The Electron-Phonon Interaction in Normal Metals

Abstract

The influence of the electron-phonon many-body renormalization effects on the electron states in normal metals is reviewed. The emphasis is on the electron-phonon mass enhancement parameter λ. The occurrence or absence of renormalization effects is discussed for different electronic properties. After a review of theoretical and experimental methods of obtaining information about λ, numerical values for this quantity are given for the elements. Other sections deal with alloys, compounds, disordered and amorphous metals, anisotropy in λ and variations in λ under pressure. Finally, brief comments are given on the electron-electron and electron-magnon renormalization of the electron mass.

Electronic structure and transport properties of CeNi9In2

“…The values of T 0 , T sf and b · J 2 sf are relatively high when compared to previous applications of the Freimuth's model [16,17] but all of them are within the same order of magnitude. Also the Grüneisen -Bloch -Mott [18,19] formula was fitted to the resistivity data. However, the fit yielded a weaker agreement with the experiment, what was reflected in lower correlation coefficient -R 2 .…”

Electron-phonon interactions and high-temperature thermodynamics of vanadium and its alloys

“…9,12 At high temperature, the extra vibrational entropy associated with softer ͑lower energy͒ phonon modes favors the expansion of the lattice. In the standard quasiharmonic model ͑QH͒, the rate of softening of the average phonon energy ͗E͘ is related to the rate of change in volume V of the crystal as:…”

Photoemission as a Probe of the Collective Excitations in Condensed Matter Systems

“…The process of coupling is illustrated in figure 1 where we consider coupling to a mode described by an Eliashberg function, α 2 F. Here α 2 F represents the product of the density of states of the relevant excitation and a matrix element reflecting the coupling strength. [8] For the present purposes, α 2 F in figure 1(a) is simply represented by a single Gaussian peak at energy Ω 0 . Coupling to such a mode (at T = 0 K) will result in a broadened step function in the scattering rate or imaginary part of the self energy, Σ 2 .…”

“…Γ e−ph increases monotonically with energy up to some cut-off defined by the Debye energy. At T = 0 K the electron-phonon coupling constant is given by [8] …”

“…The self energy corrections resulting in these changes reflect three principal contributions, electron-electron scattering, electron-phonon scattering and electron-impurity scattering. These different contributions all add linearly to give the total scattering rate Γ such that Γ = Γ e−e + Γ e−ph + Γ imp (8) In a Fermi liquid the electron-electron scattering term is given by Γ e−e (ω, T ) = 2β (πk B T ) 2 + ω 2 where, within the Born approximation, 2β = (πU 2 )/(2W 3 ), with U the on-site Coulomb repulsion and W the bandwidth of the state. As noted earlier the electron-phonon contribution may be calculated via the Eliashberg equation, eq.…”