Interaction phonon-electron

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... 

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 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. 

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... 

The linear and nonlinear optical properties of the conjugated polymeric crystals are reviewed. It is shown that the dimensionality of the rr-electron distribution and electron-phonon interaction drastically influence the order of magnitude and time response of these properties. The one-dimensional conjugated crystals show the strongest nonlinearities their response time is determined by the diffusion time of the intrinsic conjugation defects whose dynamics are described within the soliton picture. 

It is also shown that the electron-phonon interaction is operative in the polymerization process of the one-dimensional conjugated polymeric crystals a simple dynamical model for the polymerisation in polydiacetylenes is presented that accounts for the existing observations. 

The polydiacetylene crystals (1-4) most strikingly corroborate these conjectures. Along this line of thought is also shown that this electron-phonon interaction is intimately interwoven with the polymerisation process in these materials and plays a profound role there. We make the conjecture that this occurs through the motion of an unpaired electron in a non-bonding p-orbital dressed with a bending mode and guided by a classical intermolecular mode. Such a polaron type diffusion combined with the theory of non radiative transitions explains the essentials of the spectral characteristics of the materials as well as their polymerisation dynamics. ... 

Hihath J, Bruot C, Tao N (2010) Electron-phonon interactions in single octanedithiol molecular junctions. ACS Nano 4 3823-3830... 

Electron-phonon interaction, 23 804 Electron probe microanalyzer (EPMA), 16 484, 488... 

With the availability of lasers, Brillouin scattering can now be used more confidently to study electron-phonon interactions and to probe the energy, damping and relative weight of the various hydro-dynamic collective modes in anharmonic insulating crystals.The connection between the intensity and spectral distribution of scattered light and the nuclear displacement-displacement correlation function has been extensively discussed by Griffin 236). 

The term H e is the electron correlation operator, the term H p corresponds to phonon-phonon interaction and H l corresponds to electron-phonon interaction. If we analyze the last term H l we see that when using crude approximation this corresponds to such phonons that force constant in eq. (17) is given as a second derivative of electron-nuclei interaction with respect to normal coordinates. Because we used crude adiabatic approximation in which minimum of the energy is at the point Rg, this is also reflected by basis set used. Therefore this approximation does not properly describes the physical vibrations i.e. if we move the nuclei, electrons are distributed according to the minimum of energy at point Rg and they do not feel correspondingly the R dependence. The perturbation term H) which corresponds to electron-phonon interaction is too large... 

Since electrons are much faster than nuclei, owing to Wg Mj, ions can be considered as fixed and one can thus neglect the //ion-ion contribution (formally Mion-ion Hee, where Vion-ion is a Constant). This hrst approximation, as formulated by N. E. Born and J. R. Oppenheimer, reflects the instantaneous adaptation of electrons to atomic vibrations thus discarding any electron-phonon effects. Electron-phonon interactions can be a-posteriori included as a perturbation of the zero-order Hamiltonian Hq. This is particularly evident in the photoemission spectra of molecules in the gas phase, as already discussed in Section 1.1 for nJ, where the 7T state exhibits several lines separated by a constant quantized energy. 

The situation discussed here is equivalent to a periodic distortion of the lattice with a period 2a, as developed above. When the perturbation //per is given by lattice vibrations, that is mediated by electron-phonon interactions, the electronic density modulation is expressed in terms of a charge-density wave (CDW), while when electron-electron repulsions dominate the modulation is induced by SDWs (Canadell Whangbo, 1991). 

There are a large number of cases where the spectra of luminescence centers remain broad up to helium temperatures. In certain cases, this is explained by a strong electron-phonon interaction, but more often the inhomogeneous broadening, connected with several types of the same center presence, causes this. In such cases it is possible to simplify the spectrum by selective excitation of specific centers. 

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 ... 

Calori, C., Combescot, R., Nozieres, P., and Saint-James, D. (1972). A direct calculation of the tunneling current IV. Electron-phonon interaction effects. Solid State Physics 5, 21—42. 

A AH < kT has important consequences. As the temperature is lowered to where AHg, kT, strong electron-phonon interactions must manifest themselves. Direct evidence for mode softening and strong electron-phonon coupling in the internal Ty < T < 250 K has been provided by measurements of the Mdssbauer recoiless fraction and the X-ray Debye-Waller factor as well as of muon-spin rotation Therefore, it would be... 

Fig. 4a-c. Models for electron hopping correlated by electrostatic electron-electron interactions plus strong electron-phonon interactions for a valence ratio Fe /Fe = 1 (a) small pola-rons, (b) diatomic polarons, (c) small polaron coupled to slower (only one phase shown) dimerization... 

---