Phonon-electron coupling

4 Process of Photon Emission and Absorption 17.4.1 Electron-Phonon Coupling 

The joint effect of crystal binding and electron-phonon coupling determines the PL or PA energies, as illustrated in Fig. 17.4. The energies of the ground state E ) and the excited state ( 2) are expressed as follows [47]  

In the process of carrier formation and recombination, an electron is excited by a photon with pL = Eq + W energy from the ground minimum to the excited state with creation of an electron-hole pair exciton. The excited electron then undergoes a thermalization, moves to the minimum of the excited state, and eventually transmits to the ground combining with the hole. The carrier recombination is associated with emission of a photon with energy pL — Eq — W. The 

The inset illustrates the Stokes shift, 2W — 2Aqo, from Epl to pa. The qo is inversely proportional to atomic distance 4, and hence, Wi = A/ Cid, in the surface region. Thus, the blueshift of the pl, the pA, and the W are correlated with the bond contraction [31]  

Although eqn (2.33) represents a highly simplified model of conjugated molecules, it still remains a considerable challenge to solve, understand and predict its physical beha viour. We discuss various additional approximations to in Section 2.8. However, in the next section we discuss going beyond the Born-Oppenheimer approximation to include explicit electron-phonon coupling. 

To derive a simple model of electron-phonon coupling, let us expand the tt-electron-nuclear interaction, Vp v] R ), around some reference set of coordinates, R°  

The next step is to quantize the nuclear degrees of freedom as phonons, giving a fully quantum mechanical description of the electron and nuclear degrees of freedom. This step will be described in Chapter 7. 

We conclude this section by making some remarks on the nuclear-nuclear potential. It is convenient to separate this into an effective nuclear-nuclear potential arising from the nuclear charges associated with the a bonds, V, and the nuclear-nuclear potential from the remaining unscreened nuclear charges associated with the 7T electrons, VI  

If we suppose that the reference structure is determined by the a bonding alone, as for example in polyethylene, and that distortions from this structure are small, then we may express as a sum of harmonic springs. 

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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]. 

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. 

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 ... 

The above dynamical description of the polymerisation strongly parallels that of nonradiative transitions and this is not accidental althouth the monomer crystal from which the polymeric one is issued, do fluoresce, the polymeric one does not, despite its strong absorption at 2 eV. This strongly indicates efficient nonradiative relaxation of the excitation and strong electron-phonon coupling. 

The linear and nonlinear optical properties of one-dimensional conjugated polymers contain a wealth of information closely related to the structure and dynamics of the ir-electron distribution and to their interaction with the lattice distorsions. The existing values of the nonlinear susceptibilities indicate that these materials are strong candidates for nonlinear optical devices in different applications. However their time response may be limited by the diffusion time of intrinsic conjugation defects and the electron-phonon coupling. Since these defects arise from competition of resonant chemical structures the possible remedy is to control this competition without affecting the delocalization. The understanding of the polymerisation process is consequently essential. 

As the lattice interacts with light only through electrons, both DECP and ISRS should rely on the electron-phonon coupling in the material. Distinction between the two models lies solely in the nature of the electronic transition. In this context, Merlin and coworkers proposed DECP to be a resonant case of ISRS with the excited state having an infinitely long lifetime [26,28]. This original resonant ISRS model failed to explain different initial phases for different coherent phonon modes in the same crystal [21,25]. Recently, the model was modified to include finite electronic lifetime [29] to have more flexibility to reproduce the experimental observations. 

Thus, as far as the overall electron-phonon coupling energy is concerned, we have reasonably good correlation here between optical and thermal processes. Recently, owing particularly to the work of Taube and of Meyer, there is beginning to be an increasing body of data of correlations of this type, which are of... 

The very simplest theoretical approach, with linear electron-phonon coupling, is in terms of a two-center (a,b) one-electron Hamiltonian (27), with just one harmonic mode, u>, associated with each center. This is (in second quantized notation, with H = 1) ... 

Electron-Phonon Coupling Energies and Frequencies from Experi-mental Data... 

Finally, I refer back to the beginning of this paper, where the assumption of near-adiabaticity for electron transfers between ions of normal size in solution was mentioned. Almost all theoretical approaches which discuss the electron-phonon coupling in detail are, in fact, non-adiabatic, in which the perturbation Golden Rule approach to non-radiative transition is involved. What major differences will we expect from detailed calculations based on a truly adiabatic model—i.e., one in which only one potential surface is considered [Such an approach is, for example, essential for inner-sphere processes.] In work in my laboratory we have, as I have mentioned above,... 

Another interesting application of the total energy approach involves superconductivity. For conventional superconductors, the 1957 theory of Bardeen, Cooper and Schrieffer [26] has been subject to extensive tests and has emerged as one of the most successful theories in physics. However, because the superconducting transition temperature Tc depends exponentially on the electron-phonon coupling parameter X and the electron-electron Coulomb parameter p, it has been difficult to predict new superconductors. The sensitivity is further enhanced because the net attractive electron-electron pairing interaction is proportional to X-p, so when these parameters are comparable, they need to be determined with precision. 

The successful prediction of superconductivity in the high pressure Si phases added much credibility to the total energy approach generally. It can be argued that Si is the best understood superconductor since the existence of the phases, their structure and lattice parameters, electronic structure, phonon spectrum, electron-phonon couplings, and superconducting transition temperatures were all predicted from first principles with the atomic number and atomic mass as the main input parameters. 

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