Phonon renormalization in reconstructed MoS2 moiré superlattices.

In moire crystals formed by stacking van der Waals materials, surprisingly diverse correlated electronic phases and optical properties can be realized by a subtle change in the twist angle. Here, we discover that phonon spectra are also renormalized in MoS2 twisted bilayers, adding an insight to moire physics. Over a range of small twist angles, the phonon spectra evolve rapidly owing to ultra-strong coupling between different phonon modes and atomic reconstructions of the moire pattern. We develop a low-energy continuum model for phonons that overcomes the outstanding challenge of calculating the properties of large moire supercells and successfully captures the essential experimental observations. Remarkably, simple optical spectroscopy experiments can provide information on strain and lattice distortions in moire crystals with nanometre-size supercells. The model promotes a comprehensive and unified understanding of the structural, optical and electronic properties of moire superlattices. Raman measurements of twisted bilayer MoS2 as a function of twist angles, with theoretical support, reveal phonon renormalization in this moire superlattice.