Tunneling Study of Superconductivity in Tl-Pb-Bi Alloys

Superconducting characteristics for selected alloys of the fcc Tl-Pb-Bi system have been measured using the technique of single-particle electron tunneling. Also, calculations of the electron-phonon coupling strength and hence the product function ${\alpha }^2\left(\omega \right)F\left(\omega \right)$ determining superconductivity in these alloys have been performed. The computations are based on neutron scattering data, an electron-ion pseudopotential form factor adjusted to fit experimental phonon dispersion curves, and a Born-von Kármán force-constant analysis. Through a solution of the Éliashberg gap equations, a critical comparison is made between the calculated ${\alpha }^2\left(\omega \right)F\left(\omega \right)$ and the experimentally determined tunneling curves. It is found that, even though fine details of the phonon-spectrum critical points do not always agree, the calculated superconducting energy gap ${\Delta }_0$ is, in all cases, in good agreement with experiment. Where confidence is felt in the Born-von Kármán analysis, the location of the experimentally determined critical points is in excellent agreement with those calculated from inelastic neutron scattering data, while the relative strengths of these singularities show discrepancies attributed to the alloy nature of the material under study.