Exciton Scattering Research Articles

Strong Exciton–Exciton Scattering of Exfoliated van der Waals InSe toward Efficient Continuous-Wave Near-Infrared P-Band Emission

P-band emission is a superlinear low-coherence emission through exciton-exciton (X-X) scattering into photon-like states. It occurs without the prerequisites of population inversion or macroscopical coherence, rendering lower power consumption than the widely explored superlinear low-coherence emissions including superfluorescence, amplified spontaneous emission, and random lasing, and holds great potential for speckle-free imaging and interferometric sensing. However, competition processes including exciton dissociation and annihilation undermine its operation at room temperature and/or low excitation conditions. Here we report room-temperature P-band emission from InSe microflakes with excitation density of 1010 cm-2, offering 2-orders-of-magnitude lower operation density compared to the state-of-the-art superlinear low-coherence emissions. The efficient P-band emission is attributed to a large X-X scattering strength of 0.25 μeV μm2 due to enhanced spatial confinement along with intrinsic material metrics of 3D/2D exciton complex and asymmetric electron/hole mass. These findings open an avenue toward strong low-coherence near-infrared light sources based on van der Waals semiconductors.

Resonant Exciton Scattering Reveals Raman Forbidden Phonon Modes in Layered GeS.

Germanium monosulfide with an anisotropic puckered crystalline structure has recently attracted much attention due to its unique optical and electronic properties; however, exciton-phonon interactions were only superficially elucidated. We study the resonant Raman scattering and the photoluminescence of the optically active Γ-exciton in layered GeS flakes and evaluate the exciton and phonon responses on variations in the excitation energy, laser-light and emission polarizations, temperature, and laser power. A double-resonance mechanism allows for observing Raman forbidden (dark) first- and second-order longitudinal-optical phonon modes whose symmetries and energies are moreover calculated by density functional perturbation theory. For (quasi)-resonant exciton excitation, the selection rules become relaxed so that a fourth-order Fröhlich intraband process is mediated by the scattering of the electron with a longitudinal-optical and an acoustic phonon. Our results demonstrate considerable coupling between phonons and photogenerated carriers in GeS flakes and the high efficiency of multiorder scattering in optical processes.

The Optical Signatures of Stochastic Processes in Many-Body Exciton Scattering.

We review our recent quantum stochastic model for spectroscopic lineshapes in the presence of a coevolving and nonstationary background population of excitations. Starting from a field theory description for interacting bosonic excitons, we derive a reduced model whereby optical excitons are coupled to an incoherent background via scattering as mediated by their screened Coulomb coupling. The Heisenberg equationsof motion for the optical excitons are then driven by an auxiliary stochastic population variable, which we take to be the solution of an Ornstein-Uhlenbeck process. Here, we present an overview of the theoretical techniques we have developed as applied to predicting coherent nonlinear spectroscopic signals. We show how direct (Coulomb) and exchange coupling to the bath give rise to distinct spectral signatures and discuss mathematical limits on inverting spectral signatures to extract the background density of states. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 74 is April 2023. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Phase relaxation control in heterostructures featuring charge-transfer excitons

Type-II quantum well heterostructures are considered high-potential candidates for next-generation active semiconductor devices. They promise low fundamental transition energies and suppressed Auger scattering as well as temperature stability in device performance. Understanding their fundamental properties, such as scattering and diffusion, and revealing intricate differences from type-I quantum structures are important steps towards optimized structure design. Using degenerate four-wave mixing spectroscopy, we investigate the phase coherence of excitonic polarizations in a (Ga,In)As/GaAs/Ga(As,Sb) type-II double-quantum-well structure. It is designed to exhibit spectrally isolated resonances in its linear absorption spectrum including a well-resolved charge-transfer exciton resonance. This allows us to study the coherent dynamics of the unperturbed charge-transfer exciton polarization. In addition, the effects of many-body interactions with free charge carriers as well as excitons that are injected by an optical prepulse are revealed. Scattering of charge-transfer excitons with free charge carriers is three times more efficient than scattering of charge-transfer excitons with each other. The comparison with Wannier excitons in a type-I quantum well structure shows that the interaction strength between charge-transfer excitons is about twice as large as for excitons in a type-I quantum well structure.

Contribution to Excitonic Linewidth from Free Carrier–Exciton Scattering in Layered Materials: The Example of hBN

Scattering of excitons by free carriers is a phenomenon, which is especially important when considering moderately to heavily doped semiconductors in low-temperature experiments, where the interaction of excitons with acoustic and optical phonons is reduced. In this paper, we consider the scattering of excitons by free carriers in monolayer hexagonal boron nitride encapsulated by a dielectric medium. We describe the excitonic states by variational wave functions, modeling the electrostatic interaction via the Rytova–Keldysh potential. Making the distinction between elastic and inelastic scattering, the relevance of each transition between excitonic states is also considered. Finally, we discuss the contribution of free carrier scattering to the excitonic linewidth, analyzing both its temperature and carrier density dependence.

Scattering of Rydberg excitons by phonon-plasmon modes

We propose a new scattering mechanism of Rydberg excitons, i.e., those with high principal quantum numbers, namely scattering by coupled LO phonon-plasmon modes, which becomes possible due to small differences in energies of the states due to different quantum defects. Already in very low-density electron–hole plasmas these provide a substantial contribution to the excitonic linewidth. This effect should allow determining plasma densities by a simple line shape analysis. Whenever one expects that low-density electron–hole plasma is present the plasmon induced broadening is of high significance and must be taken into account in the interpretation.

Observation of Photoinduced Terahertz Gain in GaAs Quantum Wells: Evidence for Radiative Two-Exciton-to-Biexciton Scattering.

We have observed photoinduced negative optical conductivity, or gain, in the terahertz frequency range in a GaAs multiple-quantum-well structure in a strong perpendicular magnetic field at low temperatures. The gain is narrow band: it appears as a sharp peak (linewidth <0.45 meV) whose frequency shifts with applied magnetic field. The gain has a circular-polarization selection rule: a strong line is observed for hole-cyclotron-resonance-active polarization. Furthermore, the gain appears only when the exciton 1s state is populated, which rules out intraexcitonic transitions to be its origin. Based on these observations, we propose a possible process in which the stimulated emission of a terahertz photon occurs while two free excitons scatter into one biexciton in an energy and angular-momentum conserving manner.

Exciton valley depolarization in monolayer transition-metal dichalcogenides

The valley degree of freedom is a sought-after quantum number in monolayer transition-metal dichalcogenides. Similar to optical spin orientation in semiconductors, the helicity of absorbed photons can be relayed to the valley (pseudospin) quantum number of photoexcited electrons and holes. Also similar to the quantum-mechanical spin, the valley quantum number is not a conserved quantity. Valley depolarization of excitons in monolayer transition-metal dichalcogenides due to long-range electron-hole exchange typically takes a few ps at low temperatures. Exceptions to this behavior are monolayers ${\mathrm{MoSe}}_{2}$ and ${\mathrm{MoTe}}_{2}$ wherein the depolarization is much faster. We elucidate the enigmatic anomaly of these materials, finding that it originates from Rashba-induced coupling of the dark and bright exciton branches next to their degeneracy point. When photoexcited excitons scatter during their energy relaxation between states next to the degeneracy region, they reach the light cone after losing the initial helicity. The valley depolarization is not as fast in monolayers ${\mathrm{WSe}}_{2}$, ${\mathrm{WS}}_{2}$, and ${\mathrm{MoS}}_{2}$, wherein the degeneracy is absent resulting in negligible Rashba-induced coupling between bright and dark excitons.

Evidence for Spatial Propagation of Photon-like Polaritons Generated by Exciton–Exciton Scattering in a GaAs/AlAs Multiple-Quantum-Well Structure

We have investigated the polariton characteristics of the photoluminescence (PL) due to exciton–exciton scattering at 10 K in a GaAs/AlAs multiple-quantum-well structure with the use of spatially-r...

Unexpectedly Fast Phonon-Assisted Exciton Hopping between Carbon Nanotubes

Carbon-nanotube (CNT) aggregates are promising light-absorbing materials for photovoltaics. The hopping rate of excitons between CNTs directly affects the efficiency of these devices. We theoretically investigate phonon-assisted exciton hopping, where excitons scatter with phonons into a same-tube transition state, followed by intertube Coulomb scattering into the final state. Second-order hopping between bright excitonic states is as fast as the first-order process (∼1 ps). For perpendicular CNTs, the high rate stems from the high density of phononic states; for parallel CNTs, the reason lies in relaxed selection rules. Moreover, second-order exciton transfer between dark and bright states, facilitated by phonons with large angular momentum, has rates comparable to bright-to-bright transfer, so dark excitons provide an additional pathway for energy transfer in CNT composites. As dark excitons are difficult to probe in experiment, predictive theory is critical for understanding exciton dynamics in CNT com...

Scattering amplitudes for dark and bright excitons

Using the composite boson many-body formalism that takes single-exciton states rather than free carrier states as a basis, we derive the integral equation fulfilled by the exciton-exciton effective scattering from which the role of fermion exchanges can be unraveled. For excitons made of -spin electrons and -spin holes, as in GaAs heterostructures, one major result is that most spin configurations lead to brightness-conserving scatterings with equal amplitude Δ, despite differences in the carrier exchanges involved. A brightness-changing channel also exists when two opposite-spin excitons scatter: dark excitons can end either in the same dark states with an amplitude , or in opposite-spin bright states , with a different amplitude , the number of carrier exchanges involved in these scatterings being even or odd, respectively. Another major result is that these amplitudes are linked by a striking relation, , which has decisive consequence on exciton Bose-Einstein condensation. By using Born values, we show that the exciton condensate can be optically observed through a bright part when excitons have large dipole only, that is, when the electrons and holes are in two well-separated layers, as in current experiments.

Exciton scattering approach for optical spectra calculations in branched conjugated macromolecules

The exciton scattering (ES) technique is a multiscale approach based on the concept of a particle in a box and developed for efficient calculations of excited-state electronic structure and optical spectra in low-dimensional conjugated macromolecules. Within the ES method, electronic excitations in molecular structure are attributed to standing waves representing quantum quasi-particles (excitons), which reside on the graph whose edges and nodes stand for the molecular linear segments and vertices, respectively. Exciton propagation on the linear segments is characterized by the exciton dispersion, whereas exciton scattering at the branching centers is determined by the energy-dependent scattering matrices. Using these ES energetic parameters, the excitation energies are then found by solving a set of generalized “particle in a box” problems on the graph that represents the molecule. Similarly, unique energy-dependent ES dipolar parameters permit calculations of the corresponding oscillator strengths, thus, completing optical spectra modeling. Both the energetic and dipolar parameters can be extracted from quantum-chemical computations in small molecular fragments and tabulated in the ES library for further applications. Subsequently, spectroscopic modeling for any macrostructure within a considered molecular family could be performed with negligible numerical effort. We demonstrate the ES method application to molecular families of branched conjugated phenylacetylenes and ladder poly-para-phenylenes, as well as structures with electron donor and acceptor chemical substituents. Time-dependent density functional theory (TD-DFT) is used as a reference model for electronic structure. The ES calculations accurately reproduce the optical spectra compared to the reference quantum chemistry results, and make possible to predict spectra of complex macromolecules, where conventional electronic structure calculations are unfeasible.

Counting the number of excited states in organic semiconductor systems using topology.

Exciton scattering theory attributes excited electronic states to standing waves in quasi-one-dimensional molecular materials by assuming a quasi-particle picture of optical excitations. The quasi-particle properties at branching centers are described by the corresponding scattering matrices. Here, we identify the topological invariant of a scattering center, referred to as its winding number, and apply topological intersection theory to count the number of quantum states in a quasi-one-dimensional system.

How Geometric Distortions Scatter Electronic Excitations in Conjugated Macromolecules.

Effects of disorder and exciton-phonon interactions are the major factors controlling photoinduced dynamics and energy-transfer processes in conjugated organic semiconductors, thus defining their electronic functionality. All-atom quantum-chemical simulations are potentially capable of describing such phenomena in complex "soft" organic structures, yet they are frequently computationally restrictive. Here we efficiently characterize how electronic excitations in branched conjugated molecules interact with molecular distortions using the exciton scattering (ES) approach as a fundamental principle combined with effective tight-binding models. Molecule geometry deformations are incorporated to the ES view of electronic excitations by identifying the dependence of the Frenkel-type exciton Hamiltonian parameters on the characteristic geometry parameters. We illustrate our methodology using two examples of intermolecular distortions, bond length alternation and single bond rotation, which constitute vibrational degrees of freedom strongly coupled to the electronic system in a variety of conjugated systems. The effect on excited-state electronic structures has been attributed to localized variation of exciton on-site energies and couplings. As a result, modifications of the entire electronic spectra due to geometric distortions can be efficiently and accurately accounted for with negligible numerical cost. The presented approach can be potentially extended to model electronic structures and photoinduced processes in bulk amorphous polymer materials.

Polariton Characteristics of Photoluminescence Dynamics of Exciton–Exciton Scattering in GaAs/AlAs Multiple Quantum Wells

We have investigated the photoluminescence (PL) dynamics of exciton–exciton scattering, the so-called P emission, at 10 K in GaAs (d nm)/AlAs (d nm) multiple quantum wells (MQWs) with d = 10 and 20. It was found that the decay rate of the P emission systematically increases with a decrease in detection energy. In contrast, the decay rate hardly depends on an excitation power, which suggests that exciton–exciton collisions do not affect the decay rate. We demonstrate that the energy dependence of the decay rate, \(\tau _{\text{p}}^{ - 1}(E)\), in each MQW is consistently scaled by that of the group velocity, \(v_{\text{g}}(E)\), of a photon-like polariton in the lower polariton branch that is the final state for the P emission: \(\tau _{\text{p}}^{ - 1}(E) = Av_{\text{g}}(E)\). This fact provides us clear evidence for the polariton characteristics of the PL dynamics of exciton–exciton scattering.

Excited-State Structure Modifications Due to Molecular Substituents and Exciton Scattering in Conjugated Molecules.

Attachment of chemical substituents (such as polar moieties) constitutes an efficient and convenient way to modify physical and chemical properties of conjugated polymers and oligomers. Associated modifications in the molecular electronic states can be comprehensively described by examining scattering of excitons in the polymer's backbone at the scattering center representing the chemical substituent. Here, we implement effective tight-binding models as a tool to examine the analytical properties of the exciton scattering matrices in semi-infinite polymer chains with substitutions. We demonstrate that chemical interactions between the substitution and attached polymer are adequately described by the analytical properties of the scattering matrices. In particular, resonant and bound electronic excitations are expressed via the positions of zeros and poles of the scattering amplitude, analytically continued to complex values of exciton quasi-momenta. We exemplify the formulated concepts by analyzing excited states in conjugated phenylacetylenes substituted by perylene.

Natural Atomic Orbital Representation for Optical Spectra Calculations in the Exciton Scattering Approach.

The exciton scattering (ES) method allows efficient calculations of spectroscopic observables in large low-dimensional conjugated molecular systems. To compute the transition dipoles between the ground and excited electronic states, we should extract the ES dipole parameters from quantum chemistry calculations in simple molecular fragments. In this manuscript, we show how to retrieve these parameters from any reference quantum chemistry model that uses an arbitrary nonorthogonal and possibly overcomplete atomic orbital basis set. Our approach relies on the natural atomic orbital (NAO) representation, in which the basis functions are orthonormal and the atom-like character is preserved. We apply the ES approach, combined with the NAO analysis to optical spectra of branched phenylacetylene oligomers. Absorption spectra predicted by the ES method demonstrate close agreement with the results of direct quantum chemistry calculations, when the Time-Dependent Density Functional Theory (TD-DFT) being used as a reference. This testifies applicability of a variety of quantum-chemical techniques, where the NAO population analysis can be conducted, for the ES framework.

Exciton Scattering Mechanism in a Single Semiconducting MgZnO Nanorod

Excitonic phenomena, such as excitonic absorption and emission, have been used in many photonic and optoelectronic semiconductor device applications. As the sizes of these nanoscale materials have approached to exciton diffusion lengths in semiconductors, a fundamental understanding of exciton transport in semiconductors has become imperative. We present exciton transport in a single MgZnO nanorod in the spatiotemporal regime with several nanometer-scale spatial resolution and several tens of picosecond temporal resolution. This study was performed using temperature-dependent cathodoluminescence and time-resolved photoluminescence spectroscopies. The exciton diffusion length in the MgZnO nanorod decreased from 100 to 70 nm with increasing temperature in the range of 5 and 80 K. The results obtained for the temperature dependence of exciton diffusion length and luminescence lifetime revealed that the dominant exciton scattering mechanism in MgZnO nanorod is exciton-phonon assisted piezoelectric field scattering.

Exciton Scattering on Symmetric Branching Centers in Conjugated Molecules

The capability of the exciton scattering approach, an efficient methodology for excited states in branched conjugated molecules, is extended to include symmetric triple and quadruple joints that connect linear segments on the basis of the phenylacetylene backbone. The obtained scattering matrices that characterize these vertices are used in application of our approach to several test structures, where we find excellent agreement with the transition energies computed by the reference quantum chemistry. We introduce topological charges, associated with the scattering matrices, which help to formulate useful relations between the number of excitations in the exciton band and the number of repeat units. The obtained features of the scattering phases are analyzed in terms of the observed excited state electronic structure.

Excited States of Donor and Acceptor Substituted Conjugated Oligomers: A Perspective from the Exciton Scattering Approach

Quantum-chemical computations allow one to predict a variety of interesting electronic properties of donor and acceptor substituted conjugated molecules. However, the complexity of such systems often limits physical interpretation of the computations and makes them impossible in larger molecules. In this study, the exciton scattering (ES) methodology is extended to analyze the excited-state structure of donor and acceptor substituted conjugated oligomers. The extracted reflection phases, transition charge, and dipole parameters of the modified termini are used to quantify the influence of the substitution on the molecular electronic and optical spectra. In particular, intuitive relationships between the substituent’s electron withdrawing or donating ability and the ES parameters are discussed. A good agreement of the absorption spectra between the ES approach and the reference quantum-chemical computations demonstrates that the ES approach is qualified for such conjugated push−pull systems.