Coherent Exciton-Phonon Coupling in CdSe/ZnS Nanocrystals Studied by Two-Dimensional Electronic Spectroscopy

Coherent exciton-phonon coupling in CdSe/ZnS nanocrystals have been investigated by temperature-dependent two-dimensional electronic spectroscopy (2DES) measurements. Benefiting from the ability of 2DES to dissect assembles in nanocrystal films, we have clearly identified experimental evidences of coherent coupling between exciton and phonon in CdSe/ZnS nanocrystals. In time domain, 2DES signals of excitonic transitions beat at a frequency resonant to a longitudinal optical phonon mode; in energy domain, phonon side bands are distinct at both Stokes and anti-Stokes sides. When temperature increases, phonon-induced exciton dephasing is observed with dramatic broadening of homogeneous linewidth. The results suggest exciton-phonon coupling is essential in elucidating the quantum dynamics of excitonic transitions in semiconductor nanocrystals.     

Quantum decoherence in finite size exciton-phonon systems

Based on the operatorial formulation of the perturbation theory, the properties of a confined exciton coupled with phonons in thermal equilibrium is revisited. Within this method, the dynamics is governed by an effective Hamiltonian which accounts for exciton-phonon entanglement. The exciton is dressed by a virtual phonon cloud whereas the phonons are clothed by virtual excitonic transitions. Special attention is thus paid for describing the time evolution of the excitonic coherences at finite temperature. As in an infinite lattice, temperature-enhanced quantum decoherence takes place. However, it is shown that the confinement softens the decoherence. The coherences are very sensitive to the excitonic states so that the closer to the band center the state is located, the slower the coherence decays. In particular, for odd lattice sizes, the coherence between the vacuum state and the one-exciton state exactly located at the band center survives over an extremely long time scale. A superimposition involving the vacuum and this specific one-exciton state behaves as an ideal qubit insensitive to its environment.     

Effect of an underdamped vibration with both diagonal and off-diagonal exciton–phonon interactions on excitation energy transfer

A numerically exact approach, named as the hierarchical stochastic Schrödinger equation, is employed to investigate the resonant vibration-assisted excitation energy transfer in a dimer system, where an underdamped vibration with both diagonal and off-diagonal exciton–phonon interactions is incorporated. From a large parameter space over the site-energy difference, excitonic coupling, and reorganization energy, it is found that the promotion effect of the underdamped vibration is significant only when the excitonic coupling is smaller than the site-energy difference. Under the circumstance, there is an optimal strength ratio between diagonal and off-diagonal exciton–phonon interactions for the resonant vibration-assisted excitation energy transfer as the site-energy difference is greater than the reorganization energy, whereas in the opposite situation the most efficient energy transfer occurs as the exciton–phonon interaction is totally off-diagonal. © 2018 Wiley Periodicals, Inc.     

Resonant energy transfer assisted by off-diagonal coupling

Dynamics of resonant energy transfer of a single excitation in a molecular dimer system are studied in the simultaneous presence of diagonal and off-diagonal exciton-phonon coupling. It is found that, at given temperatures, the off-diagonal coupling can enhance both the coherence of the resonant energy transfer and the net quantity of energy transferred from an initially excited monomer to the other. Also studied is the dynamics of entanglement between the dimer system and the phonon bath as measured by the von Neumann entanglement entropy, and the inter-monomer entanglement dynamics for the excitonic system.     

Transport of excitation energy in a three-dimensional doped molecular crystal. IV. Fourth-order propagation,exciton clothing,and exciton diffusion

The problem of excitons in interaction with phonons in a molecular crystal has been reinvestigated as a continuation of our earlier work. The exciton-phonon interaction has been taken to be linear in lattice displacements. The external medium, the phonon assembly, has been considered to be in thermal equilibrium. Following Simons, we have incorporated the effects of the medium on the exciton dynamics into a time-dependent effective potential that contains the equilibrium average exciton-phonon interaction as well as terms arising from the fluctuations in the medium's coordinates about their equilibrium values. A correlation function that represents the probability of exciton transfer has been given in the interaction picture. The time evolution of this correlation function has been determined by following Kubo's technique of cumulant expansion. The zeroth-, second-, and fourth-order contributions to the correlation function have been calculated in this way. The second- and fourth-order contributions have been diagrammatically represented. The second-order contribution has been explicitly calculated in different physical limits, namely, the slow exciton and the slow phonon limits at high and low temperatures and for very large and very small time. A few simple formulas for the transfer probability of a bare exciton in a molecular crystal of cubic symmetry have been derived from the Debye approximation for the dispersion of phonons. It has been specifically shown that the sum over phonon modes in the large time dynamics leads to a fully destructive interference in second order at a very low temperature and gives rise to a diffusive transport at a high enough temperature. A natural way of clothing the excitons has been considered and the clothed exciton has been represented diagrammatically. The dressing requires the correlation function to be redefined in terms of the clothed states and the clothed operators. The clothed exciton correlation function that represents the probability of transfer of excitons fully clothed by the phonons in thermal equilibrium turns out to be identical with the bare exciton correlation function. This attaches a novel interpretation to the correlation function which was originally defined by Simons. Transfer probabilities for a clothed exciton in a cubic crystal has been explicitly worked out for different physical limits under the Debye model of phonon dispersion. From these results a few expressions for the macroscopic diffusion coefficient of the clothed exciton have been obtained. A few critical comments have been incorporated. © 1996 John Wiley & Sons, Inc.     

Exciton-phonon self-trapping: A continuous transition

An exciton-phonon system of a linear aggregate is investigated in the intermediate-coupling regime. For sufficiently large intermolecular coupling. the variational approach predicts a discontinuous transition from a mobile exciton at weak exciton-phonon coupling to an immobile exciton at strong coupling. Fully converged numerical calculations exhibit strong deviations from the variational approach at intermediate exciton-phonon coupling strength and do not show a discontinuous transition. In the strong-coupling regime, results from the variational approach (which are closely related to the small polaron theory) deviate considerably from numerically converged calculations and an appropriate perturbation approximation.     

Enhancement of coherent energy transport by disorder and temperature in light harvesting processes

We investigate the influence of static disorder and thermal excitations on excitonic energy transport in the light-harvesting apparatus of photosynthetic systems by solving the Schro?dinger equation and taking into account the coherent hoppings of excitons, the rates of exciton creation and annihilation in antennas and reaction centers, and the coupling to thermally excited phonons. The antennas and reaction centers are modeled, respectively, as the sources and drains which provide the channels for creation and annihilation of excitons. Phonon modes below a maximum frequency are coupled to the excitons that are continuously created in the antennas and depleted in the reaction centers, and the phonon population in these modes obeys the Bose-Einstein distribution at a given temperature. It is found that the energy transport is not only robust against the static disorder and the thermal noise, but it can also be enhanced by increasing the randomness and temperature in most parameter regimes. Relevance of our work to the highly efficient energy transport in photosynthetic systems is discussed.     

A model calculation on the transport of excitation energy in a molecular crystal

We report a model calculation of the transport of a local (site) excitation in a doped molecular crystal containing one impurity. We do not consider the impurity as a direct trap for electronic excitations (zero trap depth) but assume that exciton-phonon interaction is exclusively given by the coupling of excitons with the vibrational displacement of the impurity. The dynamical problem is solved by using a time-dependent effective potential consisting of equilibrium average exciton-phonon interaction and fluctuations around this average. Two correlation functions are computed using the slow phonon limit and assuming that the temperature of the system is 300 K. Transmission of the excitation energy over a distance of eight spacings takes place, electronically, within a few picoseconds. With the exciton-phonon interaction switched on, calculated correlation functions diminish very rapidly with increasing time, indicating that an irreversible transfer of excitonic energy to the thermal bath takes place. Thus transmission of the excitation energy over such a distance (and without a high rate of trapping) is not an efficient process.     

Exciton dynamics in molecular crystals from line shape analysis. Spectral moment analysis of the origin region of the 4000 Å transition of crystal anthracene

A spectral moment analysis of the line shape function ω?₂(ω) in the region of the (0—0) band of the 4000 ŹB_2u ← ¹A_g transition in crystal anthracene at various temperatures is performed. The data are compared with the predictions of three coupling models, viz., weak exciton—photon with weak exciton—phonon coupling, strong exciton—photon with weak exciton—phonon coupling, weak exciton—photon with strong exciton—phonon coupling. The terms contributing to each spectral moment for each model are rendered explicit. The experimental data indicate that the exciton—intermolecular phonon coupling is primarily weak. The exciton interacts with optical phonons of about 90 cm^-1 frequency with a coupling strength of about 140 cm^-1 , a value near that predicted by a weak coupling model. The coupling strength is nearly the same irrespective of whether the exciton is created by b- or a-polarized light probably indicative of the importance of higher multipole contributions to the coupling although the existence of strong interband scattering could affect that suggestion. The coupling parameters g_op and g_ac are about 10^-1 and 10^-4 respectively.     

Vibronic spectra of charge transfer excitons and of mixed charge transfer and Frenkel excitons

The linear absorption spectra in the excitonic and vibronic regions in the case of mixing of Frenkel excitons (FEs) and charge-transfer excitons (CTEs) have been theoretically studied for the exciton parameters of the crystals of MePTCDI and PTCDA. Two coupling parameters for the exciton–phonon coupling are introduced: the FE–phonon coupling and the CTE–phonon coupling. The main features of the vibronics in the absorption spectra are the following: (a) the existence of a doublet structure in the vibronic spectra of CTEs; (b) the vibronic levels of the FE at intermediate values of both coupling parameters are located in the continuum of the many-particle exciton–phonon states which makes its absorption line wide and flat; (c) in the case of strong coupling (coupling constants larger than 1) a doublet of bound states appears above this continuum; (d) in the case of vanishing CTE–phonon coupling the vibronics of the charge transfer excitons practically disappear in the absorption spectra.     

Influence of hydrogen bonding on excitonic coupling and hierarchal structure of a light-harvesting porphyrin aggregate

Helical porphyrin nanotubes of tetrakis(4-sulfonatophenyl)porphyrin (TSPP) were examined in DCl/D(2)O solution using resonance Raman and resonance light scattering spectroscopy to probe the influence of hydrogen bonding on the excitonic states. Atomic force microscopy reveals similar morphology for aggregates deposited from DCl/D(2)O and from HCl/H(2)O solution. Deuteration results in subtle changes to the aggregate absorption spectrum but large changes in the relative intensities of Raman modes in the J-band excited resonance Raman spectra, revealing relatively more reorganization along lower-frequency vibrational modes in the protiated aggregate. Depolarization ratio dispersion and changes in the relative Raman intensities for excitation wavelengths spanning the J-band demonstrate interference from overlapping excitonic transitions. Distinctly different Raman excitation profiles for the protiated and deuterated aggregates reveal that isotopic substitution influences the excitonic structure of the J-band. The deuterated aggregate exhibits a nearly two-fold increase in intensity of resonance light scattering as a result of an increase in the coherence number, attributed to decreased exciton-phonon scattering. We propose that strongly coupled cyclic N-mers, roughly independent of isotopic substitution, largely decide the optical absorption spectrum, while water-mediated hydrogen bonding influences the further coherent coupling among them when they are assembled into nanotubes. The results show that, similar to natural light-harvesting complexes such as chlorosomes, hydrogen bonding can have a critical influence on exciton dynamics.     

Valence transitions of Br2 in Ar matrices: interaction with the lattice and predissociation

Fluorescence spectra from v(')=0 of the B, A and A(') states of Br(2)Ar are presented for excitation wavelengths from 630 to 540 nm with high resolution, to evaluate isotopic splittings in emission and absorption. The observed progression of sharp zero phonon lines (ZPLs) from v(')=2 to v(')=19 in B excitation is used to derive spectroscopic constants. The ZPL broadening and the growing phonon sideband (PSB) contributions indicate an increase of matrix influence on the X-B transition with rising v('). Contributions of the PSB are parameterized with the Huang-Rhys coupling constant S, where S=1 near the potential minimum reflects the electron-phonon coupling and S=4 close to Franck-Condon maximum originates from vibrational coupling. The PSB spectral composition correlates with the matrix phonon density of states, and the ZPL broadens and shifts with temperature. Two crossings with repulsive states (between v(')=4-5 and v(')=7-9) leading to matrix induced predissociation and a third tentative one between v(')=14 and 15 are indicated by ZPL broadening, population flow, and spectral shifts. The crossing energies are close to gas phase and matrix calculations. The stepwise flow of intensity from B via repulsive states to A(') and, similarly, from the A continuum to A(') is discussed. Emission quantum efficiency of the B state decreases from near unity at v(')=0 to less than 10(-3) at v(')=19. Broadening of ZPL near crossings yields predissociation times of 5 and 2.5 ps corresponding to probabilities of 5% and 10% per round-trip for the two lowest crossings, respectively.     

Structure of the phonon sidebands in the t1 → s0 transition of naphthalene in p-dibromobenzene, α-phase p-dichlorobenzene,and γ-phase p-dichlorobenzene host crystals

The theory used for predicting the intensity distributions in phonon sidebands in the electronic spectra of molecular crystals is briefly reviewed with particular emphasis on chemically mixed crystals. Criteria are suggested for the identification of pseudolocalized features in phonon sidebands. The phonon sidebands associated with the phosphorescence of naphthalene in p-dibromobenzene and α-phase p-dichlorobenzene seem to exhibit some degree of localization, while the phonon sideband of the phosphorescence of naphthalene in γ-phase p-dichlorobenzene appears to be entirely delocalized. The results are compared with those of other workers and a correlation is established between the degree of localization and the strength of the exciton-phonon coupling as measured by the optical Debye-Waller factor. It is further shown that the strength of coupling of the phonons to the electronic transition is independent of the gas-to-crystal shift of the impurity.     

Variable temperature spectroscopy of as-grown and passivated CdS nanowire optical waveguide cavities

Semiconductor nanowire waveguide cavities hold promise for nanophotonic applications such as lasers, waveguides, switches, and sensors due to the tight optical confinement in these structures. However, to realize their full potential, high quality nanowires, whose emission at low temperatures is dominated by free exciton emission, need to be synthesized. In addition, a proper understanding of their complex optical properties, including light-matter coupling in these subwavelength structures, is required. We have synthesized very high-quality wurztite CdS nanowires capped with a 5 nm SiO(2) conformal coating with diameters spanning 100-300 nm using physical vapor and atomic layer deposition techniques and characterized their spatially resolved photoluminescence over the 77-298 K temperature range. In addition to the Fabry-Pe?rot resonator modulated emission from the ends of the wires, the low temperature emission from the center of the wire shows clear free excitonic peaks and LO phonon replicas, persisting up to room-temperature in the passivated wires. From laser scanning measurements we determined the absorption in the vicinity of the excitonic resonances. In addition to demonstrating the high optical quality of the nanowire crystals, these results provide the fundamental parameters for strong light-matter coupling studies, potentially leading to low threshold polariton lasers, sensitive sensors and optical switches at the nanoscale.     

Masking of trap effects on exciton bands by exciton-phonon coupling

In a rigid lattice the effect on the exciton band of a trap with a lower transition energy than the host is to push a level down from the band edge to an extent depending on the trap depth and the structure of the band. In a non-rigid lattice, in which the levels of the band have mixed exciton-phonon character, interferences caused by the phonon additions to the eigenstates belonging to the same total wavevector (exciton plus phonon) can, especially for shallow traps, greatly weaken the effect of the traps. The effective trap depth may be reduced to a small fraction of its true value. In such cases shallow traps will not be detectable by their influence on exciton band structure. The effect of deep traps is not changed by this mechanism.     

Vibrational Coupling between Organic and Inorganic Sublattices of Hybrid Perovskites

The interplay of electronic and nuclear degrees of freedom in semiconductor hybrid organic–inorganic perovskites determines many of their fundamental photophysical properties. For instance, charge carriers are dressed with phonons, that is, form polarons, and combination modes composed of strongly mixed localized vibrations and delocalized phonons can provide pathways for electronic energy relaxation and dissipation. Mixing of the different types of nuclear motion in vibrational combination modes requires their strong coupling. The direct measurement of coupling between the high‐frequency N?H stretch modes of the organic methylammonium and formamidinium ions and low‐frequency Pb?I phonon modes of the inorganic sub‐lattice in hybrid organic–inorganic perovskites is presented. The results reveal direct and substantial coupling between the non‐covalently interacting organic and inorganic sub‐lattices.     

Photoreflectance investigation of exciton-acoustic phonon scattering in GaN grown by MOVPE

In this paper, we report a systematic investigation of the near band edge (NBE) excitonic states in GaN using low temperature photoluminescence (PL) and photoreflectance (PR) measurements. For this purpose, GaN films of different thicknesses have been grown on silicon nitride (SiN) treated c-plane sapphire substrates by atmospheric pressure metalorganic vapor phase epitaxy (MOVPE). Low temperature PR spectra exhibit well-defined spectral features related to the A, B and C free excitons denoted by FX_A FX_B and FX_C, respectively. In contrast, PL spectra are essentially dominated by the A free and donor bound excitons. By combining PR spectra and Hall measurements a strong correlation between residual electron concentration and exciton linewidths is observed. From the temperature dependence of the excitonic linewidths, the exciton-acoustic phonon coupling constant is determined for FX_A, FX_B and FX_C. We show that this coupling constant is strongly related to the exciton kinetic energy and to the strain level.     

Spectral characteristics of zero-phonon transitions in crystal impurities: A diagrammatic approach

The zero-phonon line shape of a localized transition in a crystal is treated by use of a general interaction between the local transition and the lattice phonons with the harmonic approximation. The theory is carried out to infinite order perturbation by diagrammatic techniques and is thus valid for arbitrarily large phonon coupling. Within our model it is found that the spectral characteristics of the zero phonon line and their temperature dependence are due to resonant Raman-ike phonon scattering processes which cause a decay of the phase coherence of the excitation. The line shape due to this mechanism is found to be lorentzian, and its width increases with temperature, but is zero at 0 K. The line position is also a function of temperature.     

Photoluminescence and Raman scattering of ZnO nanorods

Zinc oxide (ZnO) nanorods were synthesized by a simple microemulsion method. The photoluminescence (PL) spectra at room temperature were measured. The strong UV excitonic emission indicates the good optical properties, and the weak deep-level emission reveals very limited structural defects in the crystals. The multiple peaks in the PL spectrum obtained at 15 K are assigned to the donor-bound exciton (DBE), free to bound transition (FB) and FB–LO phonon replicas. The temperature dependence of energy, intensity, and linewidth of each emission band confirms the effect of thermal ionization progress of excitons and nonradiative recombination activated thermally. The nonresonant Raman scattering spectra at room temperature were excited by He–Ne laser (wavelength ～632.8 nm). The perfect wurtzite structure in ZnO nanorods has been verified by the intense E₂ modes, which include low and high frequency vibrations. The possible reasons for the red shift and broadening of vibration modes were studied by the resonant Raman scattering spectra at room temperature. The power-dependence of Raman shift and FWHM shows the laser irradiation effect on the vibrational modes.     

Exciton dynamics in molecular crystals from line shape analysis. Time response function of singlet excitons in crystal anthracene

From an accurate measure of the temperature dependence of the line shape function ω ?₂ (ω) information is obtained about the time behaviour of the response function of singlet excitons of small wavevector encompassed by the (0-0) band of the 4000 A Å transition in crystal anthracene. An apparatus to determine the reflection band profile with high accuracy needed to give correct ω ?₂ (ω) data is described. Although the data analysis is not without problems, there is strong evidence that the time behaviour of excitons in this transition is characterized by a stochastic collision time τ_c. The temperature dependence of τ_c is consistent with a model in which the intermolecular phonons are weakly coupled with the exciton created by either b or a polarized light. Phonon annihilation is predominant for the b-polarized transition but both phonon creation and annihilation are active for these polarized transition. The similar values of the exciton—phonon coupling function for both polarizations may indicate either the importance of higher multipole terms for that function or strong interband scattering. The relationships between τ_c and parameters from other experimental results on singlet excitons in crystal anthracene are considered. The results may allow for a better understanding of the mechanism of exciton—phonon coupling in crystals.