Of electron-phonon interaction

Ga( Zn), Sn, Te( I) Mossbauer spectroscopy, no modifications of the local symmetry of lattice sites, electronic structure of atoms and intensity of electron-phonon interaction are revealed for Pbi Sn Te solid solutions in the gapless state at 80 and 295 K... 

Physically, S is the number of emitted phonons accompanying the optical transition. It is commonly used as a measure of electron-phonon interaction and is called the Huang-Rhys factor. At m = 0, the transition probabihty is given by the simple relation ... 

Shirai, M., Suzuki, N. and Motizuki, K., Microscopic Theory of Electron - Phonon Interaction and Superconductivity of BaPbj.jjB Og. Solid State Comm. 60(6) 489 (1986). 

A.V.Khotkevich and I.K.Yanson. Atlas of Point Contact Spectra of Electron-Phonon Interactions in Metals. - Kluwer Academic Publishers Boston/Dordrecht/London, 168 p (1995). 

Third, the existence of regular periodic structure leads, when an additional electron moves along such structure, to quantization of it energy (due to Flocke theorem). The quantization leads to additional energetic levels in carbon nanotube spectrums and may also lead to suppression of electron-phonon interaction (if energy levels enough separate from phonon spectrum) and to increasing of carbon nanotubes conductivity. Especially appreciably it can be shown in case of low temperatures at sufficient electron concentration. 

The onset of electron-phonon interaction in the superconducting state is unusual in term of conventional electron-phonon interaction where one would expect that the phonon contribution is weakly dependent on the temperature [19], and increase at high T. Indeed, based on this naive expectation, this type of unconventional T dependence has been often used to rule out phonons. Here, however, we see clearly that this reasoning is not justified. Moreover, this type of unconventional enhancement of the electron phonon interaction below a characteristic temperature scale is actually expected for other systems such as spin-Peierls systems or charge density wave (CDW) systems. Thus, our results put an important constraint on the nature of the electron phonon interaction in these systems. 

For review of earlier results see Kulic M., (2000). Interplay of electron-phonon interaction and strong correlations the possible way to high-temperature superconductivity. Phys. Rep. 338 1-264. 

The zero-approximation in expansion of I(V) in d/l is the ohmic current considered by Sharvin [5]. From the Sharvin s formula the characteristic size d of the contact can be determined in the ballistic limit. The second derivative of the first approximation in expansion of I(V) in d/l is directly proportional to the spectral function of electron-phonon interaction (PC EPI) gpc w) = apc (w) F (w) °f the specific point-contact transport both in the normal and in the superconducting states [1, 6, 7], This term is the basis of the canonical inelastic point-contact spectroscopy (PCS). Here, ot2pC (oj) is the average electron-phonon matrix element taking into account the kinematic restriction imposed by contact geometry and F (oj) is the phonon density of states. 

The second drawback of the mean-field approximation is neglect of electron-phonon interaction, which should contribute attractively to the gi contribution and lead to a lattice modulation (Peierls instability). However, a ground state of such a nature is not stabilized in the TM2X family. The absence of long-range order is deeply rooted in the one-dimensional problem and arises when the effect of interactions on the different response functions is calculated perturbatively [26]. 

The theoretical problems raised by the study of CPs will be discussed below as the need arises. Many special properties of CPs are related to their quasi-one-dimensional character for instance, the large influence of disorder, the importance of residual three-dimensional coupling, and the importance of electron-phonon interactions, which, among other consequences, manifests itself in the case of a half-filled band by the occurrence of the Peierls instability. Much of the early theoretical work was concerned with PA, which, as we shall see, is peculiar among presently known CPs by having a degenerate ground state (see Section IV.B). 

Wavefunctions and Charge Distributions. Though the quality of the wavefunction obtained in a crystal orbital study cannot be assessed by direct comparison with experiment it is of decisive importance from the point of view of prospective transport calculations on conducting polymers (calculation of electron-phonon interaction matrix elements, optical properties, etc.). Of course, the wavefunction also plays a fundamental role when properties related to the many-electron energy are calculated, and therefore the quality of these quantities partially characterizes that of the wavefunction. 

Raman spectroscopy or far-IR spectroscopy can determine the fundamental vibration frequencies of the host. However, these methods give information about the whole glass matrix and do not account for the local nature of electron-phonon interactions. So, the fundamental frequencies are preferably determined by recording the phonon-side bands (PSB) of rare-earth transitions or by studying the temperature-dependence of multiphonon relaxations [42,43]. The phonon energies determined by PSB spectroscopy, which is the most direct method, are usually lower (400 cm-1 in ZBLAN) than those measured by other methods ( 500 cm-1) suggesting that weak M—F bonds are coupled to the rare-earth [43]. 

The effect of electron-phonon interaction on the localization and conductivity in Id conductors is investigated. 

Although these experimental findings testify to an important role of electron-phonon interactions in UC processes in CdTe NCs, this mechanism alone is not a sufficient explanation of all the experimental results. The thermal energy available from the phonon bath is too small to explain the obtained AE value. 

To evaluate the rate of energy transfer we write the Hamiltonian for the crystal In the Initial state having an exclmer at the mth lattice site. The Hamiltonian of the final state Is for the crystal with exclmer or ground-state pair In nonequilibrium configuration as a consequence the linear terms of electron-phonon Interaction Is large In this case, exactly as It was for consideration of the llneshape. 

The effects of electron-phonon interactions alone were described in Chapter 4. We showed that these interactions lead to a dimerized, semiconducting ground state and to solitonic structures in the excited states. On the other hand, the effects of electron-electron interactions in a polymer with a fixed geometry were described in Chapters 5 and 6. There it was shown that the electronic interactions cause a metal-insulator (or Mott-Hubbard) transition in undimerized chains. Electron-electron interactions also cause Mott-Wannier excitons in the weak-coupling limit of dimerized chains, and to both Mott-Hubbard excitons and spin density wave excitations in the strong coupling limit. 

As we have already discussed in Section 4.11, self-trapping can never be a true consequence of electron-phonon interactions in a translationally invariant Hamiltonian it is an artefact of the adiabatic approximation, which freezes the nuclear degrees of freedom. When the nuclear degrees of freedom are quantized it is possible to construct a translationally invariant wave-packet of both the electron and nuclear degrees of freedom. The band width of this wavepacket is a function of the phonon frequency, and in the adiabatic limit (w —> 0) it will vanish. ... 

Since only information on the energy spectrum and wave functions of the ground multiplets is necessary for interpretation and prediction of magnetic properties of lanthanide compounds, and bearing in mind an essential role of electron-phonon interaction, we shall confine ourselves in this case to semiphenomenological models of the crystal field which allow one to represent parameters Bpq as definite functions of structural parameters of the crystal lattice. All the models developed until recently are... 

Thus in the superposition model six parameters are used for describing a certain type of the ligand field in a particular lattice. If the sum (5) is restricted to the nearest neighbours of the R ion, artificial overestimation of the short-range interaction occurs. Disregard of the electrostatic component of the crystal field brings about inadequate results when estimating parameters B29 of tbe crystal field quadrupole components and the parameters of electron-phonon interaction (Newman 1978). 

The paper is organized as follows. Section II contains a discussion of band bounds in disordered materials, distinguishing between band edges and band limits. Section III introduces the mobility-edge concept. Section IV introduces the current version of the simplest band model of an amorphous semiconductor. Section V contains a discussion of the band-edge features in the electronic structure of a disordered material and classifies them according to the degree to which they can be represented as universal. In Section VI the effects of electron-phonon interaction are discussed. In Section VII there is a brief dicussion of fast processes such as the optical absorption and in Section VIII of slow processes such as the dc transport properties. We conclude in Section IX with an overall summary of the present status of the theory. 

Calculation of Electron-Phonon Interaction and Solution of the Boitzmann Equation in the Generai Case... 

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