Electron-Tunneling Studies of Dilute Pb-Based In Alloys

Abstract

The technique of electron tunneling has been used to obtain the effective phonon spectra, ${\alpha }^2\mathrm{}\left(w\right)F\left(w\right)\mathrm{}$, and the parameters defining the superconductivity for dilute Pb-In alloys by solving the Eliashberg equations. These quantities were extracted from the measured energy gap of the alloy films and the measured normalized conductance of the thin-film tunnel junctions of the form Al-${\mathrm{Al}}_2$ ${\mathrm{O}}_3$-Pb-In. All the measurements were carried out around 1 K, at which temperature both the aluminum and the alloy films were in the superconducting state. The normal-state data were taken by raising the temperature above the transition temperature of both the films. A band of frequencies, the so-called impurity band, appeared beyond the high-frequency cutoff of the phonon spectrum of pure Pb. For all the alloys studied the impurity band was found to consist of at least two peaks which are attributed to the vibrations of isolated indium atoms and the vibrations of the pairs of indium atoms, both surrounded by the host lead atoms. The position of the first peak has been found to be constant (9.57 ± 0.03 meV), and its width has been found to vary linearly with concentration of indium. The position of the second peak remains constant up to 2-at.% indium but increases with the further addition of indium. The width of the second peak also varies linearly with the indium concentration. The fraction of modes in the impurity band has been found to be a factor 1.5-2.0 less than the concentration of indium. A determination of the ratio of the energy gap to the superconducting transition temperature for the alloy films shows that the electron-phonon interaction remains nearly constant for all the alloys studied.