The electron-phonon interaction in solids is important for many interesting properties of solids, among them the critical temperature of phonon-mediated superconductors, the effective electron mass in metals and semiconductors, and the carrier dynamics in semiconductors. Modern density-functional techniques have made it possible to perform $a\phantom{\rule{0}{0ex}}b$ $i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o$ calculations of the electron-phonon interaction. This review explains these techniques and discusses their applications.

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Electron-phonon interactions from first principles

Point contacts between normal metals at low temperatures show very interesting non-linear phenomena in the current-voltage characteristics. The observed deviations from Ohm's law in metallic constrictions can be used for an energy-resolved spectral analysis of the interaction mechanisms of the conduction electrons with elementary excitations in a metal. A review is given on the theoretical and experimental work dealing with this spectroscopic method. A theoretical analysis, involving an iterative solution of the full non-linear Boltzmann equation for the transport problem of a current through a point-contact geometry, is able to show that the observed second-derivative signal is proportional to Eliashberg's form of the electron-phonon interaction alpha 2F( omega ), with a slight modification due to a transport efficiency function. Non-equilibrium effects of the phonon system are discussed in relation to the observed background signal on which the alpha 2F signal is thought to be superimposed. The theory can easily be extended to other scattering mechanisms than the electron-phonon interaction, and some experiments show that the interactions of conduction electrons with magnons and paramagnetic impurities can be detected using point contacts between ferromagnetic metals and between magnetically dilute alloys.

/pdf/point-contact-spectroscopy-in-metals-2ep152hpyj.pdf

Point-contact spectroscopy in metals

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.

https://iopscience.iop.org/article/10.1088/0031-8949/14/1-2/013/pdf

The Electron-Phonon Interaction in Normal Metals

https://www.onlinelibrary.wiley.com/doi/pdf/10.1002/adom.202001225

Controlling Light, Heat, and Vibrations in Plasmonics and Phononics

The resistivities at constant volume and constant pressure and the volume derivative ( delta ln rho / delta lnV) were calculated over a range of temperatures (20K to melting) employing a fundamental calculation of the form factor and phonon spectrum No parameters were adjusted to fit experimental data yet the agreement obtained with experiment was very good The phonon frequencies were calculated using the recently-developed model potentials of Dagens et al (1975) and the Geldart and Taylor (1970) screening The form factors were calculated using the same model potential and screening but also incorporating the non-local electron-electron vertex correction of Rasolt (1975)

Calculation of the phonon-limited ideal resistivity of potassium and sodium

We have calculated the constant pressure and constant volume ideal electrical resistivities of the alkali metals Na, K, and Rb. In addition we have also calculated the ideal thermal resistivities o...

Transport in some Alkalis

The authors have calculated the variation on the Fermi surface of the transport scattering times in the alkali metals. The Fermi surface is taken to be a sphere and the scattering is assumed to be due only to the electron-phonon interaction. The anisotropy in the scattering times is a direct result of the anisotropy in the phonon spectrum. The variation with position on the Fermi surface is found to be considerable. It is most significant for Li at low temperatures. As the temperature is increased, the anisotropy decreases. The results are used in a discussion of the ideal resistivity of the alkali metals.

Anisotropic transport scattering times in the alkali metals

We have calculated the effect of the anisotropy in the electron-phonon interaction on the temperature dependence of the Hall constant in the alkali metals. We find that the effective number of carriers ${n}^{*}$ decreases with temperature in qualitative agreement with experiment. At low temperatures, we find a minimum in ${n}^{*}$.

Hall Coefficients in the Alkali Metals

In Li, at high temperature, the constant volume resistivity becomes larger than the zero (atmospheric) pressure value. This is contrary to what is observed in the other alkalis. It has been suggested that it is a result of an increase in the distortions of the lithium Fermi surface with application of hydrostatic pressure. We show that the effect can be understood much more simply and naturally on the basis of a spherical Fermi surface and a simple electron-ion pseudopotential form factor. The form factor is used to evaluate the absolute value and the volume dependence of the thermoelectric power. the thermal conductivity and the electron-phonon mass renormalization.

Resistivity and electron-phonon interaction in Li

We have calculated the effect of phonon drag on the electrical resistivity and the thermopower of the alkali metals. The calculations are an extension of our previous work on select transport properties of the alkalis. For the electron–ion interaction we use the pseudopotentials that we developed from resistivity data. Realistic phonons obtained from inelastic neutron scattering results on the dispersion curves are employed. This means that no adjustable parameters enter our calculations. Good qualitative agreement with experiment is obtained for the phonon drag thermopower.

B. Hayman

Papers

Transport in some Alkalis

Anisotropic transport scattering times in the alkali metals

Hall Coefficients in the Alkali Metals

Resistivity and electron-phonon interaction in Li

Phonon Drag in the Alkalis