Polariton-polariton scattering in microcavities: A microscopic theory

Atomically thin transition metal dichalcogenides exhibit a remarkably strong Coulomb interaction. This results in a fascinating many-particle physics including a variety of bright and dark excitonic states that determine optical and electronic properties of these materials. So far, the impact of dark states has remained literally in the dark to a large extent, since a measurement of these optically forbidden states is very challenging. Here we demonstrate a strategy to measure a direct fingerprint of dark states even in standard linear absorption spectroscopy. We present a microscopic study on bright and dark higher excitonic states in the presence of disorder for the exemplary material of tungsten disulfide (WS2). We show that the geometric phase cancels the degeneration of 2s and 2p states and that a significant disorder-induced coupling of these bright and dark states offers a strategy to circumvent optical selection rules. As a proof, we show a clear fingerprint of dark 2p states in the absorption spectrum of WS2. The predicted softening of optical selection rules through exciton-disorder coupling is of general nature and therefore applicable to related two-dimensional semiconductors.

Dark exciton states show great potential in condensed matter physics and optoelectronics because of their long lifetime and rich distribution in band structures. Therefore, they can theoretically serve as efficient energy reservoirs, providing a platform for future applications. However, their optical-transition-forbidden nature severely limits their experimental exploration and hinders their current application. Here, we demonstrate a universal dark state nonlinear energy transfer (ET) mechanism in monolayer WS2/CsPbBr3 van der Waals heterostructures under two-photon excitation, which successfully utilizes the enormous energy reserved in the dark exciton state of CsPbBr3 to significantly improve the photoelectric performance of monolayer WS2. We first propose the scenario of resonant ET between the dark state of CsPbBr3 and WS2, and then reveal that this is a typical Förster resonant ET and belongs to the 2D-2D category. Interestingly, the dark state ET in CsPbBr3 is identified as a long-range donor-bridge-acceptor hopping mode, with a potential distance exceeding 200 nm. Finally, we successfully achieve nearly an order of magnitude enhancement in the near-infrared detection performance of monolayer WS2. Our results enrich the theory of dark exciton states and ET, and they provide a way of using dark exciton states for future practical applications.

We present a detailed study of the angular distribution in photoionization of H+2 in different geometrical arrangements between the internuclear axis and the polarization vector. We compare the results of an exact calculations with those obtained employing approximate initial and final state wave functions. We find large and unexpected differences if we employ the 2C or exact final state continuum wave functions with the same initial state. We find also that the results depend on the accuracy of the initial bound state. As the quality of the final state is improved we obtain results in closer agreement with the exact angular distributions.

The tightly bound excitons and strong dipole-dipole interactions in two-dimensional molecular crystals enable rich physics. Among them, superradiance (SR), the spontaneous coherent emission from bright excitons, has sparked considerable interest in quantum-information applications. In addition, optically forbidden states (dark exciton states) have potential to both achieve Bose-Einstein condensation and modulate exciton dynamics. Here, we report a unique series of dark exciton states in highly crystalline organic monolayers (MLs) via two-photon excitation spectroscopy (TP-PLE). These dark exciton states convert to the emissive, delocalized exciton states that undergo room temperature SR. Using a vibronic exciton model, we show that these dark exciton states are mixed character states of Frenkel exciton (FE) and charge transfer exciton (CTE) with majority intralayer CTE character (>99.9%) and weak coupling to the emissive FE states. We observe significantly higher photochemical stability of MLs under two-photon excitation, which we attribute to the suppression of exciton-exciton annihilation.

When a detuned and strong laser pulse acts on an optical transition, a Stark shift of the corresponding energies occurs. We analyze how this optical Stark effect can be used to prepare and control the dark exciton occupation in a semiconductor quantum dot. The coupling between the bright and dark exciton states is facilitated by an external magnetic field. Using sequences of laser pulses, we show how the dark exciton and different superposition states can be prepared. We give simple analytic formulas, which yield a good estimate for optimal preparation parameters. The preparation scheme is quite robust against the influence of acoustic phonons. We further discuss the experimental feasibility of the used Stark pulses. Giving a clear physical picture our results will stimulate the usage of dark excitons in schemes to generate photons from quantum dots.

Shape-dependent exciton relaxation dynamics of CdSe 0-D nanocrystals and 1-D nanorods were studied using low-temperature (4.2 K), time-resolved and intensity-integrated magneto-photoluminscence (MPL) spectroscopy. Analysis of the average MPL rate constants from several different nanocrystal quantum dots and rods excited by 400 nm light in applied magnetic fields up to 17.5 T revealed size-dependent energy gaps separating bright and dark exciton fine-structure states. For 1-D nanorods under strong cross-sectional confinement and large length-to-diameter aspect ratios, efficient mixing of bright and dark exciton states was achieved using relatively low applied field strengths (≤4 T). The effect was attributed, in part, to decreased confinement of CdSe hole states associated with the long axis of the nanorod, which resulted in reduction of the energy gaps separating the bright and dark states. Increased control over the angle formed between the applied field vectors and the nanocrystal c-axis led to more efficient and uniform mixing of nanorod exciton states than for quantum dots. The findings suggest 1-D nanostructures are advantageous over 0-D ones for field-responsive applications.

We present a theory to address the photoluminescence (PL) intensity and valley polarization (VP) dynamics in monolayer WSe2, under the impact of excitonic dark states of both excitons and biexcitons. We find that the PL intensity of all excitonic channels including intravalley exciton (Xb), intravalley biexciton (XXk,k) and intervalley biexciton (XX) in particular for the XXk,k PL is enhanced by laser excitation fluence. In addition, our results indicate the anomalous temperature dependence of PL, i.e. increasing with temperature, as a result of favored phonon assisted dark-to-bright scatterings at high temperatures. Moreover, we observe that the PL is almost immune to intervalley scatterings, which trigger the exchange of excitonic states between the two valleys. As far as the valley polarization is concerned, we find that the VP of Xb shrinks as temperature increases, exhibiting opposite temperature response to PL, while the intravalley XXk,k VP is found almost independent of temperature. In contrast to both Xb and XXk,k, the intervalley XX VP identically vanishes, because of equal populations of excitons in the K and valleys bounded to form intervalley biexcitons. Notably, it is found that the Xb VP much more strongly depends on bright–dark scattering than that of XXk,k, making dark state act as a robust reservoir for valley polarization against intervalley scatterings for Xb at strong bright–dark scatterings, but not for XXk,k. Dark excitonic states enabled enhancement of VP benefits quantum technology for information processing based on the valley degree of freedom in valleytronic devices. Furthermore, the VP has strong dependence on intervalley scattering but maintains essentially constant with excitation fluence. Finally, the dependence of time evolution of PL and VP on temperature and excitation fluence is discussed.

The screened electromagnetic field is calculated for light incident on a jellium sphere; this is then used to calculate the photoemission from spheres of radius 20-30 au, using initial and final state wavefunctions appropriate to a square-well potential. The probability of photoemission is enhanced by a factor of about 100 around the Mie plasmon frequency compared with emission from a plane surface, an important contribution coming from resonances in the final state wavefunctions at low energies. The photoemission from an Ag sphere of radius 25 au is also calculated, using the bulk dielectric properties to find the screened electromagnetic field, and free-electron-like initial and final states. As the Mie frequency is well below the threshold for Ag, the photoyield is enhanced by a factor of only 5, and much smaller than the experimentally observed enhancement.

A protein dynamics simulation of the photosynthetic reaction center of Rps. viridis is performed by using the CHARMM program. The relevant part of the protein contains the special pair and the proximate cytochrome c. In the center is a tyrosine residue (L162) which is believed to support the electron transfer from the cytochrome c to the special pair by mixing the initial and final state wave functions. Preliminary calculations have shown that the 31 water molecules which are in the relevant part of the x-ray structure are much to mobile. Hence 8 extra water molecules have been added to improve the set-up for the dynamics simulation. The dynamics of the water molecules play an important role for the electron transfer due to their large mobility and the formation of hydrogen bridges with the OH-group of the tyrosine residue L162. The anisotropy, asymmetry and anharmonicity of the potential envelope governing the motion of a water molecule can be analysed by evaluating the second order moments 〈(XK−〈XK〉)*(XI − 〈XI〉)〉 of the cartesian components xk, k, 1=1, 2, 3 of the oxygen atom trajectory from the water molecule. The fluctuations of the nonbonded interactions of the tyrosine residue with its protein environment are as large as 4 kcal/mol, a value which is of the same order of magnitude as the difference of initial and final state energies of an electron transfer system. The statistical properties of these energy fluctuations must enter a model description of the electron transfer process.KeywordsWater MoleculeTyrosine ResidueOrder MomentProtein DynamicSpecial PairThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The exceptionally strong Coulomb interaction in semiconducting transition-metal dichalcogenides (TMDs) gives rise to a rich exciton landscape consisting of bright and dark exciton states. At elevated densities, excitons can interact through exciton-exciton annihilation (EEA), an Auger-like recombination process limiting the efficiency of optoelectronic applications. Although EEA is a well-known and particularly important process in atomically thin semiconductors determining exciton lifetimes and affecting transport at elevated densities, its microscopic origin has remained elusive. In this joint theory-experiment study combining microscopic and material-specific theory with time- and temperature-resolved photoluminescence measurements, we demonstrate the key role of dark intervalley states that are found to dominate the EEA rate in monolayer WSe$_2$. We reveal an intriguing, characteristic temperature dependence of Auger scattering in this class of materials with an excellent agreement between theory and experiment. Our study provides microscopic insights into the efficiency of technologically relevant Auger scattering channels within the remarkable exciton landscape of atomically thin semiconductors.

Exciton luminescence of a CdSe quantum dot (QD) inserted in a ZnSe nanowire is strongly influenced by the dark exciton states. Because of the small size of these QDs (2--5 nm), exchange interaction between hole and electron is highly enhanced and we measured large energy splitting between bright and dark exciton states ($\ensuremath{\Delta}E\ensuremath{\in}[4,9.2]$ meV) and large spin-flip rates between these states. Statistics on many QDs showed that this splitting depends on the QD size. Moreover, we measured an increase of the spin-flip rate to the dark states with increasing energy splitting. We explain this observation with a model, taking into account the fact that the exciton-phonon interaction depends on the bright to dark exciton energy splitting, as well as on the size and shape of the exciton wave function. It also has consequences on the exciton line intensity at high temperature.

Monolayer transition metal dichalcogenides (TMDs) exhibit a remarkably strong Coulomb interaction that manifests in tightly bound excitons. Due to the complex electronic band structure exhibiting several spin-split valleys in the conduction and valence band, dark excitonic states can be formed. They are inaccessibly by light due to the required spin-flip and/or momentum transfer. The relative position of these dark states with respect to the optically accessible bright excitons has a crucial impact on the emission efficiency of these materials and thus on their technological potential. Based on the solution of the Wannier equation, we present the excitonic landscape of the most studied TMD materials including the spectral position of momentum- and spin-forbidden excitonic states. We show that the knowledge of the electronic dispersion does not allow to conclude about the nature of the material's band gap, since excitonic effects can give rise to significant changes. Furthermore, we reveal that an exponentially reduced photoluminescence yield does not necessarily reflect a transition from a direct to a non-direct gap material, but can be ascribed in most cases to a change of the relative spectral distance between bright and dark excitonic states.

The high energy behavior of many atomic processes can be understood in terms of the theory of asymptotic Fourier transforms (AFT). In high energy atomic processes initial or final state wave functions will include continuum states of asymptotic plane wave character, and these will often result in a matrix element which can be viewed as a (multi‐dimensional) Fourier transform. The result will be a behavior of matrix elements and cross sections as inverse powers of the asymptotic momenta, associated with singular behaviors of atomic wave functions, which in turn are associated with the singular (Coulomb) behavior of the interaction of the atomic constituents. The situation is complicated by the Coulomb functions which modify these plane wave behaviors; these result in slowly convergent factors (we call them Stobbe factors) which may be explicitly factored out, yielding a matrix element as a product of a Stobbe factor and a residual matrix element which converges rapidly to its asymptotic form. We will illustrate these ideas here in a discussion of single and double non‐relativistic photoionization, though the approach may also be applied to electron scattering (and with excitation or ionization) and in the relativistic case. The main ideas of the approach can already be illustrated in the discussion of ionization of a particle in a central potential. Within this approach we explain both (for single ionization) the persistent high energy deviations from independent particle approximation predictions and (for double ionization) the shake–off and quasi–free contributions. We also discuss the importance of final state interactions and retardation corrections.

CESD97 — A revised version to expand jj-coupled symmetry functions into determinants

Owing to nonzero charge and spin degrees of freedom, trions offer unprecedented tunability and open new paths for applications in devices based on 2D semiconductors. However, in monolayer WSe2, the trion photoluminescence is commonly detected only at low temperatures and vanishes at room temperature, which undermines practical applications. To unveil how to overcome this obstacle, we have developed a comprehensive theory to probe the impact of different excitonic channels on the trion emission in WSe2 monolayers, which combines ab initio tight-binding formalism, Bethe–Salpeter equation and a set of coupled rate equations to describe valley dynamics of excitonic particles. Through a systematic study in which new scattering channels are progressively included, we found that, besides the low electron density, strong many-body correlations between bright and dark excitonic states quenches the trion emission in WSe2. Therefore, the reduction of scatterings from bright to dark states is required to achieve trion emission at room temperature for experimentally accessible carrier concentrations.