Electron-phonon interaction in impure metals

Making use of the theory for the phonon damping in an impure metal developed recently by Eisenriegler, we study the interaction between electrons and long wave-length longitudinal phonons, and its effects on electronic properties at low temperatures. On account of the inelastic scattering of electrons by impurity ions, a minimum in the electrical resistivity is found when plottedvs temperature, although its value is extremely small.     

Electron-phonon interaction in polar solids with application to the tungsten bronzes

We investigate the interaction between electrons and lattice vibrations in polar solids taking into account their microscopic dielectric properties and constructing in a semi-phenomenological manner the nonlocal dielectric function, ?_GG'(q). The results of earlier, phenomenological theories, such as the Clausius-Mossotti formula for the macroscopic screening constant and Fröhlich's electron-phonon coupling parameter α are obtained from the RPA dielectric function when the dipole approximation is used to calculate the screening by the strongly localized valence electrons. For polar metals we also consider the screening by the free conduction electrons. We present and discuss the results of the screened electron-phonon interaction as a function of the phonon wavevector q for the sodium tungsten bronzes.     

Shift and damping of optical phonons caused by interaction with electrons

Frequency shift and damping of long-wave optical phonons caused by interaction with electrons are calculated. The equations of the dynamic theory of elasticity are considered together with the Maxwell equations and the kinetic equation for determining the deformation field, the electric field, and the distribution function of electrons. Changes in the spectrum of electrons are described using a local potential. Coulomb screening of the longitudinal electric field is taken into account.     

Electron-phonon interactions in transition metals

The tight-binding method is used to calculate 〈I²〉, the Fermi surface average of the squared electron-phonon coupling constant for 4d b.c.c.—transition metals and alloys. When nonorthogonality effects are properly included, our results for 〈I²〉 agree very well with empirical values. Moreover, the variation of 〈I²〉 can be understood in simple physical terms.     

Electron-phonon interaction in LaAg

Magnetoacoustic de Haas-van Alphen data on LaAg are compared with a new relativistic band structure calculation including La-4f states. We find convincing agreement of the measured and calculated dHvA frequencies. The deformation of the Fermi surface under strain is determined from the magnetoacoustic dHvA amplitude. The strongest deformation potential coupling is found for three equivalent pockets which become inequivalent under orthorhombic strain. The lifting of their degeneracy leads to the softening of theT ₃ elastic constant. This is different from the useual band Jahn-Teller effect which is based on the lifting of subband degeneracy at a single point ink-space.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

Anomaly of the soft-mode damping function near phase-transition points due to interaction with acoustic phonons

An expression is derived for the anomalous part (T, ) of the soft-mode damping function due to third-order interaction between critical optical phonons and acoustic phonons. It is shown that in crystals with a large elastic viscosity the damping function of critical phonons can have stronger temperature anomalies near phase-transition points. The frequency dispersion of () is investigated; it is found that the damping is a maximum at =_o for the soft-mode vibrational dynamics and at =0 for the relaxational dynamics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 47–49, March, 1982.     

Electron-phonon interaction and antiferromagnetic correlations

We study effects of the Coulomb repulsion on the electron-phonon interaction (EPI) in the Holstein-Hubbard model, using the antiferromagnetic (AF) dynamical mean-field approximation. AF correlations strongly enhance EPI effects on the electron Green's function with respect to the paramagnetic correlated system, but the net effect of the Coulomb interaction is a moderate suppression of the EPI. Doping leads to additional suppression. In contrast, the Coulomb interaction strongly suppresses EPI effects on phonons, but the suppression weakens with doping.     

Electron-phonon interaction in tetrahedral semiconductors

Considerable progress has been made in recent years in the field of ab initio calculations of electronic band structures of semiconductors and insulators. The one-electron states (and the concomitant two-particle excitations) have been obtained without adjustable parameters, with a high degree of reliability. Also, more recently, the electron-hole excitation frequencies responsible for optical spectra have been calculated. These calculations, however, are performed with the constituent atoms fixed in their crystallographic positions and thus neglect the effects of the lattice vibrations (i.e. electron-phonon interaction) which can be rather large, even larger than the error bars assumed for ab initio calculations.Effects of electron-phonon interactions on the band structure can be experimentally investigated in detail by measuring the temperature dependence of energy gaps or critical points (van Hove singularities) of the optical excitation spectra. These studies have been complemented in recent years by observing the dependence of such spectra on isotopic mass whenever different stable isotopes of a given atom are available at affordable prices. In crystals composed of different atoms, the effect of the vibration of each separate atom can thus be investigated by isotopic substitution. Because of the zero-point vibrations, such effects are present even at zero temperature (T=0).In this paper, we discuss state-of-the-art calculations of the dielectric function spectra and compare them with experimental results, with emphasis on the differences introduced by the electron-phonon interaction. The temperature dependence of various optical parameters will be described by means of one or two (in a few cases three) Einstein oscillators, except at the lowest temperatures where the T⁴ law (contrary to the Varshni T² result) will be shown to apply. Increasing an isotopic mass increases the energy gaps, except in the case of monovalent Cu (e.g. CuCl) and possibly Ag (e.g. AgGaS₂). It will be shown that the gaps of tetrahedral materials containing an element of the first row of the periodic table (C,N,O) are strongly affected by the electron-phonon interaction. It will be conjectured that this effect is related to the superconductivity recently observed in heavily boron-doped carbon.     

Electron-phonon interaction in superconducting Nb

Acoustic phonon damping in Nb due to superconductivity is accurately measured by the inelastic neutron scattering technique. The phonon line widths can be characterized by the reduced parameters $\text{h}\text{?}\text{ω}{}_{\mathrm{p}}\text{/2Δ(0)}$ and T/T_c, and are in good qualitative agreement with the calculation by Bobetic based on the BCS theory.     

Electron-phonon interaction in carbon schwarzites

The recent synthesis of random schwarzites has stimulated the present ab initio calculation of the electronic structure and electron-phonon interaction in two different periodic D-type schwarzites, fcc-(C₂₈)₂ (made of 24 seven-membered rings per unit cell) and fcc-(C₆₄)₂ (made of 12 eight membered and 48 six-membered rings per unit cell). Like in fullerenes, also in schwarzites the electron-phonon interaction potential is found to increase with the absolute Gauss curvature, though it remains smaller than for doped fullerenes. Received 19 December 2002 Published online 1st April 2003 RID="a" ID="a"e-mail: marco.bernasconi@unimib.it     

Electron-phonon interaction close to a Mott transition

The effect of Holstein electron-phonon interaction on a Hubbard model close to a Mott-Hubbard transition at half filling is investigated by means of dynamical mean-field theory. We observe a reduction of the effective mass that we interpret in terms of a reduced effective repulsion. When the repulsion is rescaled to take into account this effect, the quasiparticle low-energy features are unaffected by the electron-phonon interaction. Phonon features are only observed within the high-energy Hubbard bands. The lack of electron-phonon fingerprints in the quasiparticle physics can be explained interpreting the quasiparticle motion in terms of rare fast processes.     

Electron-phonon coupling in transition metals and resonant scattering

An explicit formula is derived for the electron-phonon coupling of transition metals in terms of parameters that are used in first principle transition metal band structure calculations. Its relevance and systematics are discussed.     

Electron-phonon interaction in a local region

It has been shown that the formation of a bound state is possible in the region with a local electron-phonon interaction. Carbon nanostructures are considered as an example of the material in which this effect can be implemented. Based on the developed concepts, it has become possible to explain the anomalously high field emission in such structures not only phenomenologically but also at the microscopic level.     

Electron-phonon interaction in the t-J model

We derive a t-J model with electron-phonon coupling from the three-band model, considering modulation of both hopping and Coulomb integrals by phonons. While the modulation of the hopping integrals dominates, the modulation of the Coulomb integrals cannot be neglected. The model explains the experimentally observed anomalous softening of the half-breathing mode upon doping and a weaker softening of the breathing mode. It is shown that other phonons are not strongly influenced, and, in particular, the coupling to a buckling mode is not strong in this model.     

Electron-phonon interaction in an impure metal

On the basis of the existing theory of ultrasonic attenuation, a model Hamiltonian is derived which has to replace the Fröhlich Hamiltonian, at least in an impure metal. Whilst the imaginary part of the phonon self-energy is easily connected with the ultrasonic attenuation constant, the same quantity of the electrons allows no conclusion on inelastic collisions in this case. Therefore, from the linear response function, a kinetic equation for the electrons is derived. It is found that the time between inelastic collisions with phonons increases if impurities are added to the metal.     

Electron-phonon interaction in hemispherical quantum dot

Within the framework of the dielectric continuum (DC) model, the optical phonon modes and electron-optical-phonon interaction in hemispherical quantum dot are investigated. The proper eigenfunctions for longitudinal optical (LO) and interface optical (IO) phonon modes are constructed. After having quantized the eigenmodes, we derive the Hamiltonian operators describing the LO and IO phonon modes as well as the corresponding Fröhlich electron-phonon interaction. The dispersion relation of IO phonon modes is size independent. The potential applications of these results are also discussed.     

Electron-phonon interaction and coupled phonon-plasmon modes

The theory of Raman scattering by the coupled electron-phonon system in metals and heavily doped semiconductors is developed with Coulomb screening and the electron-phonon deformation interaction taken into account. The Boltzmann equation for carriers is applied. Phonon frequencies and optic coupling constants are renormalized due to interactions with carriers. The k-dependent semiclassical dielectric function is employed instead of the Lindhard-Mermin expression. The results of calculations are presented for various values of the carrier concentration and the electron-phonon coupling constant.     

Electron-phonon interaction in spherical multilayer nanoheterostructures

The complete hamiltonian of an electron-phonon system in the second quantization representation for a complex spherical nanoheterostructure with an arbitrary number of semiconducting layers is obtained in a polarized continuum model for bounded volume and interface phonons. The energy of the electron ground state is calculated using the experimentally realized CdS/HgS/H₂O system as an example. The cause of the nonmonotonic dependence of the shift in the electron ground state on the HgS thickness is established as due to the interaction with bounded phonons. Fiz. Tverd. Tela (St. Petersburg) 39, 1109–1113 (June 1997)     

Physical nature of specific features in interaction of electrons with long-wavelength phonons in one-dimensional metals

Physical mechanisms leading to nearly complete cancellation of the known deformation interaction of electrons with long-wavelength phonons by the self-consistent electric field are discussed. In the range of ql < 1 such cancelation is caused by the forces responsible for electron localization and convertion of 1-D metal into insulator, while at ql > 1 this compensation is ensured by Coulomb's forces. The criteria are established for deformation interaction to be small compared to cross-deformational one. It is shown that at weak localization, $\text{p}{}_0\text{l}\text{a}\text{?}\text{1}$, there is a wide region of low frequencies where the interelectronic interaction is negligibly small and one-particle approximation is justified.