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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 MoS 2 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 MoS 2 as a function of twist angles, with theoretical support, reveal phonon renormalization in this moiré superlattice.

Moiré superlattices host a rich variety of correlated electronic phases. However, the moiré potential is fixed by interlayer coupling, and it is dependent on the nature of carriers and valleys. In contrast, it has been predicted that twisted hexagonal boron nitride (hBN) layers can impose a periodic electrostatic potential capable of engineering the properties of adjacent functional layers. Here, we show that this potential is described by a theory of electric polarization originating from the interfacial charge redistribution, validated by its dependence on supercell sizes and distance from the twisted interfaces. This enables controllability of the potential depth and profile by controlling the twist angles between the two interfaces. Employing this approach, we further demonstrate how the electrostatic potential from a twisted hBN substrate impedes exciton diffusion in semiconductor monolayers, suggesting opportunities for engineering the properties of adjacent functional layers using the surface potential of a twisted hBN substrate. The authors demonstrate that the electrostatic potential originating on the surface of twisted bilayer and multilayer hexagonal boron nitride can be used to generate a moiré potential modulation on adjacent semiconductor layers, enabling the possibility of controlling the properties of this adjacent layer.

A Correction to this paper has been published: https://doi.org/10.1038/s41563-021-00998-1.

Recent advances in the isolation and stacking of monolayers of van der Waals materials have provided approaches for the preparation of quantum materials in the ultimate two-dimensional limit 1 , 2 . In van der Waals heterostructures formed by stacking two monolayer semiconductors, lattice mismatch or rotational misalignment introduces an in-plane moiré superlattice 3 . It is widely recognized that the moiré superlattice can modulate the electronic band structure of the material and lead to transport properties such as unconventional superconductivity 4 and insulating behaviour driven by correlations 5 – 7 ; however, the influence of the moiré superlattice on optical properties has not been investigated experimentally. Here we report the observation of multiple interlayer exciton resonances with either positive or negative circularly polarized emission in a molybdenum diselenide/tungsten diselenide (MoSe 2 /WSe 2 ) heterobilayer with a small twist angle. We attribute these resonances to excitonic ground and excited states confined within the moiré potential. This interpretation is supported by recombination dynamics and by the dependence of these interlayer exciton resonances on twist angle and temperature. These results suggest the feasibility of engineering artificial excitonic crystals using van der Waals heterostructures for nanophotonics and quantum information applications. Multiple interlayer exciton resonances in a MoSe 2 /WSe 2 heterobilayer with a small twist angle are attributed to excitonic ground and excited states confined within the moiré potential.

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 MoS 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.

Moiré superlattices formed by vertically stacking van der Waals layers host a rich variety of correlated electronic phases and function as novel photonic materials. The moiré potential of the superlattice, however, is fixed by the interlayer coupling of the stacked functional layers (e.g. graphene) and dependent on carrier types (e.g. electrons or holes) and valleys (e.g. {\\Gamma} vs. K). In contrast, twisted hexagonal boron nitride (hBN) layers are predicted to impose a periodic electrostatic potential that may be used to engineer the properties of an adjacent functional thin layer. Here, we show that this potential is described by a simple theory of electric polarization originating from the interfacial charge redistribution, validated by its dependence on supercell sizes and distance from the twisted interfaces. We demonstrate that the potential depth and profile can be further controlled by assembling a double moiré structure. When the twist angles are similar at the two interfaces, the potential is deepened by adding the potential from the two twisted interfaces, reaching ~ 400 meV. When the twist angles are dissimilar at the two interfaces, multi-level polarization states are observed. As an example of controlling a functional layer, we demonstrate how the electrostatic potential from a twisted hBN substrate impedes exciton diffusion in a semiconductor monolayer. These findings suggest exciting opportunities for engineering properties of an adjacent functional layer using the surface potential of a twisted hBN substrate.

In van der Waals (vdW) heterostructures formed by stacking two monolayer semiconductors, lattice mismatch or rotational misalignment introduces an in-plane moiré superlattice. While it is widely recognized that a moiré superlattice can modulate the electronic band structure and lead to novel transport properties including unconventional superconductivity and insulating behavior driven by correlations, its influence on optical properties has not been investigated experimentally. We present spectroscopic evidence that interlayer excitons are confined by the moiré potential in a high-quality MoSe2/WSe2 heterobilayer with small rotational twist. A series of interlayer exciton resonances with either positive or negative circularly polarized emission is observed in photoluminescence, consistent with multiple exciton states confined within the moiré potential. The recombination dynamics and temperature dependence of these interlayer exciton resonances are consistent with this interpretation. These results demonstrate the feasibility of engineering artificial excitonic crystals using vdW heterostructures for nanophotonics and quantum information applications.

In moiré 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 moiré 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 moiré pattern. We develop a new low-energy continuum model for phonons that overcomes the outstanding challenge of calculating properties of large moiré supercells and successfully captures essential experimental observations. Remarkably, simple optical spectroscopy experiments can provide information on strain and lattice distortions in moiré crystals with nanometer-size supercells. The newly developed theory promotes a comprehensive and unified understanding of structural, optical, and electronic properties of moiré superlattices.