Quantifying Strain in Moiré Superlattice.

In twisted van der Waals (vdW) bilayers, intrinsic strain associated with the moiré superlattice and unintentionally introduced uniaxial strain may be present simultaneously. Both strains are able to lift the degeneracy of the E2g phonon modes in Raman spectra. Because of the different rotation symmetry of the two types of strain, the corresponding Raman intensity exhibits a distinct polarization dependence. We compare a 2.5° twisted MoS2 bilayer, in which the maximal intrinsic moiré strain is anticipated, and a natural MoS2 bilayer with an intentionally introduced uniaxial strain. By analyzing the frequency shift of the E2g doublet and their polarization dependence, we can not only determine the direction of unintentional uniaxial strain in the twisted bilayer but also quantify both strain components. This simple strain characterization method based on far-field Raman spectra will facilitate the studies of electronic properties of moiré superlattices under the influence of combined intrinsic and external strains.

Photonic effects in the non-equilibrium optical response of two-dimensional semiconductors.

Transient absorption spectroscopy is a powerful tool to monitor the out-of-equilibrium optical response of photoexcited semiconductors. When this method is applied to two-dimensional semiconductors deposited on different substrates, the excited state optical properties are inferred from the pump-induced changes in the transmission/reflection of the probe, i.e., ΔT/T or ΔR/R. Transient optical spectra are often interpreted as the manifestation of the intrinsic optical response of the monolayer, including effects such as the reduction of the exciton oscillator strength, electron-phonon coupling or many-body interactions like bandgap renormalization, trion or biexciton formation. Here we scrutinize the assumption that one can determine the non-equilibrium optical response of the TMD without accounting for the substrate used in the experiment. We systematically investigate the effect of the substrate on the broadband transient optical response of monolayer MoS2 (1L-MoS2) by measuring ΔT/T and ΔR/R with different excitation photon energies. Employing the boundary conditions given by the Fresnel equations, we analyze the transient transmission/reflection spectra across the main excitonic resonances of 1L-MoS2. We show that pure interference effects induced by the different substrates explain the substantial differences (i.e., intensity, peak energy and exciton linewidth) observed in the transient spectra of the same monolayer. We thus demonstrate that the substrate strongly affects the magnitude of the exciton energy shift and the change of the oscillator strength in the transient optical spectra. By highlighting the key role played by the substrate, our results set the stage for a unified interpretation of the transient response of optoelectronic devices based on a broad class of TMDs.

Strain control of hybridization between dark and localized excitons in a 2D semiconductor.

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 WSe2 kept at cryogenic temperatures. 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 excitons 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.

Challenges of modeling nanostructured materials for photocatalytic water splitting.

Understanding the water splitting mechanism in photocatalysis is a rewarding goal as it will allow producing clean fuel for a sustainable life in the future. However, identifying the photocatalytic mechanisms by modeling photoactive nanoparticles requires sophisticated computational techniques based on multiscale modeling. In this review, we will survey the strengths and drawbacks of currently available theoretical methods at different length and accuracy scales. Understanding the surface-active site through Density Functional Theory (DFT) using new, more accurate exchange-correlation functionals plays a key role for surface engineering. Larger scale dynamics of the catalyst/electrolyte interface can be treated with Molecular Dynamics albeit there is a need for more generalizations of force fields. Monte Carlo and Continuum Modeling techniques are so far not the prominent path for modeling water splitting but interest is growing due to the lower computational cost and the feasibility to compare the modeling outcome directly to experimental data. The future challenges in modeling complex nano-photocatalysts involve combining different methods in a hierarchical way so that resources are spent wisely at each length scale, as well as accounting for excited states chemistry that is important for photocatalysis, a path that will bring devices closer to the theoretical limit of photocatalytic efficiency.

Phonon renormalization in reconstructed MoS2 moiré superlattices.

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 MoS2 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.

Local embedding of coupled cluster theory into the random phase approximation using plane waves.

We present an embedding approach to treat local electron correlation effects in periodic environments. In a single consistent framework, our plane wave based scheme embeds a local high-level correlation calculation [here, Coupled Cluster (CC) theory], employing localized orbitals, into a low-level correlation calculation [here, the direct Random Phase Approximation (RPA)]. This choice allows for an accurate and efficient treatment of long-range dispersion effects. Accelerated convergence with respect to the local fragment size can be observed if the low-level and high-level long-range dispersions are quantitatively similar, as is the case for CC in RPA. To demonstrate the capabilities of the introduced embedding approach, we calculate adsorption energies of molecules on a surface and in a chabazite crystal cage, as well as the formation energy of a lattice impurity in a solid at the level of highly accurate many-electron perturbation theories. The absorption energy of a methane molecule in a zeolite chabazite is converged with an error well below 20 meV at the CC level. As our largest periodic benchmark system, we apply our scheme to the adsorption of a water molecule on titania in a supercell containing more than 1000 electrons.

Time-Dependent Screening Explains the Ultrafast Excitonic Signal Rise in 2D Semiconductors.

We calculate the time evolution of the transient reflection signal in an MoS2 monolayer on a SiO2/Si substrate using first-principles out-of-equilibrium real-time methods. Our simulations provide a simple and intuitive physical picture for the delayed, yet ultrafast, evolution of the signal whose rise time depends on the excess energy of the pump laser: at laser energies above the A- and B-exciton, the pump pulse excites electrons and holes far away from the K valleys in the first Brillouin zone. Electron-phonon and hole-phonon scattering lead to a gradual relaxation of the carriers toward small Active Excitonic Regions around K, enhancing the dielectric screening. The accompanying time-dependent band gap renormalization dominates over Pauli blocking and the excitonic binding energy renormalization. This explains the delayed buildup of the transient reflection signal of the probe pulse, in excellent agreement with recent experimental data. Our results show that the observed delay is not a unique signature of an exciton formation process but rather caused by coordinated carrier dynamics and its influence on the screening.

Secondary Electron Emission by Plasmon-Induced Symmetry Breaking in Highly Oriented Pyrolytic Graphite.

Two-particle spectroscopy with correlated electron pairs is used to establish the causal link between the secondary electron spectrum, the (π+σ) plasmon peak, and the unoccupied band structure of highly oriented pyrolytic 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 ΓA 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 hybridization of the interlayer resonances with atomlike σ^{*} bands along the ΓA direction. These hybrid states have a high density of states as well as sufficient mobility along the graphite c axis leading to the sharp ∼3 eV resonance in the spectrum of emitted secondary electrons reported throughout the literature.

Atomic-Scale Carving of Nanopores into a van der Waals Heterostructure with Slow Highly Charged Ions.

The growing family of 2D materials led not long ago to combining different 2D layers and building artificial systems in the form of van der Waals heterostructures. Tailoring of heterostructure properties postgrowth would greatly benefit from a modification technique with a monolayer precision. However, appropriate techniques for material modification with this precision are still missing. To achieve such control, slow highly charged ions appear ideal as they carry high amounts of potential energy, which is released rapidly upon ion neutralization at the position of the ion. The resulting potential energy deposition is thus limited to just a few atomic layers (in contrast to the kinetic energy deposition). Here, we irradiated a freestanding van der Waals MoS2/graphene heterostructure with 1.3 keV/amu xenon ions in high charge states of 38, which led to nanometer-sized pores that appear only in the MoS2 facing the ion beam, but not in graphene beneath the hole. Reversing the stacking order leaves both layers undamaged, which we attribute to the high conductivity and carrier mobility in graphene acting as a shield for the MoS2 underneath. Our main focus is here on monolayer MoS2, but we also analyzed areas with few-layer structures and observed that the perforation is limited to the two topmost MoS2 layers, whereas deeper layers remain intact. Our results demonstrate that in addition to already being a valuable tool for materials processing, the usability of ion irradiation can be extended to mono- (or bi)layer manipulation of van der Waals heterostructures when the localized potential energy deposition of highly charged ions is also added to the toolbox.

Band Nesting in Two-Dimensional Crystals: An Exceptionally Sensitive Probe of Strain.

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.

Localized Intervalley Defect Excitons as Single-Photon Emitters in WSe_{2}.

Single-photon emitters play a key role in present and emerging quantum technologies. Several recent measurements have established monolayer 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 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.

Energy of the 229Th nuclear clock transition.

Owing to its low excitation energy and long radiative lifetime, the first excited isomeric state of thorium-229, 229mTh, can be optically controlled by a laser1,2 and is an ideal candidate for the creation of a nuclear optical clock3, which is expected to complement and outperform current electronic-shell-based atomic clocks4. A nuclear clock will have various applications-such as in relativistic geodesy5, dark matter research6 and the observation of potential temporal variations of fundamental constants7-but its development has so far been impeded by the imprecise knowledge of the energy of 229mTh. Here we report a direct measurement of the transition energy of this isomeric state to the ground state with an uncertainty of 0.17 electronvolts (one standard deviation) using spectroscopy of the internal conversion electrons emitted in flight during the decay of neutral 229mTh atoms. The energy of the transition between the ground state and the first excited state corresponds to a wavelength of 149.7 ± 3.1 nanometres, which is accessible by laser spectroscopy through high-harmonic generation. Our method combines nuclear and atomic physics measurements to advance precision metrology, and our findings are expected to facilitate the application of high-resolution laser spectroscopy on nuclei and to enable the development of a nuclear optical clock of unprecedented accuracy.

Dissociative Chemisorption of O2 on Al(111): Dynamics on a Correlated Wave-Function-Based Potential Energy Surface.

Dissociative chemisorption of O2 on the Al(111) surface represents an extensively studied prototype for understanding the interaction between O2 and metal surfaces. It is well known that the experimentally observed activation barrier for O2 dissociation is not captured by conventional density functional theory. The interpretation of this barrier as a result of spin transitions along the reaction path has been challenged by recent embedded correlated wave function (ECW) calculations that naturally yield an adiabatic barrier. However, the ECW calculations have been limited to a static analysis of the reaction pathways and have not yet been tested by dynamics simulations. We present a global six-dimensional potential energy surface (PES) for this system parametrized with ECW data points. This new PES provides a reasonable description of the site-specific and orientation-dependent activation barriers. Quasi-classical trajectory calculations on this PES semiquantitatively reproduce both the observed translational energy dependence of the sticking probability and steric effects with aligned O2 molecules.

Large tunable valley splitting in edge-free graphene quantum dots on boron nitride.

Coherent manipulation of the binary degrees of freedom is at the heart of modern quantum technologies. Graphene offers two binary degrees: the electron spin and the valley. Efficient spin control has been demonstrated in many solid-state systems, whereas exploitation of the valley has only recently been started, albeit without control at the single-electron level. Here, we show that van der Waals stacking of graphene onto hexagonal boron nitride offers a natural platform for valley control. We use a graphene quantum dot induced by the tip of a scanning tunnelling microscope and demonstrate valley splitting that is tunable from -5 to +10 meV (including valley inversion) by sub-10-nm displacements of the quantum dot position. This boosts the range of controlled valley splitting by about one order of magnitude. The tunable inversion of spin and valley states should enable coherent superposition of these degrees of freedom as a first step towards graphene-based qubits.

Topologically Nontrivial Valley States in Bilayer Graphene Quantum Point Contacts.

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.

High visibility in two-color above-threshold photoemission from tungsten nanotips in a coherent control scheme.

In this article, we present coherent control of above-threshold photoemission from a tungsten nanotip achieving nearly perfect modulation. Depending on the pulse delay between fundamental ([Formula: see text]) and second harmonic ([Formula: see text]) pulses of a femtosecond fiber laser at the nanotip, electron emission is significantly enhanced or depressed during temporal overlap. Electron emission is studied as a function of pulse delay, optical near-field intensities, DC bias field and final photoelectron energy. Under optimized conditions modulation amplitudes of the electron emission of 97.5% are achieved. Experimental observations are discussed in the framework of quantum-pathway interference supported by local density of states simulations.

Potential Functional Embedding Theory at the Correlated Wave Function Level. 2. Error Sources and Performance Tests.

Quantum mechanical embedding theories partition a complex system into multiple spatial regions that can use different electronic structure methods within each, to optimize trade-offs between accuracy and cost. The present work incorporates accurate but expensive correlated wave function (CW) methods for a subsystem containing the phenomenon or feature of greatest interest, while self-consistently capturing quantum effects of the surroundings using fast but less accurate density functional theory (DFT) approximations. We recently proposed two embedding methods [for a review, see: Acc. Chem. Res. 2014 , 47 , 2768 ]: density functional embedding theory (DFET) and potential functional embedding theory (PFET). DFET provides a fast but non-self-consistent density-based embedding scheme, whereas PFET offers a more rigorous theoretical framework to perform fully self-consistent, variational CW/DFT calculations [as defined in part 1, CW/DFT means subsystem 1(2) is treated with CW(DFT) methods]. When originally presented, PFET was only tested at the DFT/DFT level of theory as a proof of principle within a planewave (PW) basis. Part 1 of this two-part series demonstrated that PFET can be made to work well with mixed Gaussian type orbital (GTO)/PW bases, as long as optimized GTO bases and consistent electron-ion potentials are employed throughout. Here in part 2 we conduct the first PFET calculations at the CW/DFT level and compare them to DFET and full CW benchmarks. We test the performance of PFET at the CW/DFT level for a variety of types of interactions (hydrogen bonding, metallic, and ionic). By introducing an intermediate CW/DFT embedding scheme denoted DFET/PFET, we show how PFET remedies different types of errors in DFET, serving as a more robust type of embedding theory.

Potential Functional Embedding Theory at the Correlated Wave Function Level. 1. Mixed Basis Set Embedding.

Embedding theories offer an elegant solution to overcome intrinsic algorithmic scaling and accuracy limitations of simulation methods. These theories also promise to achieve the accuracy of high-level electronic structure techniques at near the computational cost of much less accurate levels of theory by exploiting positive traits of multiple methods. Of crucial importance to fulfilling this promise is the ability to combine diverse theories in an embedding simulation. However, these methods may utilize different basis set and electron-ion potential representations. In this first part of a two-part account of implementing potential functional embedding theory (PFET) at a correlated wave function level, we discuss remedies to basis set and electron-ion potential discrepancies and assess the performance of the PFET scheme with mixed basis sets.

Ultrafast electronic response of graphene to a strong and localized electric field.

The way conduction electrons respond to ultrafast external perturbations in low dimensional materials is at the core of the design of future devices for (opto)electronics, photodetection and spintronics. Highly charged ions provide a tool for probing the electronic response of solids to extremely strong electric fields localized down to nanometre-sized areas. With ion transmission times in the order of femtoseconds, we can directly probe the local electronic dynamics of an ultrathin foil on this timescale. Here we report on the ability of freestanding single layer graphene to provide tens of electrons for charge neutralization of a slow highly charged ion within a few femtoseconds. With values higher than 1012 A cm-2, the resulting local current density in graphene exceeds previously measured breakdown currents by three orders of magnitude. Surprisingly, the passing ion does not tear nanometre-sized holes into the single layer graphene. We use time-dependent density functional theory to gain insight into the multielectron dynamics.