Exciton Wave Function Research Articles

Plasmon-Enhanced Exciton Delocalization in Squaraine-Type Molecular Aggregates.

Enlarging exciton coherence lengths in molecular aggregates is critical for enhancing the collective optical and transport properties of molecular thin film nanostructures or devices. We demonstrate that the exciton coherence length of squaraine aggregates can be increased from 10 to 24 molecular units at room temperature when preparing the aggregated thin film on a metallic rather than a dielectric substrate. Two-dimensional electronic spectroscopy measurements reveal a much lower degree of inhomogeneous line broadening for aggregates on a gold film, pointing to a reduced disorder. The result is corroborated by simulations based on a Frenkel exciton model including exciton-plasmon coupling effects. The simulation shows that localized, energetically nearly resonant excitons on spatially well separated segments can be radiatively coupled via delocalized surface plasmon polariton modes at a planar molecule-gold interface. Such plasmon-enhanced delocalization of the exciton wave function is of high importance for improving the coherent transport properties of molecular aggregates on the nanoscale. Additionally, it may help tailor the collective optical response of organic materials for quantum optical applications.

Simultaneous fermion and exciton condensations from a model Hamiltonian

Fermion-exciton condensation in which both fermion-pair (i.e., superconductivity) and exciton condensations occur simultaneously in a single coherent quantum state has recently been conjectured to exist. Here, we capture the fermion-exciton condensation through a model Hamiltonian that can recreate the physics of this new class of highly correlated condensation phenomena. We demonstrate that the Hamiltonian generates the large-eigenvalue signatures of fermion-pair and exciton condensations for a series of states with increasing particle numbers. The results confirm that the dual-condensate wave function arises from the entanglement of fermion-pair and exciton wave functions, which we previously predicted in the thermodynamic limit. This model Hamiltonian---generalizing well-known model Hamiltonians for either superconductivity or exciton condensation---can explore a wide variety of condensation behavior. It provides significant insights into the required forces for generating a fermion-exciton condensate, which will likely be invaluable for realizing such condensations in realistic materials with applications from superconductors to excitonic materials.

Effects of the Structure and Temperature on the Nature of Excitons in the Mo0.6W0.4S2 Alloy.

We studied the nature of excitons in the transition metal dichalcogenide alloy Mo0.6W0.4S2 compared to pure MoS2 and WS2 grown by atomic layer deposition (ALD). For this, optical absorption/transmission spectroscopy and time-dependent density functional theory (TDDFT) were used. The effects of temperature on A and B exciton peak energies and line widths in optical transmission spectra were compared between the alloy and pure MoS2 and WS2. On increasing the temperature from 25 to 293 K, the energy of the A and B exciton peaks decreases, while their line width increases due to exciton–phonon interactions. The exciton–phonon interactions in the alloy are closer to those for MoS2 than those for WS2. This suggests that exciton wave functions in the alloy have a larger amplitude on Mo atoms than that on W atoms. The experimental absorption spectra could be reproduced by TDDFT calculations. Interestingly, for the alloy, the Mo and W atoms had to be distributed over all layers. Conversely, we could not reproduce the experimental alloy spectrum by calculations on a structure with alternating layers, in which every other layer contains only Mo atoms and the layers in between also contain W atoms. For the latter atomic arrangement, the TDDFT calculations yielded an additional optical absorption peak that could be due to excitons with some charge transfer character. From these results, we conclude that ALD yields an alloy in which Mo and W atoms are distributed uniformly among all layers.

Optimal condition to probe strong coupling of two-dimensional excitons and zero-dimensional cavity modes

The light-matter interaction associated with a two-dimensional (2D) excitonic transition coupled to a zero-dimensional (0D) photonic cavity is fundamentally different from coupling localized excitations in quantum dots or color centers, which have negligible spatial extent compared to the cavity-confined mode profile. By calculating the radiation-matter coupling of the exciton transition of a surface deposited 2D material and a 0D photonic crystal nanobeam mode, we found that there is an optimal spatial extent of the monolayer material that maximizes such an interaction strength due to the competition between minimizing the excitonic envelope function area and maximizing the total integrated field. This is counter to the intuition from the Dicke model, where the oscillator strength is expected to monotonically grow with the number of oscillators, which correlates to the monolayer area assuming the excitonic wavefunction is delocalized over the entire quantum well. We also found that at near zero exciton-cavity detuning, the direct transmission efficiency of a waveguide-integrated cavity can be severely suppressed, which suggests performing experiments by using a side-coupled cavity to get better performances.

Evidence for equilibrium exciton condensation in monolayer WTe2

We present evidence that the two-dimensional bulk of monolayer WTe2 contains electrons and holes bound by Coulomb attraction—excitons—that spontaneously form in thermal equilibrium. On cooling from room temperature to 100 K, the conductivity develops a V-shaped dependence on electrostatic doping, while the chemical potential develops a step at the neutral point. These features are much sharper than is possible in an independent-electron picture, but they can be accounted for if electrons and holes interact strongly and are paired in equilibrium. Our calculations from first principles show that the exciton binding energy is larger than 100 meV and the radius as small as 4 nm, explaining their formation at high temperature and doping levels. Below 100 K, more strongly insulating behaviour is seen, suggesting that a charge-ordered state forms. The observed absence of charge density waves in this state is surprising within an excitonic insulator picture, but we show that it can be explained by the symmetries of the exciton wavefunction. Therefore, in addition to being a topological insulator, monolayer WTe2 exhibits strong correlations over a wide temperature range.

Valley-contrasting interband transitions and excitons in symmetrically biased dice model

We study the exciton states in the symmetrically biased dice model, the electronic structures of which have an isolated flat band between two dispersive bands. At 1/3 or 2/3 filling, the model describes a two-dimensional semiconductor with the band edge at two degenerate valleys. Because of qualitative changes in the eigenvectors resulting from the bias term, the interband transition between the flat band and a dispersive band is valley contrasting under circularly polarized light. In terms of an effective-mass model and a realistic electron-hole interaction, we numerically calculate the spectrum and wave functions of the intravalley excitons, which are treated as Wannier-Mott excitons. We also discuss the fine structures of the exciton spectrum induced by the intravalley and intervalley exchange interactions. The symmetrically biased dice model thereby proves to be a new platform for valley-contrasting optoelectronics.

Exciton maps for thermally activated delayed fluorescence active/inactive carbazole benzonitrile derivatives.

The all-electron first-principles GW+Bethe-Salpeter method was applied to six carbazole benzonitrile (CzBN) derivatives, which were recently reported to be both thermally activated delayed fluorescence (TADF) active and inactive despite their singlet-triplet splittings being commonly around 0.2 eV. The present method successfully reproduced very similar photoabsorption spectra as experiments from the viewpoint of the peak positions and relative peak heights. We also performed exciton analysis with the exciton wave functions for several lowest singlet and triplet exciton states to reveal the details of the optical properties. We applied this to not only the present six CzBN derivatives but also 18 other TADF molecules and proposed a new exciton map to classify the molecules as the TADF active/inactive by using the exciton binding energy in the vertical axis and the ratio of electron and hole delocalization in the horizontal axis. Our results suggest two possible TADF mechanisms: spatially less localized hole states than the electron states where the exciton binding energy is proportional to the ratio of hole and electron delocalization and spatially more localized hole states than the electron states where the exciton binding energy should be large.

Exciton-exciton and exciton–charge carrier interaction and exciton collisional broadening in GaAs/AlGaAs quantum wells

Wave functions of heavy-hole excitons in GaAs/Al$_{0.3}$Ga$_{0.7}$As square quantum wells (QWs) of various widths are calculated by the direct numerical solution of a three-dimensional Schr\"odinger equation using a finite-difference scheme. These wave functions are then used to determine the exciton-exciton, exciton-electron and exciton-hole fermion exchange constants in a wide range of QW widths (5-150 nm). Additionally, the spin-dependent matrix elements of elastic exciton-exciton, exciton-electron and exciton-hole scattering are calculated. From these matrix elements, the collisional broadening of the exciton resonance is obtained within the Born approximation as a function of the areal density of excitons, electrons and holes respectively for QW widths of 5, 15, 30 and 50 nm. The obtained numerical results are compared with other theoretical works.

Twist versus heterostrain control of optical properties of moiré exciton minibands

We investigate the optical properties of interlayer excitons in heterobilayer transition metal dichalcogenides where moiré pattern is introduced by heterostrain, in comparison with that introduced by twisting (and/or lattice mismatch). Besides being a cause of the moiré texture, strain also effectively introduces a constant gauge potential on either electron or hole, which shifts the dispersion of kinetic energy with respect to the excitonic crystal momenta in the moiré superlattices. This leads to distinct exciton mini-band dispersions and light coupling properties from the twisting induced moiré, even if the excitonic moiré superlattice potentials have the similar real-space profile for the two cases. For strain that breaks the three-fold rotational symmetry at the atomic scale, the exciton wave packets trapped at the superlattice potential minima have elliptically polarized valley optical selection rules, in contrast to the circularly polarized ones in the twisting moiré. We investigate the evolution of the excitonic mini-bands and the optical dipoles of the bright states inside the light cones with the decrease of the moiré periodicity, upon which the excitonic wave functions evolve from localized wave packets to the extended Bloch states. Furthermore, moiré exciton properties under the interplay of twisting and heterostrain are also discussed.

Tuning the interfacial stoichiometry of InP core and InP/ZnSe core/shell quantum dots

We demonstrate fine-tuning of the atomic composition of InP/ZnSe quantum dots (QDs) at the core/shell interface. Specifically, we control the stoichiometry of both anions (P, As, S, and Se) and cations (In and Zn) at the InP/ZnSe core/shell interface and correlate these changes with the resultant steady-state and time-resolved optical properties of the nanocrystals. The use of reactive trimethylsilyl reagents results in surface-limited reactions that shift the nanocrystal stoichiometry to anion-rich and improve epitaxial growth of the shell layer. In general, anion deposition on the InP QD surface results in a redshift in the absorption, quenching of the excitonic photoluminescence, and a relative increase in the intensity of broad trap-based photoluminescence, consistent with delocalization of the exciton wavefunction and relaxation of exciton confinement. Time-resolved photoluminescence data for the resulting InP/ZnSe QDs show an overall small change in the decay dynamics on the ns timescale, suggesting that the relatively low photoluminescence quantum yields may be attributed to the creation of new thermally activated charge trap states and likely a dark population that is inseparable from the emissive QDs. Cluster-model density functional theory calculations show that the presence of core/shell interface anions gives rise to electronic defects contributing to the redshift in the absorption. These results highlight a general strategy to atomistically tune the interfacial stoichiometry of InP QDs using surface-limited reaction chemistry allowing for precise correlations with the electronic structure and photophysical properties.

Identification of twist-angle-dependent excitons in WS2/WSe2 heterobilayers.

Stacking atomically thin films enables artificial construction of van der Waals heterostructures with exotic functionalities such as superconductivity, the quantum Hall effect, and engineered light-matter interactions. In particular, heterobilayers composed of monolayer transition metal dichalcogenides have attracted significant interest due to their controllable interlayer coupling and trapped valley excitons in moiré superlattices. However, the identification of twist-angle-modulated optical transitions in heterobilayers is sometimes controversial since both momentum-direct (K–K) and -indirect excitons reside on the low energy side of the bright exciton in the monolayer constituents. Here, we attribute the optical transition at ∼1.35 eV in the WS2/WSe2 heterobilayer to an indirect Γ–K transition based on a systematic analysis and comparison of experimental photoluminescence spectra with theoretical calculations. The exciton wavefunction obtained by the state-of-the-art GW-Bethe-Salpeter equation approach indicates that both the electron and hole of the excitons are contributed by the WS2 layer. Polarization-resolved k-space imaging further confirms that the transition dipole moment of this optical transition is dominantly in-plane and is independent of the twist angle. The calculated absorption spectrum predicts that the so-called interlayer exciton peak coming from the K–K transition is located at 1.06 eV, but with a much weaker amplitude. Our work provides new insight into the steady-state and dynamic properties of twist-angle-dependent excitons in van der Waals heterostructures.

Valley-Dependent Interlayer Excitons in Magnetic WSe2/CrI3.

Heterostructures of two-dimensional transition-metal dichalcogenides and ferromagnetic substrates are important candidates for the development of viable new spin- or valleytronic devices. For the prototypical bilayer of WSe2 on top of a ferromagnetic layer of CrI3, we find substantially different coupling of both WSe2 K-valleys to the sublayer. Besides an energy splitting of a few meV, the corresponding excitons have significantly different interlayer character with charge transfer allowed at the K̅- point but forbidden at K̅+. The different exciton wave functions result in a distinctly different response to magnetic fields with g factors of about -4.4 and -4.0, respectively. By means of ab initio GW/Bethe-Salpeter equation calculations, these findings establish g factors as tool for investigating the exciton character and shedding light on the detailed quantum-mechanical interplay of magnetic and optical properties which are essential for the targeted development of optoelectronic devices.

Direct measurement of key exciton properties: Energy, dynamics, and spatial distribution of the wave function

AbstractExcitons, Coulomb‐bound electron–hole pairs, are the fundamental excitations governing the optoelectronic properties of semiconductors. Although optical signatures of excitons have been studied extensively, experimental access to the excitonic wave function itself has been elusive. Using multidimensional photoemission spectroscopy, we present a momentum‐, energy‐, and time‐resolved perspective on excitons in the layered semiconductor WSe2. By tuning the excitation wavelength, we determine the energy–momentum signature of bright exciton formation and its difference from conventional single‐particle excited states. The multidimensional data allow to retrieve fundamental exciton properties like the binding energy and the exciton–lattice coupling and to reconstruct the real‐space excitonic distribution function via Fourier transform. All quantities are in excellent agreement with microscopic calculations. Our approach provides a full characterization of the exciton properties and is applicable to bright and dark excitons in semiconducting materials, heterostructures, and devices.Key points The full life cycle of excitons is recorded with time‐ and angle‐resolved photoemission spectroscopy. The real‐space distribution of the excitonic wave function is visualized. Direct measurement of the exciton‐phonon interaction.

From carriers and virtual excitons to exciton populations: Insights into time-resolved ARPES spectra from an exactly solvable model

We calculate the {\em exact} time-resolved ARPES spectrum of a two-band model semiconductor driven out of equilibrium by resonant and nonresonant laser pulses, highlighting the effects of phonon-induced decoherence and relaxation. {\em Resonant} excitations initially yield a replica of the {\em valence} band shifted upward by the energy of the exciton peak in photoabsorption. This phase is eventually destroyed by phonon-induced decoherence: the valence-band replica lowers in energy by the Stokes shift, locating at the energy of the exciton peak in photoluminescence, and its width grows due to phonon dressing. {\em Nonresonant} excitations initially yield a map of the conduction band. Then electrons transfer their excess energy to the lattice and bind with the holes left behind to form excitons. In this relaxed regime a replica of the {\em conduction} band appears inside the gap. At fixed momentum the lineshape of the conduction-band replica versus the photoelectron energy is proportional to the exciton wavefunction in "energy space" and it is highly asymmetric. Although the two-band model represents an oversimplified description of real materials the highlighted features are qualitative in nature; hence they provide useful insights into time-resolved ARPES spectra and their physical interpretation.

(Invited) Ab Initio Exciton and Phonon Dynamics in Transition Metal Dichalcogenides

Interest in the properties of transition metal dichalcogenides (TMDs) has increased due to the discovery of the coupling between spin and valley degrees of freedom, which can be seen experimentally using a circularly polarised laser. After excitation the newly formed carrier populations must move towards the other valley until balance is reached. However, this relaxation process is not entirely understood in the literature, where the relative importance of the electron-electron (e-e) or electron-phonon (e-p) interactions is still a subject of debate. Previous works on WSe2 [A. Molina- Sánchez, et al - Nano letters, 2017] have shown that the e-p interaction is a good candidate to describe the relaxation process. Using a fully ab-initio framework based on the Baym-Kadanoff equations [P. M. M. C. de Melo and A. Marini, Phys. Rev. B 93, 155102 (2016)] we study the influence of the e-p interaction on MoSe2 after its excitation by a laser field. We show how phonons allow carrier relaxation and how the Kerr signal and total magnetisation are affected at different temperatures, with the latter exhibiting a non-monotonic behaviour as the temperature increases [M Ersfeld et al - Nano Letters 2019 19 (6), 4083-4090]. An important conclusion is that long lived spin states probably reside within defects. We calculate the spectral signatures of point defects in TMDs, finding two main classes based on the presence of in-gap states, and estimating the experimental resolution needed to provide quantification of the defect concentration [P de Melo et al. https://arxiv.org/abs/2010.10222]. The localization of excitonic states around the defect provides a benchmark for scanning probe characterization (figure shows a S vacancy exciton wave function, the green ball is the hole position). Figure 1

Theoretical description of optical and x-ray absorption spectra of MgO including many-body effects

Here we report the optical and x-ray absorption (XAS) spectra of the wide-band-gap oxide MgO using density functional theory (DFT) and many-body perturbation theory (MBPT). Our comprehensive study of the electronic structure shows that while the band gap is underestimated with the exchange-correlation functional PBEsol (4.58 eV) and the hybrid functional HSE06 (6.58 eV) compared to the experimental value (7.7 eV), it is significantly improved (7.52 eV) and even overcompensated (8.53 eV) when quasiparticle corrections are considered. Inclusion of excitonic effects by solving the Bethe-Salpeter equation (BSE) yields the optical spectrum in excellent agreement with experiment. Excellent agreement is observed also for the O and Mg K-edge absorption spectra, demonstrating the importance of the electron-hole interaction within MBPT. Projection of the electron-hole coupling coefficients from the BSE eigenvectors on the band structure allows us to determine the origin of prominent peaks and identify the orbital character of the relevant contributions. The real space projection of the lowest energy exciton wavefunction of the optical spectrum indicates a Wannier-Mott type, whereas the first exciton in the O K-edge is more localized.

Experimental measurement of the intrinsic excitonic wave function.

An exciton, a two-body composite quasiparticle formed of an electron and hole, is a fundamental optical excitation in condensed matter systems. Since its discovery nearly a century ago, a measurement of the excitonic wave function has remained beyond experimental reach. Here, we directly image the excitonic wave function in reciprocal space by measuring the momentum distribution of electrons photoemitted from excitons in monolayer tungsten diselenide. By transforming to real space, we obtain a visual of the distribution of the electron around the hole in an exciton. Further, by also resolving the energy coordinate, we confirm the elusive theoretical prediction that the photoemitted electron exhibits an inverted energy-momentum dispersion relationship reflecting the valence band where the partner hole remains, rather than that of conduction band states of the electron.

Exciton-Phonon Interactions in Monolayer Germanium Selenide from First Principles.

We investigate from first principles exciton-phonon interactions in monolayer germanium selenide, a direct gap two-dimensional semiconductor. By combining the Bethe-Salpeter approach and the special displacement method, we explore the phonon-induced renormalization of the exciton wave functions, excitation energies, and oscillator strengths. We determine a renormalization of the optical gap of 0.1 eV at room temperature, which results from the coupling of the exciton with both acoustic and optical phonons, with the strongest coupling to optical phonons at ∼100 cm-1. We also find that the exciton-phonon interaction is similar between monolayer and bulk GeSe. Overall, we demonstrate that the combination of many-body perturbation theory and special displacements offers a new route to investigate electron-phonon couplings in excitonic spectra, the resulting band gap renormalization, and the nature of phonons that couple to the exciton.

Quantification and Healing of Defects in Atomically Thin Molybdenum Disulfide: Beyond the Controlled Creation of Atomic Defects.

Atomically thin 2D materials provide an opportunity to investigate the atomic-scale details of defects introduced by particle irradiation. Once the atomic configuration of defects and their spatial distribution are revealed, the details of the mesoscopic phenomena can be unveiled. In this work, we created atomically small defects by controlled irradiation of gallium ions with doses ranging from 4.94 × 1012 to 4.00 × 1014 ions/cm2 on monolayer molybdenum disulfide (MoS2) crystals. The optical signatures of defects, such as the evolution of defect-activated LA-bands and a broadening of the first-order (E' and A'1) modes, can be studied by Raman spectroscopy. High-resolution scanning transmission electron microscopy (HR-STEM) analysis revealed that most defects are vacancies of few-molybdenum atoms with surrounding sulfur atoms (VxMo+yS) at a low ion dose. When increasing the ion dose, the atomic vacancies merge and form nanometer-sized holes. Utilizing HR-STEM and image analysis, we propose the estimation of the finite crystal length (Lfc) via the careful quantification of 0D defects in 2D systems through the formula Lfc = 4.41/, where ηion corresponds to the ion dose. Combining HR-STEM and Raman spectroscopy, the formula to calculate Lfc from Raman features, I(LA)/I(A'1) = 5.09/Lfc2, is obtained. We have also demonstrated an effective route to healing the ion irradiation-induced atomic vacancies by annealing defective MoS2 in a hydrogen disulfide (H2S) atmosphere. The H2S annealing improved the crystal quality of MoS2 with Lfc greater than the calculated size of the A exciton wave function, which leads to a partial recovery of the photoluminescence signal after its quenching by ion irradiation.

Synthesis of Colloidal Quantum Dots with an Ultranarrow Photoluminescence Peak

Localization of exciton wavefunctions away from the inorganic–organic interface is proposed for synthesizing colloidal spheroidal quantum dots (QDs) with an ultranarrow photoluminescence (PL) peak ...