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Monolayer transition metal dichalcogenides have strong intracovalent bonding. When stacked in multilayers, however, weak van der Waals interactions dominate interlayer mechanical coupling and, thus, influence their lattice vibrations. This study presents the frequency evolution of interlayer phonons in twisted WS 2 bilayers, highly subject to the twist angle. The twist angle between the layers is controlled to modulate the spacing between the layers, which, in turn, affects the interlayer coupling that is probed by Raman spectroscopy. The shifts of high-frequency E 2g 1 (Γ) and A 1g (Γ) phonon modes and their frequency separations are dependent on the twist angle, reflecting the correlation between the interlayer mechanical coupling and twist angle. In this work, we fabricated large-area, twisted bilayer WS 2 with a clean interface with controlled twist angles. Polarized Raman spectroscopy identified new interlayer modes, which were not previously reported, depending on the twist angle. The appearance of breathing modes in Raman phonon spectra provides evidence of strong interlayer coupling in bilayer structures. We confirm that the twist angle can alter the exciton and trion dynamics of bilayers as indicated by the photoluminescence peak shift. These large-area controlled twist angle samples have practical applications in optoelectronic device fabrication and twistronics.

Magic-angle twisted bilayer graphene (TBG) has attracted significant interest recently due to the discoveries of diverse correlated and topological states. In this work, we study the phonon properties in magic-angle TBG based on many-body classical potential and interatomic forces generated by a deep neural network trained with data from ab initio calculations. We have discovered a number of soft modes which can exhibit dipolar, quadrupolar, and octupolar vibrational patterns in real space, as well as some time-reversal breaking chiral phonon modes. We have further studied the phonon effects on the electronic structures by freezing certain soft phonon modes. We find that if a soft quadrupolar phonon mode is assumed to be frozen, the system would exhibit a charge order which is perfectly consistent with recent experiments. Moreover, once some low-frequency C 2 z -breaking modes get frozen, the Dirac points at the charge neutrality point would be gapped out, which provides an alternative perspective to the origin of correlated insulator state at charge neutrality point.

We discover chiral phonons at the lowest energy bands in moiré superlattices. The moiré chiral phonons we uncover are the collective excitations of the stacking domains. Their origin is uniquely attributed to the stacking configurations whose interlayer binding energy breaks the C 2 z symmetry on the moiré length scale. Within elastic theory, we use a general symmetry analysis to provide a complete classification of van der Waals heterostructures in respect to hosting moiré chiral phonons and show the calculation for twisted MoS 2 as an example. We present a low-energy effective model to qualitatively understand the moiré chiral phonons and show that it captures the essential physics remarkably well. Our result potentially opens up new possibilities in phononic twistronics as the moiré chiral phonons have high tunability, moiré scale wavelengths, excitation energies in only a few meV and can possibly be mechanically excited.

Moiré superlattices can induce correlated-electronic phases in twisted van der Waals materials: strongly correlated quantum phenomena emerge, such as superconductivity and the Mott-insulating state. However, moiré superlattices produced through artificial stacking can be quite inhomogeneous, which hampers the development of a clear correlation between the moiré period and the emerging electrical and optical properties. Here, it is demonstrated in twisted-bilayer transition-metal dichalcogenides that low-frequency Raman scattering can be utilized not only to detect atomic reconstruction, but also to map out the inhomogeneity of the moiré lattice over large areas. The method is established based on the finding that both the interlayer-breathing mode and moiré phonons are highly susceptible to the moiré period and provide characteristic fingerprints. Hyperspectral Raman imaging visualizes microscopic domains of a 5° twisted-bilayer sample with an effective twist-angle resolution of about 0.1°. This ambient methodology can be conveniently implemented to characterize and preselect high-quality areas of samples for subsequent device fabrication, and for transport and optical experiments., (© 2021 The Authors. Advanced Materials published by Wiley-VCH GmbH.)

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.