Excitonic Line Shapes Research Articles

Manipulating Transition Metal Dichalcogenide Exciton Linewidths and Lineshapes with Dielectric Engineering as Uncovered by Electron Spectroscopies

Manipulating Transition Metal Dichalcogenide Exciton Linewidths and Lineshapes with Dielectric Engineering as Uncovered by Electron Spectroscopies

Engineering 2D Material Exciton Line Shape with Graphene/h-BN Encapsulation.

Control over the optical properties of atomically thin two-dimensional (2D) layers, including those of transition metal dichalcogenides (TMDs), is needed for future optoelectronic applications. Here, the near-field coupling between TMDs and graphene/graphite is used to engineer the exciton line shape and charge state. Fano-like asymmetric spectral features are produced in WS2, MoSe2, and WSe2 van der Waals heterostructures combined with graphene, graphite, or jointly with hexagonal boron nitride (h-BN) as supporting or encapsulating layers. Furthermore, trion emission is suppressed in h-BN encapsulated WSe2/graphene with a neutral exciton red shift (44 meV) and binding energy reduction (30 meV). The response of these systems to electron beam and light probes is well-described in terms of 2D optical conductivities of the involved materials. Beyond fundamental insights into the interaction of TMD excitons with structured environments, this study opens an unexplored avenue toward shaping the spectral profile of narrow optical modes for application in nanophotonic devices.

Impact of substrates and quantum effects on exciton line shapes of 2D semiconductors at room temperature

Abstract Exciton resonances in monolayer transition-metal dichalcogenides (TMDs) provide exceptionally strong light–matter interaction at room temperature. Their spectral line shape is critical in the design of a myriad of optoelectronic devices, ranging from solar cells to quantum information processing. However, disorder resulting from static inhomogeneities and dynamical fluctuations can significantly impact the line shape. Many recent works experimentally evaluate the optical properties of TMD monolayers placed on a substrate and the line shape is typically linked directly to the material’s quality. Here, we highlight that the interference of the substrate and TMD reflections can strongly influence the line shape. We further show how basic, room-temperature reflection measurements allow investigation of the quantum mechanical exciton dynamics by systematically controlling the substrate reflection with index-matching oils. By removing the substrate contribution with properly chosen oil, we can extract the excitonic decay rates including the quantum mechanical dephasing rate. The results provide valuable guidance for the engineering of exciton line shapes in layered nanophotonic systems.

High-resolution nanosecond spectroscopy of even-parity Rydberg excitons in Cu2O

We present a study of even parity Rydberg exciton states in cuprous oxide using time-resolved second harmonic generation (SHG). Excitonic states with principal quantum number n = 5 - 12 were excited by nanosecond pulses around 1143 nm. Using time-resolved single-photon counting, the coherently generated second harmonic was isolated both temporally and spectroscopically from inelastic emission due to lower-lying free and bound excitonic states, which included narrow resonances at 1.99 eV associated with an exceptional lifetime of 641 $\pm$ 7 $\mu$s. The near transform-limited excitation bandwidth enabled detailed measurements of the exciton lineshape and position, from which we obtained values for the quantum defects of the S and D excitonic states associated with the appropriate crystal symmetries. Odd parity P and F excitonic states were also observed, in accordance with predicted quadrupole-allowed two-photon excitation processes. We compared our measurements to conventional one-photon spectroscopy in the same sample, and find that the SHG spectrum is cut off at a lower principal quantum number (n = 12 vs n = 15). We attribute this effect to a combination of spatial inhomogeneities and local heating, and discuss the prospects for observing higher principal quantum number even parity states in future experiments.

Doping-induced non-Markovian interference causes excitonic linewidth broadening in monolayer WSe2

Strong Coulomb interactions in atomically thin semiconductors like monolayer WSe$_2$ induce not only tightly bound excitons, but also make their optical properties very sensible to doping. By utilizing a microscopic theory based on the excitonic Heisenberg equations of motion, we systematically determine the influence of doping on the excitonic linewidth, lineshift, and oscillator strength. We calculate trion resonances and demonstrate that the Coulomb coupling of excitons to the trionic continuum generates a non-Markovian interference, which, due to a time retardation, builds up a phase responsible for asymmetric exciton line shapes and increased excitonic linewidths. Our calculated doping dependence of exciton and trion linewidths, lineshifts, and oscillator strengths explains recent experiments. The gained insights provide the microscopic origin of the optical fingerprint of doped atomically thin semiconductors.

Effect of intravalley and intervalley electron-hole exchange on the nonlinear optical response of monolayer MoSe2

The coherent third-order nonlinear response of monolayer transition-metal dichalcogenide semiconductors, such as ${\mathrm{MoSe}}_{2}$, is dominated by the nonlinear exciton response, as well as biexciton and trion resonances. The fact that these resonances may be spectrally close together makes identification of the signatures, for example in differential transmission (DT), challenging. Instead of focusing on explaining a given set of experimental data, a systematic study aimed at elucidating the roles of intravalley and intervalley long-range electron-hole $(e\ensuremath{-}\mathrm{h})$ exchange on the DT spectra is presented. Previous works have shown that the $e\ensuremath{-}\mathrm{h}$ long-range exchange introduces a linear leading-order term in the exciton dispersion. Based on a generalized Lippmann-Schwinger equation, we show that the presence of this linear dispersion term can reduce the biexciton binding energy to zero, contrary to the conventional situation of quadratic dispersion where an arbitrarily weak (well-behaved) attractive interaction always supports bound state(s). The effects of spin scattering and the spin-orbit interaction caused by $e\ensuremath{-}\mathrm{h}$ exchange are also clarified, and the DT line shape at the exciton and trion resonance is studied as a function of $e\ensuremath{-}\mathrm{h}$ exchange strength. In particular, as the exciton line shape is determined by the interplay of linear exciton susceptibility and the bound-state two-exciton resonance in the $T$ matrix, the line shape at the trion is similarly determined by the interplay of the linear trion susceptibility and the bound-state exciton-trion resonance in the $T$ matrix.

Ultrafast evolution of the complex dielectric function of monolayer WS2 after photoexcitation.

Transition metal dichalcogenides emerged as ideal materials for the investigation of exciton physics. Retrieving the excitonic signature in optical spectra, and tracking their time evolution upon photoexcitation requires appropriate analysis procedures, particularly when comparing different measurements, experimental techniques, samples, and substrates. In this work, we investigate the ultrafast time evolution of the exciton resonance of a monolayer of WS2 deposited on fused silica and Si/SiO2, and using two different measurement techniques: time-resolved reflectance and transmittance contrast. By modelling the dielectric function of the exciton with a Lorentz oscillator, using a Fresnell equations formalism, we derive analytical expressions of the exciton lineshape in both cases. The 2D linearized model introduced by Li et al. [Y. Li and T. F. Heinz, 2D Mater., 2018, 5, 025021] is used for the transmittance of the transparent substrate and a Fresnel transfer matrix method [O. Stenzel, The Physics of Thin Film Optical Spectra, Springer Series in Surface Science, 2016] is used to derive the reflectance in the case of the layered Si/SiO2 substrate. By fitting two models to the time-dependent optical spectra, we extract and quantify the time evolution of the parameter describing the excitonic resonance. We find a remarkable agreement between the extracted dynamics from both experiments despite the different side conditions, showing the equivalence and reliability of the two analysis methods in use. With this work, we pave the way to the resilient comparison of the exciton dynamics from different samples, measurements technique and substrates.

Stochastic scattering theory for excitation-induced dephasing: Time-dependent nonlinear coherent exciton lineshapes.

We develop a stochastic theory that treats time-dependent exciton-exciton s-wave scattering and that accounts for dynamic Coulomb screening, which we describe within a mean-field limit. With this theory, we model excitation-induced dephasing effects on time-resolved two-dimensional coherent optical lineshapes and we identify a number of features that can be attributed to the many-body dynamics occurring in the background of the exciton, including dynamic line narrowing, mixing of real and imaginary spectral components, and multi-quantum states. We test the model by means of multidimensional coherent spectroscopy on a two-dimensional metal-halide semiconductor that hosts tightly bound excitons and biexcitons that feature strong polaronic character. We find that the exciton nonlinear coherent lineshape reflects many-body correlations that give rise to excitation-induced dephasing. Furthermore, we observe that the exciton lineshape evolves with the population time over time windows in which the population itself is static in a manner that reveals the evolution of the multi-exciton many-body couplings. Specifically, the dephasing dynamics slow down with time, at a rate that is governed by the strength of exciton many-body interactions and on the dynamic Coulomb screening potential. The real part of the coherent optical lineshape displays strong dispersive character at zero time, which transforms to an absorptive lineshape on the dissipation timescale of excitation-induced dephasing effects, while the imaginary part displays converse behavior. Our microscopic theoretical approach is sufficiently flexible to allow for a wide exploration of how system-bath dynamics contribute to linear and non-linear time-resolved spectral behavior.

Structures and exciton dynamics of aggregated lutein and zeaxanthin in aqueous media

We carried out comprehensively experimental and theoretical studies of the aggregates of lutein and zeaxanthin. The experimental absorption, Circular Dichroism (CD) spectra of these aggregates are measured in aqueous ethanol media with different concentrations of water at temperature range of 20–65 °C. Comparing with the broad absorption of monomers around 450 nm, the sharp peaks of absorption band ca. at 369 and 384 nm of lutein evidence two tightly packed H–aggregates, exhibiting non-vibrational bands of monomer. Zeaxanthin tends to form H–type at 20 °C and J–type at 65 °C, based on the absorption spectral shifts. The helical structures of these aggregates are proved by CD spectra with classic excitonic bisignate line-shape due to Cotton effect. Combining with Frenkel exciton model and line-shape spectral theory, the theoretical simulations of experimental absorption and CD spectra are carried out to investigate the helical details of these aggregates. The calculated distance ranges from 0.57 to 0.66 nm with the overlay angle of 10° for all H–types of helical aggregates, which is coherent to the value of nearest distance (~0.65 nm) of lutein and zeaxanthin dimers optimized by Gaussian program. Furthermore, with the help of Pauli master equation, we studied theoretically the dynamics and diffusion of Frenkel exciton in the one-dimensional carotenoid aggregates, using the parameters obtained from the fit of the absorption spectra. As compared with loosely packed J–aggregate, the exciton of tightly structured H–aggregate experiences a faster relaxation within 10 ps from highest excited state to lowest one along with the exciton traveling on the aggregate chain to be trapped. We propose a pattern of gradient diagonal disorder that can localize the exciton at the segment of certain molecules on the aggregate chain. The study involved would be helpful and valuable to understand energy absorption, transfer and trapping in antenna system.

Non-Markovian Exciton-Phonon Interactions in Core-Shell Colloidal Quantum Dots at Femtosecond Timescales.

We perform two-dimensional coherent spectroscopy on CdSe/CdZnS core-shell colloidal quantum dots at cryogenic temperatures. In the two-dimensional spectra, sidebands due to electronic coupling with CdSe lattice LO-phonon modes are observed to have evolutions deviating from the exponential dephasing expected from Markovian spectral diffusion, which is instantaneous and memoryless. Comparison to simulations provides evidence that LO-phonon coupling induces energy-gap fluctuations on the finite timescales of nuclear motion. The femtosecond resolution of our technique probes exciton dynamics directly on the timescales of phonon coupling in nanocrystals.

Fourth order expressions for the electronic absorption lineshape of molecular excitons.

The line shape of electronic absorption spectroscopy reflects the information on quantum dynamical processes accompanying the electronic excitation, and its accurate description is an important component for validating theoretical models and assumptions. The present work provides detailed expressions for the absorption line shape of molecular excitons that are valid up to the fourth order of exciton-bath interactions within the quantum master equation approach. These expressions can serve as the basis for developing general and systematic methods to model the line shape for a broad class of molecular exciton systems and environments. For the bath model of linearly coupled harmonic oscillators, more detailed expressions employing the spectral densities of the bath are presented. These expressions are then tested for a linear aggregate of identical chromophores each coupled to the harmonic oscillator bath. Calculation results for a super-Ohmic spectral density with exponential cutoff demonstrate the feasibility of calculations and also offer insights into the utility and difficulty of going beyond the second order approximation.

Charge neutral crystal field transitions: A measure of electron–phonon interaction

We report a study on the charge neutral crystal field (d–d) transitions and their possible correlation with coupling between continuum states above the optical band gap in pure and irradiated PrFeO3. For this purpose, room temperature optical absorption spectroscopy and Raman spectroscopy measurements were carried out. It was observed that width (Wd–d) and relative intensity (ID) of d–d transition scaled with the extent of disorder created by laser irradiation. The consistent broadening of the d–d transition with irradiation indicates enhanced coupling between crystal field excitations and continuum states above the gap. These results are consistent with observed asymmetry in Raman modes and the Gaussian-like nature of excitonic spectral line shapes of optical absorption spectra with laser irradiation. Thus, we demonstrated a new way to probe the electron–exciton interactions in terms of crystal field transitions and excitonic line shapes in highly correlated systems. Additionally, the present work provides crucial information regarding lattice disordering in polycrystalline PrFeO3 with irradiation and may have significant implications for caution in using this material in extremely high radiation environments at room temperature. The results are further supported with a first-principle calculation carried out using density functional theory.

Many-body theory of optical absorption in doped two-dimensional semiconductors

In this article, we use a many-body approach to study the absorption spectra of electron-doped two-dimensional semiconductors. Optical absorption is modeled by a many-body scattering Hamiltonian which describes an exciton immersed in a Fermi sea. The interaction between electron and exciton is approximated by an effective scattering potential, and optical spectra are calculated by solving for the exciton Green's function. From this approach, a trion state can be assigned as a bound state of an electron-exciton scattering process, and the doping-dependent phenomena observed in the spectra can be attributed to several many-body effects induced by the interaction with the Fermi sea. While the many-body scattering Hamiltonian can not solved exactly, we reduce the problem to two limiting solvable situations. The first approach approximates the full many-body problem by a simple scattering process between the electron and the exciton, with a self-energy obtained by solving a Bethe-Salpeter equation (BSE). An alternate approach assumes an infinite mass for the exciton, such that the many-body scattering Hamiltonian reduces to a Mahan-Nozieres-De Dominicis (MND) model. The exciton Green's function can then be solved numerically exactly by a determinantal formulation, and the optical spectra show signatures of the Fermi-edge singularity at high doping densities. The full doping dependence and temperature dependence of the exciton and trion lineshapes are simulated via these two approximate approaches, with the results compared to each other and to experimental expectations.

Spatially defined molecular emitters coupled to plasmonic nanoparticle arrays

This paper describes how metal-organic frameworks (MOFs) conformally coated on plasmonic nanoparticle arrays can support exciton-plasmon modes with features resembling strong coupling but that are better understood by a weak coupling model. Thin films of Zn-porphyrin MOFs were assembled by dip coating on arrays of silver nanoparticles (NP@MOF) that sustain surface lattice resonances (SLRs). Coupling of excitons with these lattice plasmons led to an SLR-like mixed mode in both transmission and transient absorption spectra. The spectral position of the mixed mode could be tailored by detuning the SLR in different refractive index environments and by changing the periodicity of the nanoparticle array. Photoluminescence showed mode splitting that can be interpreted as modulation of the exciton line shape by the Fano profile of the surface lattice mode, without requiring Rabi splitting. Compared with pristine Zn-porphyrin, hybrid NP@MOF structures achieved a 16-fold enhancement in emission intensity. Our results establish MOFs as a crystalline molecular emitter material that can couple with plasmonic structures for energy exchange and transfer.

Growth of ZnSe nanowires on quartz substrates and their photomodulated transmittance spectra

ZnSe nanowires were grown on fused quartz substrates by a vapor transport method in which the ZnSe powder is heated at 1100 °C in a tube of the furnace. The scanning electron microscopy images showed that the nanowires have the average diameter of ∼110 nm. The X-ray diffraction measurement indicates that the ZnSe nanowires were a single phase of zinc-blende ZnSe. The photomodulated transmittance (PT) measurements were performed for the ZnSe nanowires at temperatures between 15 and 300 K. The measured PT spectra revealed distinct structures of E0 critical point at ∼2.6−2.8 eV. This E0 critical point structure was successfully explained by adding an excitonic line shape to a one-electron line shape. The temperature dependence of E0 energy was analyzed using an analytical formula that takes into account the band-gap shrinkage effect by the electron-phonon interaction in semiconductors. The exciton binding energy of ZnSe nanowires was determined to be 20 meV.

Investigating exciton structure and dynamics in colloidal CdSe quantum dots with two-dimensional electronic spectroscopy.

Two-Dimensional Electronic Spectroscopy (2DES) is performed on CdSe colloidal quantum dots. These experiments reveal new observations on exciton structure and dynamics in quantum dots, expanding upon prior transient absorption measurements of excitonics in these systems. The 2DES method enables the separation of line broadening mechanisms, thereby better revealing the excitonic lineshapes and biexcitonic interactions. 2DES enables more information rich spectral probing of coherent phonons and their coupling to excitons. The data show spectral modulations and drifts, with differences based upon whether one monitors the excitation energy (E1) or emission energy (E3). These measurements reveal both homogeneous and inhomogeneous broadenings, as well as static and dynamic line broadening. The longitudinal optical phonon modulates the dynamic absorption spectrum both in energy and linewidth. These experiments enable measurement of hot exciton cooling with improved resolution in energy and time. These 2DES results are consistent with prior excitonic state-resolved transient absorption measurements, albeit with the addition of contributions due to coherent phonons. Finally these 2DES experiments enable disentangling of coupling versus relaxation contributions to the signals, further offering a test of electronic structure theory.

Contribution of piezoelectric and deformation-potential coupling mechanisms on the excitonic line shape of a single GaN/AlN quantum dot

Coupling of acoustic phonons to an exciton in a single GaN/AlN quantum dot is investigated. Contributions of piezoelectric and deformation-potential couplings on the dot spectral distribution are analyzed separately. We find that, these two types of coupling lead to an important zero-phonon line-degradation but contribute differently on the excitonic line shape. The former involves only low energy phonons but with higher coupling factors leading to the widening of the zero phonon line. The second includes all energy phonons and is therefore responsible for the extension of the lateral phonon wings.

Exciton-polaron spectral structures in two-dimensional hybrid lead-halide perovskites

Owing to both electronic and dielectric confinement effects, two-dimensional organic-inorganic hybrid perovskites sustain strongly bound excitons at room temperature. Here, we demonstrate that there are non-negligible contributions to the excitonic correlations that are specific to the lattice structure and its polar fluctuations, both of which are controlled via the chemical nature of the organic counter-cation. We present a phenomenological, yet quantitative framework to simulate excitonic absorption lineshapes in single-layer organic-inorganic hybrid perovskites, based on the two-dimensional Wannier formalism. We include four distinct excitonic states separated by $35\pm5$\,meV, and additional vibronic progressions. Intriguingly, the associated Huang-Rhys factors and the relevant phonon energies show substantial variation with temperature and the nature of the organic cation. This points to the hybrid nature of the lineshape, with a form well described by a Wannier formalism, but with signatures of strong coupling to localized vibrations, and polaronic effects perceived through excitonic correlations. Our work highlights the complexity of excitonic properties in this class of nanostructured materials.

Phonon Sidebands in Monolayer Transition Metal Dichalcogenides.

Excitons dominate the optical properties of monolayer transition metal dichalcogenides (TMDs). Besides optically accessible bright exciton states, TMDs exhibit also a multitude of optically forbidden dark excitons. Here, we show that efficient exciton-phonon scattering couples bright and dark states and gives rise to an asymmetric excitonic line shape. The observed asymmetry can be traced back to phonon-induced sidebands that are accompanied by a polaron redshift. We present a joint theory-experiment study investigating the microscopic origin of these sidebands in different TMD materials taking into account intra- and intervalley scattering channels opened by optical and acoustic phonons. The gained insights contribute to a better understanding of the optical fingerprint of these technologically promising nanomaterials.

Ultrafast Dynamics within the 1S Exciton Band of Colloidal PbSe Quantum Dots Using Multiresonant Coherent Multidimensional Spectroscopy

The simple particle-in-a-sphere model of quantum dot excitons is the basis for understanding the excitonic peak positions, line widths, and relaxation dynamics in many spectroscopic experiments. Recent multiresonant coherent multidimensional spectroscopy (CMDS) with picosecond excitation pulses measured the two-dimensional spectra of PbSe quantum dots and successfully used this simple model of an inhomogeneous distribution of spherically confined exciton and biexciton states and rate constants to describe the dephasing and population relaxation dynamics. The long excitation pulses prevented resolution of faster dynamics. This work reports the development of multiresonant CMDS with femtosecond excitation pulses to resolve the spectra and dynamics associated with the 1S exciton line shape of PbSe quantum dots. The experiments use different combinations of excitation frequencies, excitation pulse time delays, and a monochromator to display and measure correlations between the spectral features and their dynamics. Line-narrowing of the inhomogeneous distribution occurs at short time delays where the excitation excites a subset of the quantum dots within the 1S line shape and the last pulse probes this subset. The line-narrowing disappears at longer delay times. Three pulse photon echo peak shifts (3PEPS) also occur when the line-narrowing is present, but the shifts disappear as the correlation between the first and last coherence frequencies disappears. Wigner plots reveal the spectral dynamics accompanying the peak shift and the disappearance of the line-narrowing. This work shows there is rapid relaxation dynamics occurring within the line profile of the quantum confined excitonic states that is not consistent with current understanding of the excitonic line broadening. The data suggest that the relaxation dynamics play a more dominant role in defining the excitonic line widths than the inhomogeneous broadening of the quantum dot size distribution. These observations are consistent with other spectroscopic experiments on CdSe and PbS quantum dots. The experiments also show the presence of a higher energy feature that lies outside the 1S line shape and undergoes very rapid relaxation.