Resonant coupling of bound excitons with LO phonons in ZnO: excitonic polaron states and Fano interference

We report on a photoluminescence observation of robust excitonic polarons due to resonant coupling of exciton and longitudinal optical (LO) phonon as well as Fano-type interference in high quality ZnO crystal. At low enough temperatures, resonant coupling of excitons and LO phonons leads to not only traditional Stokes lines (SLs) but also up to second-order anti-Stokes lines (ASLs) besides the zero-phonon line (ZPL). The SLs and ASLs are found to be not mirror symmetric with respect to the ZPL, strongly suggesting that they are from different coupling states of exciton and phonons. Besides these spectral features showing the quasiparticle properties of exciton-phonon coupling system, the first-order SL is found to exhibit characteristic Fano lineshape, caused by quantum interference between the LO components of excitonic polarons and the continuous phonon bath. These findings lead to a new insight into fundamental effects of exciton-phonon interactions.     

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.     

Triplet—triplet annihilation and exciton—exciton interactions

A theoretical discussion is presented on the nature of direct and indirect interactions between two triplet excitons. It is shown that the direct exciton interaction through the coulombic interaction of electrons is important when there is a large change in the polarizability of the molecule during its excitation. The indirect exciton—exciton interaction is mainly due to the exciton—phonon interaction arising from the variation in the D-shift term. It is independent of temperature and spin substate. It is attractive in nature for excitons of narrow band-width, and if the exciton—acoustic phonon coupling is inducing the indirect interaction, it falls as R⁻³. It is suggested that a kinematic theory of the triplet—triplet annihilation should incorporate the effects of such interactions.     

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.     

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.     

The exciton—phonon interaction for triplet exciton bands of organic solids: An experimental and theoretical study

Very high resolution optical data on the temperature dependences of the Davydov component absorption profiles and polarization dependent one-phonon structures associated with the lowest triplet exciton band of anthracene are presented along with a theoretical framework for their interpretation. The interpretation of the one-particle exciton—phonon transitions involving both one-phonon creation and annihilation (cold and hot phonon transitions) is entirely consistent with the analysis of the T-dependent dephasing of the lowest zero-phonon Davydov transition in terms of two mechanisms: delocalized exciton—delocalized phonon scattering operative for the low frequency (< 30 cm^?) phonons which undergo no lattice distortion and: Raman like phonon scattering operative for the higher frequency phonons which do. It is the latter which leads to the identical T² linewidth dependences of the two Davydov components in the high T limit. The former scattering is dominant at the lowest temperatures. In addition, the, marked and polarization dependent mirror symmetry breakdown between the hot and cold one-particle transitions can be nicely understood in terms of interferences occurring between the Condon and phononic (from the dependence of the pure exciton transition dipoles on phonon coordinate displacement) contributions to the one-particle transition dipoles. It is argued that our findings for anthracene should prove useful for triplet exciton bands in other organic solids.     

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.     

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.     

Exciton-exciton interaction resulting from phonon-exciton coupling

It is shown using second quantization formalism and treating excitons as bosons that phonon-exciton coupling leads to exciton-exciton interaction. This interaction limits substantially the possibility of exciton condensation.

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Zusamenfassung Es wurde mit Hilfe des Formalismus der zweiten Quantisierung gezeigt, daß die Phonon-Exziton Kopplung zu einer Exziton-Exziton Wechselwirkung führt. Dabei wurden die Exzitonen als Bosonen behandelt. Diese Wechselwirkung begrenzt wesentlich die Möglichkeit einer Kondensation der Exzitonen.

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Resume En traitant les excitons comme bosons on a demontré par le formalisme de la deuxiéme quantisation que le couplage exciton-phonon conduit à l'interaction exciton-exciton. Cette interaction limite sensiblement la possibilité de la condensation des excitons.

     

Comparative reinvestigation of the interaction of phonons with Wannier and Frenkel excitons in crystalline solids

The interaction of lattice vibrations with excitons in inorganic and organic semiconductors/insulators is reinvestigated. These results expose the comparative nature of exciton—phonon interaction in the two types of solids and produce two new coupling functions useful for Frenkel exciton—phonon interaction.     

An improved approximate diagonalization for exciton—phonon coupling in molecular crystals

New operators representing mixed exciton—phonon particles are introduced, enabling the linear coupling hamiltonian for molecular crystals to be diagonalized within a basis of zero-phonon excitons and one- and two-phonon additions.     

An adiabatic local model for the internal structure of charge-transfer excitons: Dimers and trimers

In charge-transfer crystals, the exciton-phonon interaction significantly influences the internal structure of charge-transfer excitons (CTEs). The formation of CTE dimers and trimers is considered in an adiabatic non-centrosymmetric model which includes phonon dispersion. Changes of lattice frequencies near the CTE are analysed.     

Dispersive and other second-order terms in exciton—phonon coupling

Analysis of the second-order corrections to the energy of an excited molecular crystal shows that there is an additional coupling between excitons and phonons which may be comparable to the usual resonance coupling. The new term couples even when the resonance term is small or zero, but does not contribute to exciton band splitting.     

Temperature dependence of ESR lineshapes of triplet excitons in molecular pairs

The ESR lineshape of triplet excitons moving between two differently oriented molecules of a pair is calculated. Our model hamiltonian contains the electronic interaction matrix element for the coherent exciton transport, the Zeeman energy of the triplet spin in an external magnetic field, the fine structure of the differently oriented molecules, the phonons in the crystal which are described as a heat bath, and the microscopic interaction between excitons and phonons. For the naphthalene pair the lineshapes are discussed with respect to the temperature and a parameter characterizing the strength of the interaction between excitons and photons.     

Temperature dependence of the exciton—phonon coupling in the strong coupling limit: Results for solid nitrogen

High resolution (ΔE = 0.75 meV) absorption profiles of the vibronic bands in the range of the w¹Δ_u ← X¹Σ⁺_g and a¹II_g ← X¹Σ⁺_g exciton progressions at hv ≈ 8.9 eV in solid N₂ have been measured in the temperature range between 6 K and 30 K. These excitations are strongly localized so that the observed temperature dependence of the fine structure, consisting of a zero phonon line and a phonon side band, can be described very well in the model of strong exciton—phonon coupling at point defects. The experimental results for the w¹Δ_u transition are found to be consistent with the assumption of a Debye spectrum for the phonon density of states and we derive a value for the Debye temperature of θ = 78 K, which is in very good agreement with that derived from other measurements.     

Calculation of the exciton green's function of a molecular crystal from a two-site dynamical coherent potential approximation

A new two-site dynamical coherent potential approximation for exciton-phonon interaction models corresponding to a homomorphic partition of the hamiltonian is described. The renormalization of both the site energy and the exciton bandwidth is accomplished in contrast to single-site CPA models.     

Temperature dependent exciton emission from herringbone aggregates of conjugated oligomers

In this work, the effect of temperature, exciton bandwidth, and size on the photoluminescence spectra of defect-free two-dimensional herringbone aggregates of pi-conjugated oligomers such as oligophenylene vinylene and oligothiophene is investigated theoretically. The model is based on exciton-phonon coupling in two-dimensional herringbone lattices with the exciton deriving from the lowest optical (1Ag-->1Bu) transition and the phonon from the most strongly coupled intramolecular vibrational mode with frequency omega0. Simple analytical expressions are obtained for the line strengths of the emission origin (0-0) and first replica (0-1) as a function of the number of molecules comprising the aggregate, N, the free exciton bandwidth, WD, and the temperature, T. At a given temperature, the 0-0 emission intensity initially scales as N/Nth, where Nth is the superradiant threshold number, but eventually converges to NT/Nth, where NT is the size independent thermal coherence number. NT is inversely proportional to temperature and proportional to the exciton band curvature (omegac) near the band bottom; NT=1+4piomegac/kbT. In striking contrast, the 0-1 line strength is relatively insensitive to temperature and size, but scales as the inverse square of WD+omega0. The insensitivity of the first replica to the exciton coherence number makes the ratio of the 0-0 to 0-1 line strengths a measure of the exciton coherence number. The ratio can be used to test for crystal purity. Comparison to experiments on thin films of quaterthiophene shows that the thermal coherence size is given by NT approximately 1+450/T (K) and that superradiance, which requires NT>Nth, can only be observed at temperatures less than 1 K.     

The Exciton Model for Molecular Materials: Past,Present and Future?

In assemblies of identical molecules or chromophores, electronic excitations can be described as excitons, bound electron-hole pairs that can move from site to site as a pair in a coherent manner. The understanding of excitons is crucial when trying to engineer favorable photophysical properties through structuring organic molecular matter. In recent decades, limitations of the concept of an exciton have become clear. The exciton can hybridize with phonon and photons. To clarify these issues, the exciton is discussed within the broader context of the gauge properties of the electromagnetic force.     

Triplet excitons in molecular pairs: Analytical investigation of electron spin resonance

For triplet excitons in pairs of differently oriented molecules ESR lineshape is investigated analytically using a microscopic model. The model hamilton takes into account the coherent tranfer of the exciton between the two molecules, the Zeeman and fine-structure energy and the interaction with phonons. The analytical expression for the line positions and linewidths are evaluated using values characteristic for triplet excitons in naphthalene pairs.