Electron-phonon Interactions description

The generally accepted theory of electric superconductivity of metals is based upon an assumed interaction between the conduction electrons and phonons in the crystal.1-3 The resonating-valence-bond theory, which is a theoiy of the electronic structure of metals developed about 20 years ago,4-6 provides the basis for a detailed description of the electron-phonon interaction, in relation to the atomic numbers of elements and the composition of alloys, and leads, as described below, to the conclusion that there are two classes of superconductors, crest superconductors and trough superconductors. 

Electron-phonon interaction in a semiconductor is the main factor for relaxation of a transferred electron. There are two different relaxation processes that decrease the efficiency of light conversion in a solar system (1) relaxation of an electron from a semiconductor conduction band to a valence band and (2) a backward electron transfer reaction. The forward and backward electron transfer processes have been already included in the tunneling interaction, HSm-qd, described by Eq. (108). However, the effect of SM e-ph interaction is important for the correct description of electron transfer in the SM-QD solar cell system. In the previous section, we have gradually considered different types of interactions in the quantum dot and obtained the exact expression for the photocurrent (128) where the exact nonequilibrium QD Green s functions determined from Eq. (127) have been used. However, in... 

Various scientists consider the time-fluctuating energy levels (Fig. 6.7) as bands of energy levels. Such a description is very convenient, especially for semiconductor-liquid interfaces, but must be used with caution. As Morrison has already pointed out in his book [12], these bands arise from the fluctuation of the solvent and they have different properties from the fixed bands in solids. There is an essential difference in concept between, on the one hand, electron-phonon interactions causing a fluctuation of electronic energy in a static distribution of levels, and, on the other hand, ion-phonon interactions causing a fluctuation of the energy levels themselves. For instance, it is not possible to have an optical transition between the occupied and unoccupied levels. 

Electron tunneling was first analyzed by Bardeen [12] and Cohen et al. [13] using the perturbative transfer Hamiltonian (TH) approach and more recently by many other authors [14-16]. Although the TH gives, in many cases, a good description of the observed effects, it lacks a firm first principles theoretical basis and does not account properly for many-body effects [17]. An improved form of TH [18] that involved energy dependent transfer matrix elements was used to incorporate many-body effects. However, this model does not describe the electron-phonon interaction properly [19]. 

Strong intersite coupiing leads to the formation of uncorrelated electron-hole pairs, in which the optical transition is described appropriately using a band description [103]. The electronic structure of conjugated polymers was described by Su et al. [2,3] (SSH model) in terms of a quasi-one-dimensional tight-binding model in which the tt electrons are coupled to distortions in the polymer backbone by the electron-phonon interaction. Photon absorption makes an electron jump from the HOMO to the LUMO band (n—tt transition). This transition creates free carriers, which subsequently self-localize, thereby forming nonlinear excitations of... 

The strong electron-phonon interaction inherent in this description leads to a coupled electronic-vibration2J. (polaron-like) excitation propagating through the crystal. If initiation occurs at random and the chain propagating excitations move out from the initiation site in both directions with a velocity v for an initiation density of p per unit chain length, the conversion rate at time t is ... 

From the above description, it should be evident that the electronic excitation-emission transition is a dynamic process which is perturbed by vibronic coupling of the phonon spectrum present in the host lattice. Thus, the host is just as important as the activator center. Another way to describe the overall process is to state that the electronic transition in the activator center involves the zero-phonon Une, broadened above absolute zero temperatures by quantized phonon interactions to form a band of permissible excitation and emission energies. 

The dimerized chain is the simplest model of semiconducting polymers, and is applied in particular to trans-polyacetylene. The noninteracting electronic structure of conjugated polymers with more complex unit cells, such as poly(para-phenylene), will be discussed in their relevant chapters. We emphasize that the noninteracting model is a simple model. It is not a realistic description of the electronic states of conjugated polymers, as it neglects two key physical phenomena electron-phonon coupling and electron-electron interactions. Despite these deficiencies it does provide a useful framework for the more complex descriptions to be described in later chapters. 

At low temperatures, when only the ground state of the lanthanide ion in the crystal field is populated, the total magnetic moment of the ion is the sum of the induced (Van Vleck) moment and the intrinsic moment (the latter differs from zero only in the degenerate state). The contributions to the magnetostriction and the elastic constants due to changes in the intrinsic magnetic moment of the lanthanide ion with lattice strain can be written explicitly when considering the effective spin Hamiltonian. The latter contains a smaller number of independent parameters (constants of spin-phonon interaction) than the Hamiltonian of the electron-deformation interaction (18) and is more suitable in the description of experimental data. 

Of all the physical characteristics of solids, the dynamical properties give a rather complete description of various aspects of the electronic ground state elasticity, phonon frequencies, dispersion, phase transformations, anharmonicity - they are all derived from the properties of interatomic bonds. Therefore it seems only natural to attempt to trace the origins of semiconductor dynamics back to the behavior of electrons, which ultimately reduces to electron - electron and electron - nuclei interactions. These are the starting point of "ab initio" theories. 

The potential V R) introduces electron-electron (e-e) interactions, and Taylor expansion of t(R) or V(R) about equilibrium generates electron-phonon (e-ph) coupling. Conjugated polymers abundantly illustrate [12,13] e-ph and e-e contributions whose joint analysis is difficult mathematically. But a joint analysis will undoubtedly emerge, and this review is a step in that direction. We seek sufficiently powerful e-ph descriptions for detailed fits of vibrational spectra and sufficiently accurate correlated states to understand excitations, including a host of recent nonlinear optical (NLO) spectra. Both e-ph and e-e interactions appear naturally in models, and both lead to characteristic susceptibilities. A related issue for vibrational spectra is the precise identification of IT-electronic contributions. We will emphasize the advantages of models for microscopic descriptions of conjugated polymers. To develop these themes. 

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