Moiré Phonons in Twisted Bilayer MoS 2 .

The material choice, layer thickness, and twist angle widely enrich the family of van der Waals heterostructures (vdWHs), providing multiple degrees of freedom to engineer their optical and electronic properties. The moiré patterns in vdWHs create a periodic potential for electrons and excitons to yield many interesting phenomena, such as Hofstadter butterfly spectrum and moiré excitons. Here, in the as-grown/transferred twisted bilayer MoS ₂ (tBLMs), one of the simplest prototypes of vdWHs, we show that the periodic potentials of moiré patterns also modify the properties of phonons of its monolayer MoS ₂ constituent to generate Raman modes related to moiré phonons. These Raman modes correspond to zone-center phonons in tBLMs, which are folded from the off-center phonons in monolayer MoS ₂ . However, the folded phonons related to crystallographic superlattices are not observed in the Raman spectra. By varying the twist angle, the moiré phonons of tBLM can be exploited to map the phonon dispersions of the monolayer constituent. The lattice dynamics of the moiré phonons are modulated by the patterned interlayer coupling resulting from periodic potential of moiré patterns, as confirmed by density functional theory calculations. The Raman intensity related to moiré phonons in all tBLMs are strongly enhanced when the excitation energy approaches the C exciton energy. This study can be extended to various vdWHs to deeply understand their Raman spectra, moiré phonons, lattice dynamics, excitonic effects, and interlayer coupling.