayer coupling strength and relaxation . As the twist angle becomes small, the frequencies of low-energy modes reorder and several mode symmetries in real space break. We exemplify our findings on twisted bilayer graphene, molybdenum disulfide (MoS₂), and Janus heterostructures.