Electron-phonon

Fledin L and Lundqvist S 1969 Effects of electron-electron and electron-phonon interactions on the one-electron states of solids Solid State Phys. 23 1... 

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]. 

Static defects scatter elastically the charge carriers. Electrons do not loose memory of the phase contained in their wave function and thus propagate through the sample in a coherent way. By contrast, electron-phonon or electron-electron collisions are inelastic and generally destroy the phase coherence. The resulting inelastic mean free path, Li , which is the distance that an electron travels between two inelastic collisions, is generally equal to the phase coherence length, the distance that an electron travels before its initial phase is destroyed ... 

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. 

FegNi. Frozen phonon calculations combined with the determination of the electron-phonon matrix in the framework of the theory of Varma and Weber have been carried out for the ferrous alloy. The resulting phonon dispersion for the bet phase was already presented elsewhere . As expected, no softening or anomalous curvatures have been detected. This confirms the existence of a bet ground state for FesNi. 

Figure 7. Phonon dispersion including the electron-phonon interaction for bcc CuZn. Force constants have been obtained from ah initio calculations. Dashed line is the phonon dispersion without the V-i contribution. Diamonds mark experimental data. ...

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]. 

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. 

In this equation v is a phonon frequency, such that hv is approximately k, with the Debye characteristic temperature of the metal. The quantity p is the product of the density of electrons in energy at the Fermi surface, N(0), and the electron-phonon interaction energy, V. 

The gap in superconductivity between the fifth and sixth groups of the periodic table, discovered by Matthias,24 is seen to correspond to the transition from crest to trough superconductivity. It does not require for its explanation the assumption20- 25 that there are mechanisms of superconductivity other than the electron-phonon interaction. 

The theory of superconductivity based on the interaction of electrons and phonons was developed about thirty years ago. I 4 In this theory the electron-phonon interaction causes a clustering of electrons in momentum space such that the electrons move in phase with a phonon when the energy of this interaction is greater than the phonon energy hm. The theory is satisfactory in most respects. 

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. 

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... 

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 ... 

These carriers of heat do not move balistically from the hotter part of the material to the colder one. They are scattered by other electrons, phonons, defects of the lattice and impurities. The result is a diffusive process which, in the simplest form, can be described as a gas diffusing through the material. Hence, the thermal conductivity k can be written as ... 

The main scattering processes limiting the thermal conductivity are phonon-phonon (which is absent in the harmonic approximation), phonon defect, electron-phonon, electron impurity or point defects and more rare electron-electron. For both heat carriers, the thermal resistivity contributions due to the various scattering processes are additive. For... 

Since the number of phonons increases with temperature, the electron-phonon and phonon-phonon scattering are temperature dependent. The number of defects is temperature independent and correspondingly, the mean free path for phonon defect and electron defect scattering does not depend on temperature. 

At high temperatures (T > 20K), the electron-phonon scattering is dominant and k decreases with T. Hence, we find a maximum of thermal conductivity (see Figs 3.16, 3.19 and 3.20) which is around 10 K for pure metals and 40 K for alloys. For example, in the case of A11050 A1 alloy, where the thermal conduction is mainly due to electrons ... 

---