Superconductivity in Simple Metals

Abstract

This paper reports an attempt to calculate directly from normal-state data the superconducting properties of a number of simple metals. Information about the lattice vibrations is taken from a Born-von Karman force-constant fit to the dispersion curves measured by means of inelastic neutron scattering. The matrix element of the electron-ion potential, for electrons scattering at the Fermi surface, is taken from pseudopotential theory. From this information we evaluate the electron-phonon part entering the Eliashberg gap equations which are then solved numerically to obtain the gap in the excitation spectrum. The calculated gap for Pb as well as for Al is in close agreement with experiment. For Na and K it is predicted that the transition temperature is certainly much less than 10"" 6 °K if, in fact, they superconduct at all.

Umklapp scattering of pairs in BCS superconductivity theory

“…Another approach, the Eliashberg formalism, is based on the one-electron Green's function, and here too superconductivity is enhanced when umklapp scattering is introduced [13]. However, in this formalism, which is non-variational and does not involve a trial function, the physics of pair scattering and interference effects may be manifest in a manner different from that in the BCS variational approach.…”

Comparison of Heine–Abarenkov and alternative pseudopotentials for electron–phonon interaction in aluminium, lead, lithium and calcium

“…Success of the McMillan procedure immediately led to an upsurge of further successful research activity, see [8] and references therein. The obvious next move was to evaluate α 2 F (ν) from first principles and at this stage difficulties started to emerge.…”

“…In 1968 Carbotte and Dynes [8] evaluated α 2 F (ν) for aluminium with the Heine-Abarenkov pseudopotential specified by Harrison [14]. In general their result, shown as the histogram in the upper part of FIG.…”

“…It showed that, while calculated α 2 F (ν) appears to be reasonably accurate [7,8], agreement between calculated and experimental ρ(T ) is not good for example at T = 297 K in the case of aluminium, and seriously worse in the case of lead [5]. Naturally we have to ask: are there better pseu- * Electronic address: dg.walmsley@qub.ac.uk dopotentials to describe the electron-phonon interaction in the metals?…”

“…In this process recognition should be given to Carbotte and coworkers who, in applying Eliashberg-Nambu formalism creatively at a very early stage of its development, set a standard that was, and still is, very challenging [5][6][7][8][9][10] They evaluated the electron-phonon interaction, responsible for both superconductivity and normal state electrical resistivity, quantitatively from first principles. They applied the Heine-Abarenkov pseudopotential, originally designed to reproduce atomic energy levels, to evaluating the electron-phonon spectral density, α 2 F (ν), for aluminium and lead in the superconducting state.…”