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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 MoS$_2$ 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., Comment: 21 pages, 4 figures

Band nesting occurs when conduction and valence bands are approximately equispaced over regions in the Brillouin zone. In two-dimensional materials, band nesting results in singularities of the joint density of states and thus in a strongly enhanced optical response at resonant frequencies. We exploit the high sensitivity of such resonances to small changes in the band structure to sensitively probe strain in semiconducting transition metal dichalcogenides (TMDs). We measure and calculate the polarization-resolved optical second harmonic generation (SHG) at the band nesting energies and present the first measurements of the energy-dependent nonlinear photoelastic effect in atomically thin TMDs (MoS2, MoSe2, WS2, and WSe2) combined with a theoretical analysis of the underlying processes. Experiment and theory are found to be in good qualitative agreement displaying a strong energy dependence of the SHG, which can be exploited to achieve exceptionally strong modulation of the SHG under strain. We attribute this sensitivity to a redistribution of the joint density of states for the optical response in the band nesting region. We predict that this exceptional strain sensitivity is a general property of all 2D materials with band nesting.

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 behavior 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 develop a technique capable of straining pristine suspended WSe2 kept at cryogenic temperatures up to 3\% to study the strain behavior of these fragile many-body states. We find that under the application of strain, dark and localized excitons in monolayer WSe2 - 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 exciton reported here may play a critical role in the operation of single quantum emitters based on WSe2. Furthermore, the techniques we developed may be used to fingerprint unidentified excitonic states, Comment: 15 pages, 5 figures

Smoothly confined graphene quantum dots (GQDs) localize Dirac electrons with conserved spin and valley degrees of freedom. Recent experimental realization of such structures using a combination of magnetic fields and a scanning tunneling microscope tip showcased their potential in locally probing and adjusting the valley degree of freedom. The present work models the influence of lattice defects on the level structure of GQDs. We study both the adiabatic level spacing ``landscape''---orbital splitting and valley splitting---as well as transition dynamics between GQD states. The system is modeled using a tight-binding approach with on-site and hopping parameters in the vicinity of the defect region extracted from density functional theory via Wannier orbitals while time propagation is done using Magnus operators. Different defect types, such as double vacancy, Stone-Wales, flower, and Si substitution, are considered. We predict tunable valley splittings of the order of 2--20 meV. The level structure can thus be tailored at will by engineering appropriate defect geometries.

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 moir\'e 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., Comment: 14 pages, 12 figures

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., Comment: 9 pages, 4 figures

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

Single-photon emitters play a key role in present and emerging quantum technologies. Several recent measurements have established monolayer ${\mathrm{WSe}}_{2}$ as a promising candidate for a reliable single-photon source. The origin and underlying microscopic processes have remained, however, largely elusive. We present a multiscale tight-binding simulation for the optical spectra of ${\mathrm{WSe}}_{2}$ under nonuniform strain and in the presence of point defects employing the Bethe-Salpeter equation. Strain locally shifts excitonic energy levels into the band gap where they overlap with localized intragap defect states. The resulting hybridization allows for efficient filling and subsequent radiative decay of the defect states. We identify intervalley defect excitonic states as the likely candidate for antibunched single-photon emission. This proposed scenario is shown to account for a large variety of experimental observations including brightness, radiative transition rates, the variation of the excitonic energy with applied magnetic and electric fields as well as the variation of the polarization of the emitted photon with the magnetic field.

We present measurements of quantized conductance in electrostatically induced quantum point contacts in bilayer graphene. The application of a perpendicular magnetic field leads to an intricate pattern of lifted and restored degeneracies with increasing field: at zero magnetic field the degeneracy of quantized one-dimensional subbands is four, because of a twofold spin and a twofold valley degeneracy. By switching on the magnetic field, the valley degeneracy is lifted. Because of the Berry curvature, states from different valleys split linearly in magnetic field. In the quantum Hall regime fourfold degenerate conductance plateaus reemerge. During the adiabatic transition to the quantum Hall regime, levels from one valley shift by two in quantum number with respect to the other valley, forming an interweaving pattern that can be reproduced by numerical calculations., We acknowledge financial support from the European Graphene Flagship, the Swiss National Science Foundation via NCCR Quantum Science and Technology, ERC Synergy Hetero 2D, WWTF Project No. MA14-002, and MECD. Calculations were performed on the Vienna Scientific Cluster (VSC). Growth of hexagonal boron nitride crystals was supported by the Elemental Strategy Initiative conducted by MEXT, Japan and the CREST (JPMJCR15F3), JST, EC Project 2D·SIPC, Grant No. 820378.

We present an approach for embedding defect structures modeled by density functional theory into large-scale tight-binding simulations. We extract local tight-binding parameters for the vicinity of the defect site using Wannier functions. In the transition region between the bulk lattice and the defect the tight-binding parameters are continuously adjusted to approach the bulk limit far away from the defect. This embedding approach allows for an accurate high-level treatment of the defect orbitals using as many as ten nearest neighbors while keeping a small number of nearest neighbors in the bulk to render the overall computational cost reasonable. As an example of our approach, we consider an extended graphene lattice decorated with Stone-Wales defects, flower defects, double vacancies, or silicon substitutes. We predict distinct scattering patterns mirroring the defect symmetries and magnitude that should be experimentally accessible.