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The authors resolve the order of magnitude discrepancy between the measured low-temperature lattice thermal conductivity of K and that previously calculated using semiclassical transport theory. This is done by assuming that phonon-electron and phonon-dislocation scattering are dominant and that all other mechanisms for scattering phonons, in particular phonon-phonon scattering, can be ignored. This assumption also leads to excellent agreement between the measured and calculated phonon drag contribution to the high-field Nernst-Ettingshausen coefficient.

An analysis is presented of the range of validity of the most commonly used empirical expression for the low-temperature phonon-limited electrical resistivity of the alkali metals. The analysis is based on the temperature dependence of the mean phonon frequency, calculated by weighting each frequency according to its contribution to the electrical resistivity at temperature T when carrying out the average over the phonon spectrum. For potassium, it is found that the important temperature range 1-2K definitely lies outside the domain of validity of the empirical expression. For those temperature ranges and situations for which the empirical expression is valid, the values of the parameters are derived. Previously results are discussed and related to the present analysis.

For pt.I see ibid., vol.13, p.665 (1983). Current-voltage characteristics of small metallic contacts provide an energy-resolved probe of the inelastic scatterers of electrons in a metal (point-contact spectroscopy). The usual treatment of this phenomenon is invalid when the elastic mean free path of the electrons is comparable with the contact size, a regime in which experiments are often conducted. The authors present a treatment valid for arbitrarily strong elastic scattering. It is found that the point-contact spectroscopy signal should be increasingly diminished, broadened and shifted to higher energies as the elastic scattering rate is increased.

A recent fundamental description of the lattice dynamics and electron-phonon interaction in potassium (L Dagens et al., see Phys. Rev., vol.11, p.2726 (1975)) is shown to lead to very good agreement with experiment for both the high-temperature electrical resistivity and thermoelectric power. When the authors allow for the possibility of mixed electron-phonon and electron-electron scattering, the calculated result for the volume derivative of the thermopower supports the suggestion that the effect of normal electron-electron scattering is seen in the measured high-temperature transport properties of potassium.

Chromium is an itinerant-electron antiferromagnet with wavelength incommensurate to any multiple of the period of the host lattice. The appropriate statistical Hamiltonian for fluctuations above the Neel temperature is derived. This itinerant-electron Hamiltonian differs considerably from a localised-spin Hamiltonian due to the presence of a free phase angle analogous to the case for fluctuations in a superconductor, and because interactions occur only among fluctuations which all have the same spin direction. The itinerant-electron statistical Hamiltonian has a stable fixed point in the recursion relations of a Wilson-Fisher in expansion, indicating a second-order phase transition at TN. The stable fixed-point Hamiltonian corresponds to the experimentally observed single Q condensate state of chromium.

The authors present the results of a calculation of the low temperature ideal electrical resistivity of potassium which includes a consistent treatment of phonon drag. These results differ significantly from those of recent calculations which include the effect of phonon drag via the variational approach using the simplest trial functions for the electron and phonon distributions. It is shown that electron-phonon scattering does not, by itself, limit phonon drag to being a low temperature effect. Finally, it is pointed out that, as phonon drag significantly increases the relative contribution of the Umklapp process to the low temperature electrical resistivity, all recent investigations of the effect on the electrical resistivity of anisotropic relaxation of the electron distribution should be re-examined in the phonon drag regime.

Recently Shukla and Taylor (1976) calculated the phonon-limited electrical resistivity of potassium using a fundamental description of the lattice dynamics and electron-phonon coupling and obtained very good agreement with experiment. Precisely the same description has been used to calculate the electronic thermal conductivity of potassium from 1 to 330K. Very satisfactory agreement with experiment is obtained when the correct energy dependence of the electron distribution function is incorporated in the calculation. The effect of impurities on the low temperature thermal resistivity is investigated assuming that the total scattering rate for mixed phonon and impurity scattering is simply the sum of the scattering rates for the two acting separately.

The contribution of electron-electron scattering to the point-contact spectroscopy signal at small V is shown to increase as ln(l/a) at large l, where l is the mean free path and a is the orifice size. Calculations are presented which give an indication of the value of l/a at which this contribution should be observable in potassium.

The Nambu-Eliashberg equations for the k state electron-hole pairing of a spin density wave (SDW) are derived, taking full advantage of the symmetries of the pairing. Using these equations, a calculation of the effects of phonon pair breaking on the commensurate SDW phase is made, together with a determination of the qualitative form of the renormalised one-electron energy bands for the more complicated incommensurate SDW phase. The energy bands for the incommensurate SDW phase and the optical absorption results for Cr lead to a calculated SDW amplitude in agreement with experiment.

The low-temperature electrical resistivity of potassium is calculated for both the Bloch and phonon drag limits taking into account the detailed energy dependence of the electron distribution function. The correction to the lowest-order variational result is quite significant. For the particular pseudopotential form factor used in the calculation it reaches a maximum of 20% at 6K. This is twice as large as the much studied anisotropy correction.

At 3K the calculated change in the resistivity obtained by Hayman and Carbotte (see ibid., vol.2, p.915 (1972)) using Ziman's one-iteration approximation (1961) to the solution of the linearised Boltzmann equation is three times as large as that obtained by Ekin and Bringer (see Phys. Rev. B., vol.7, p.4468 (1973)) using the variational technique with a rather simple trial function. In an attempt to resolve the discrepancy between two widely used techniques, the Boltzmann equation was iterated to convergence to determine accurately the anisotropic relaxation time tau (k) as a function of position on the Fermi surface. It was found that the variational result for tau (k) is in good agreement with the accurate one except on those parts of the Fermi surface that are least heavily weighted in a calculation of the electrical resistivity; on the other hand, the Ziman one-iteration solution is much too anisotropic, at least for the temperature range considered. The electrical resistivity calculated with the accurately determined anisotropic relaxation times is only marginally better than the variational result. The same applies to the effective number of carriers in the Hall effect.

There is wide disagreement over which parameter describing the electron-phonon interaction is most important in determining the transition temperature of a strong-coupling superconductor. This role has been claimed for three different frequency moments of the electron-phonon spectral function alpha 2F( omega ). The Eliashberg theory is used to derive some rigorous upper bounds on Tc that are helpful in clearing up the confusion. It is found that the zeroth moment is the most important moment for the strong-coupling materials so far encountered in practice. In the limit of very strong electron-phonon coupling (a situation that appears not to occur in nature because of lattice instabilities) it is the first moment which is important. The mass enhancement parameter lambda appears to play a secondary role for strong-coupling superconductors.