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In moire 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 MoS$_2$ twisted bilayers, adding a new perspective to moire 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 moire pattern. We develop a new low-energy continuum model for phonons that overcomes the outstanding challenge of calculating properties of large moire supercells and successfully captures essential experimental observations. Remarkably, simple optical spectroscopy experiments can provide information on strain and lattice distortions in moire crystals with nanometer-size supercells. The newly developed theory promotes a comprehensive and unified understanding of structural, optical, and electronic properties of moire superlattices.
Moire superlattices in transition metal dichalcogenide (TMD) heterostructures can host novel correlated quantum phenomena due to the interplay of narrow moire flat bands and strong, long-range Coulomb interactions1-5. However, microscopic knowledge o
The quasiparticle band-gap renormalization induced by the doped carriers is an important and well-known feature in two-dimensional semiconductors, including transition-metal dichalcogenides (TMDs), and it is of both theoretical and practical interest
Moire superlattices in van der Waals (vdW) heterostructures have given rise to a number of emergent electronic phenomena due to the interplay between atomic structure and electron correlations. A lack of a simple way to characterize moire superlattic
Intercalation of lithium atoms between layers of 2D materials can alter their atomic and electronic structure. We investigate effects of Li intercalation in twisted bilayers of the transition metal dichalcogenide MoS$_2$ through first-principles calc
We theoretically demonstrate that moire phonons at the lowest-energy bands can become chiral. A general symmetry analysis reveals that they originate from stacking configurations leading to an asymmetric interlayer binding energy that breaks the $C_{