Physics

Mathematics

Optics

Superlattice

van der Waals force

Materials science

Phonon

Geometry

Condensed matter physics

Twist

Molecule

Nuclear magnetic resonance

Quantum mechanics

Stacking

Moiré pattern

Nature Materials

In moiré 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 moiré 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 moiré pattern. We develop a low-energy continuum model for phonons that overcomes the outstanding challenge of calculating the properties of large moiré supercells and successfully captures the essential experimental observations. Remarkably, simple optical spectroscopy experiments can provide information on strain and lattice distortions in moiré crystals with nanometre-size supercells. The model promotes a comprehensive and unified understanding of the structural, optical and electronic properties of moiré superlattices. Raman measurements of twisted bilayer MoS2 as a function of twist angles, with theoretical support, reveal phonon renormalization in this moiré superlattice.

Phonon renormalization in reconstructed MoS2 moiré superlattices