Phonon coupling

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). 

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... 

Semiconductivity in oxide glasses involves polarons. An electron in a localized state distorts its surroundings to some extent, and this combination of the electron plus its distortion is called a polaron. As the electron moves, the distortion moves with it through the lattice. In oxide glasses the polarons are very localized, because of substantial electrostatic interactions between the electrons and the lattice. Conduction is assisted by electron-phonon coupling, ie, the lattice vibrations help transfer the charge carriers from one site to another. The polarons are said to "hop" between sites. 

It will be intriguing to theoretically examine the possibility of superconductivity in CNT prior to the actual experimental assessment. A preliminary estimation of superconducting transition temperature (T ) for metallic CNT has been performed considering the electron-phonon coupling within the framework of the BCS theory [31]. It is important to note that there can generally exist the competition between Peierls- and superconductivity (BCS-type) transitions in lowdimensional materials. However, as has been described in Sec. 2.3, the Peierls transition can probably be suppressed in the metallic tube (a, a) due to small Fermi integrals as a whole [20]. 

Lattice vibrations are calculated by applying the second order perturbation theory approach of Varma and Weber , thereby combining first principles short range force constants with the electron-phonon coupling matrix arising from a tight-binding theory. 

The Coulomb interaction between the re-electrons is neglected. The standard tra/is-polyacetylene parameters are ta=2.5 eV for the hopping amplitude in the undimcrizcd chain, u-4. cV/A for the electron-phonon coupling, and K= 21 eV/A2 for the spring constant [1,4, 8]. 

A further clear establishment of the absoiption due to singlet excitons and the phonons coupled to them is the electroabsorption experiment reported in Ref. [18]. The main results are shown in Figure 9-14 the top panel shows the absorption spectrum of m-LPPP at 20 K. It becomes clear that the peaks at 2.7, 2.9, and 3.1 eV, representing A0, A i, and A2 (see Fig. 9-10) are not the only vibronic replicas. There are additional peaks between these dominant ones if the experiment is conducted at low temperature. The bottom panel in Figure 9-14 shows a so-called electroabsorption spectrum which is obtained as the modulation (or change) of the absorption under the application of an electric field. Below 3.2 eV the electroab-... 

An accurate calculation of the heat conductivity requires solving a kinetic equation for the phonons coupled with the multilevel systems, which would account for thermal saturation effects and so on. We encountered one example of such saturation in the expression (21) for the scattering strength by a two-level system, where the factor of tanh((3co/2) reflected the difference between thermal populations of the two states. Neglecting these effects should lead to an error on the order of unity for the thermal frequencies. Within this single relaxation time approximation for each phonon frequency, the Fermi golden rule yields, for the scattering rate of a phonon with Ha kgT,... 

Figure 19. The predicted low T heat conductivity. The no coupling case neglects phonon coupling effects on the ripplon spectrum. The (scaled) experimental data are taken from Smith [112] for a-Si02 (AsTj/ScOd 4.4) and from Freeman and Anderson [19] for polybutadiene (ksTg/Hcao — 2.5). The empirical universal lower T ratio l /l 150 [19], used explicitly here to superimpose our results on the experiment, was predicted by the present theory earlier within a factor of order unity, as explained in Section lllB. The effects of nonuniversaUty due to the phonon coupling are explained in Section IVF.

We approximate the phonon coupling effects by replacing in our spectral sums in Eqs. (41)-(43) and (46)-(49) the discrete summation over different ripplon harmonics by integration over Lorentzian profiles ... 

Finally, we return to the specific heat. The effects of the phonon coupling on the ripplon spectrum can be taken into account in the same fashion as in the conductivity case. Here we replace the discrete summation in Eq. (38) by integration over the broadened resonances, as prescribed by Eq. (57). The bump, as shown in Fig. 15, is also predicted to be nonuniversal depending on Tg/oio-The predicted bump for Tg/(Od = 2 seems to match well the available data for... 

Bonn M, Denzler DN, Eunk S, Wolf M. 2000. Ultrafast electron dynamics at metal surfaces Competition between electron-phonon coupling and hot-electron transport. Phys Rev B 61 1101-1105. 

The scaling parameter cOq in (9.8a) determines the strength of spin-phonon coupling. 

Figure 6. Representation of the three totally symmetric alg vibrations of (EuBr Mgi) that is responsible of the electron phonon coupling in the 4f6Sd1—4fi transitions of Eu2+ in CsMgBr3. Color code Eu2+ in violet, Br in red, and Mg2 in yellow.

Egami T (2005) Electron-Phonon Coupling in High-Tc Superconductors 114 267-286 Egami T (2007) Local Structure and Dynamics of Ferroelectric Solids. 124 69-88 Eisenstein O, see Clot E (2004) 113 1-36... 

The model of the chain of hydrogen atoms with a completely delocalized (metallic) type of bonding is outlined in the preceding section. Intuitively, a chemist will find this model rather unreal, as he or she expects the atoms to combine in pairs to give H2 molecules. In other words, the chain of equidistant H atoms is expected to be unstable, so it undergoes a distortion in such a way that the atoms approach each other in pairs. This process is called Peierls distortion (or strong electron-phonon coupling) in solid-state physics ... 

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