In moir\'e crystals formed by stacking van der Waals (vdW) 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 a new perspective to moir\'e physics. Over a range of small twist angles, the phonon spectra evolve rapidly due to ultra-strong coupling between different phonon modes and atomic reconstructions of the moir\'e pattern. We develop a new low-energy continuum model for phonons that overcomes the outstanding challenge of calculating properties of large moir\'e supercells and successfully captures essential experimental observations. Remarkably, simple optical spectroscopy experiments can provide information on strain and lattice distortions in moir\'e crystals with nanometer-size supercells. The newly developed theory promotes a comprehensive and unified understanding of structural, optical, and electronic properties of moir\'e superlattices.
@article{arxiv.2009.10650,
title = {Phonon Renormalization in Reconstructed MoS$_2$ Moir\'e Superlattices},
author = {Jiamin Quan and Lukas Linhart and Miao-Ling Lin and Daehun Lee and Jihang Zhu and Chun-Yuan Wang and Wei-Ting Hsu and Junho Choi and Jacob Embley and Carter Young and Takashi Taniguchi and Kenji Watanabe and Chih-Kang Shih and Keji Lai and Allan H. MacDonald and Ping-Heng Tan and Florian Libisch and Xiaoqin Li},
journal= {arXiv preprint arXiv:2009.10650},
year = {2021}
}