Probing the structure of low-energy moiré phonons in twisted bilayer heterostructures

Theoretical modeling of moiré phonons is critical to understanding the origin of superconductivity and the Raman spectroscopy in twisted layered heterostructures. In this work, we develop a low-energy continuum model for phonons in twisted moiré bilayers, based on a local configuration-space approach that combines density functional theory (DFT). Based on this framework, we show how the low-energy phonon modes, including interlayer shearing and layer-breathing modes, vary with the twist angle. As the twist angle decreases, the frequencies of the low-energy modes are reordered and the atomic displacement fields corresponding to phonon eigenmodes break translational symmetry, developing periodicity on the moiré length scale. On three representatives crystals—bilayer graphene, bilayer molybdenum disulfide (MoS2), and molybdenum diselenide-tungsten diselenide (MoSe2/WSe2) —we describe these moiré phonons in terms of frequency, real-space geometry, and their magnitudes that correspond to their optical activities.