Exciton-phonon couplings

In order to demonstrate the NDCPA a model of a system of excitons strongly coupled to phonons in a crystal with one molecule per unit cell is chosen. This model is called here the molecular crystal model. The Hamiltonian of... 

Here ak a ) is the annihilation (creation) operator of an exciton with the momentum k and energy Ek, operator an(a ) annihilates (creates) an exciton at the n-th site, 6,(6lt,) is the annihilation (creation) operator of a phonon with the momentum q and energy u) q), x q) is the exciton-phonon coupling function, N is the total number of crystal molecules. The exciton energy is Ek = fo + tfcj where eo is the change of the energy of a crystal molecule with excitation, and tk is the Fourier transform of the energy transfer matrix elements. 

It is possible to make elastic scattering corrections to the algorithm (24) in the case of an Einstein phonon spectrum and purely local exciton-phonon coupling. If we calculate the energy of the polaron state at the value E ss nuio only the matrix elements 5 " should be considered in Eqs.(16). In this case... 

Above mathematics shows that the changes in the model Hamiltonian (1) that do not involve the exciton-phonon coupling terms, - for instance inclusion the exciton-exciton (electron-electron) interaction, lead only to the respective change of in Eqs.(16). 

To verify effectiveness of NDCPA we carried out the calculations of absorption spectra for a system of excitons locally and linearly coupled to Einstein phonons at zero temperature in cubic crystal with one molecule per unit cell (probably the simplest model of exciton-phonon system of organic crystals). Absorption spectrum is defined as an imaginary part of one-exciton Green s function taken at zero value of exciton momentum vector... 

The NDCPA seems to be a very reasonable way to treat the properties of both electrons and excitons interacting with phonons with dispersion. In principal, the NDCPA can be applied to a system of the Hamiltonian with the electron(exciton)-phonon coupling terms of arbitrary structure. The NDCPA results in an algorithm which can be effectively treated numerically (for example, iteratively). The application of the NDCPA is not restricted to the... 

Exciton Phonon and Phonon Phonon Couplings in Carbon Nanotubes... 

Coherent optical phonons can couple with localized excitations such as excitons and defect centers. For example, strong exciton-phonon coupling was demonstrated for lead phtalocyanine (PbPc) [79] and Cul [80] as an intense enhancement of the coherent phonon amplitude at the excitonic resonances. In alkali halides [81-83], nuclear wave-packets localized near F centers were observed as periodic modulations of the luminescence spectra. 

Exciton-phonon coupling, 42 Excursion time, 65 Exploding-foil technique, 152 External injection, 172... 

In Section I, the spectra of e"(ai) consist of Dirac 5 peaks (1.79). In a real crystal these peaks are broadened by static disorder, thermal fluctuations, and excitation-relaxation processes. Discarding for the moment the static disorder, we focus our attention on broadening processes due to lattice phonons, which may be described alternatively in terms of fluctuations of the local energies of the sites, or in terms of exciton relaxation by emission and absorption of phonons. These two complementary aspects of the fluctuation-dissipation theorem64 will allow us to treat the exciton-phonon coupling in the so-called strong and weak cases. The extraordinary (polariton) 0-0 transition of the anthracene crystal will be analyzed on the basis of these theoretical considerations and the semiexperimental data of the Kramers-Kronig analysis. 

The exciton-phonon coupling strength may be characterized by the stabilization53 S obtained when the lattice is left to relax around an exciton localized on site n. If we consider the independent variables (b-qs + b flS) as continuous, we find, with the use of the last two terms of (2.44),... 

According to the value of S relative to the exciton bandwidth B, the relaxed form of the exciton will be delocalized or localized for — B < — S or — S < — B, respectively. Adopting Toyozawa s terminology,53 we can say that for S < gcB the exciton-phonon coupling is weak and for S > g(B it is strong, where gc is a characteristic parameter of the lattice structure of the order of unity (gc = 0.87 for the square lattice53). 

We must make a remark on the exciton-phonon coupling Rigorously speaking the hamiltonian H (2.96) should contain the retarded interactions,... 

To the second order of perturbation in the exciton-phonon coupling, we obtain for the self-energy... 

In this model of weak exciton-phonon coupling (S < B), o(T) is larger than unity. In addition, the exponential wing disappears for T- 0, which is consistent with the absence of phonons to assist the optical absorption. 

Figs. 2.9,2.10, recorded at very low temperatures and in high resolution. For a crystal of very high quality, the broadening of these transitions is mainly due to phone- >. We briefly analyze their influence on the reflectivity in order to assure that no spurious structures are considered. These spectra have been recorded for the first time and analyzed by Turlet et al.1-67. We simply summarize a few points necessary to test the KK transformation, to point out the specificity of the intrinsic relaxation mechanisms related to exciton-phonon couplings, and to evaluate quantitatively the corresponding coupling parameters. 

Exciton-phonon coupling The wave-vector dependence of /op(q) was... 

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