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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.

Mechanical strain is a powerful tuning knob for excitons, Coulomb-bound electron–hole complexes dominating optical properties of two-dimensional semiconductors. While the strain response of bright free excitons is broadly understood, the behaviour of dark free excitons (long-lived excitations that generally do not couple to light due to spin and momentum conservation) or localized excitons related to defects remains mostly unexplored. Here, we study the strain behaviour of these fragile many-body states on pristine suspended WSe 2 kept at cryogenic temperatures. We find that under the application of strain, dark and localized excitons in monolayer WSe 2 —a prototypical 2D semiconductor—are brought into energetic resonance, forming a new hybrid state that inherits the properties of the constituent species. The characteristics of the hybridized state, including an order-of-magnitude enhanced light/matter coupling, avoided-crossing energy shifts, and strain tunability of many-body interactions, are all supported by first-principles calculations. The hybridized excitons reported here may play a critical role in the operation of single quantum emitters based on WSe 2 . Furthermore, the techniques we developed may be used to fingerprint unidentified excitonic states. Mechanical strain is a powerful tuning knob for excitons in two-dimensional semiconductors. Here, the authors find that under the application of strain, dark and localized excitons in monolayer WSe 2 are brought into energetic resonance, forming a new hybrid state that inherits the properties of the constituent species.

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

Afforestation of marginal agricultural lands is an important issue in the land use changes running in Europe at present. The aim of the presented study is the documentation of effects of site improving material Alginite three years after afforestation of agricultural land in the locality with unfavourable hydrophysical regime. The impact was evaluated on growth parameters (height increment, mortality and foliar nutrient content) of Douglas fir (Pseudotsuga menziesii (Mirb.) Franco), Scots pine (Pinus sylvestris L.) and a mixture of English oak (Quercus robur L.), red oak (Quercus rubra L.) and Norway maple (Acer platanoides L.) seedlings on former agricultural land in central Bohemia, Czech Republic. The research plot consists of 36 square sub-plots, each sub-plot is 400 m2 in size. Each sub-plot consists of 400 individuals, except Douglas-fir with 200 individuals. The following doses of Alginite were applied: control (variant A without Alginite), 0.5 kg of Alginite (B) and 1.5 kg of Alginite (C) on both conifers and broadleaves. The results showed that Alginite application had greater positive effect on height growth of seedlings than mortality, especially variant C. In most of the cases height increments were significantly positively affected (p < 0.05) by both variants of Alginite application only in the third year after planting. Alginite applications were also connected with differences in the foliar nutrient content, especially with higher magnesium and phosphorus values. The highest differences among Alginite variants were observed for Norway maple and English oak, while the lowest for red oak and Scots pine within all monitored parameters.

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.

The moiré potential of graphene on hexagonal boron nitride (hBN) generates a supercell sufficiently large as to thread a full magnetic flux quantum \\(\\Phi_0\\) for experimentally accessible magnetic field strengths. Close to rational fractions of \\(\\Phi_0\\), \\(p/q \\cdot\\Phi_0\\), magnetotranslation invariance is restored giving rise to Brown-Zak fermions featuring the same dispersion relation as in the absence of the field. Employing a highly efficient numerical approach we have performed the first realistic simulation of the magnetoconductance for a 250 nm wide graphene ribbon on hexagonal boron nitride using a full ab-initio derived parametrization including strain. The resulting Hofstadter butterfly is analyzed in terms of a novel Wannier diagram for Landau spectra of Dirac particles that includes the lifting of the spin and valley degeneracy by the magnetic field and the moiré potential. This complex diagram can account for many experimentally observed features on a single-particle level, such as spin and valley degeneracy lifting and a non-periodicidy in \\(\\Phi_0\\).

We construct a continuum model of twisted trilayer graphene using {\\it ab initio} density-functional-theory calculations, and apply it to address twisted trilayer electronic structure. Our model accounts for moiré variation in site energies, hopping between outside layers and within layers. We focus on the role of a mirror symmetry present in ABA graphene trilayers with a middle layer twist. The mirror symmetry is lost intentionally when a displacement field is applied between layers, and unintentionally when the top layer is shifted laterally relative to the bottom layer. We use two band structure characteristics that are directly relevant to transport measurements, the Drude weight and the weak-field Hall conductivity, and relate them via the Hall density to assess the influence of the accidental lateral stacking shifts currently present in all experimental devices on electronic properties, and comment on the role of the possible importance of accidental lateral stacking shifts for superconductivity in twisted trilayers.

Two-particle spectroscopy with correlated electron pairs is used to establish the causal link between the secondary electron spectrum, the \\((\\pi+\\sigma)-\\)plasmon peak and the unoccupied band structure of highly oriented pyrolitic graphite. The plasmon spectrum is resolved with respect to the involved interband transitions and clearly exhibits final state effects, in particular due to the energy gap between the interlayer resonances along the \\(\\Gamma\\)A-direction. The corresponding final state effects can also be identified in the secondary electron spectrum. Interpretation of the results is performed on the basis of density functional theory and tight binding calculations. Excitation of the plasmon perturbs the symmetry of the system and leads to hybridisation of the interlayer resonances with atom-like \\(\\sigma^*\\) bands along the \\(\\Gamma A\\)-direction. These hybrid states have a high density of states as well as sufficient mobility along the graphite \\(c\\)-axis leading to the sharp \\(\\sim\\)3\\ eV resonance in the spectrum of emitted secondary electrons reported throughout the literature.

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.