## Document Type

Dissertation

## Date of Award

1972

## Keywords

Superconductivity, Tunneling (physics), Lead alloys

## Degree Name

Doctor of Philosophy (PhD)

## Department

Physics

## First Advisor

Robert L. Pompi

## Second Advisor

Sol Raboy

## Third Advisor

Newton Greenberg

## Series

Science and Mathematics

## Abstract

This dissertation deals with the pressure induced changes in the vibrational spectrum of the lattice and the electron-phonon interaction of a metal in both the normal and superconducting states. Specifically, the effects of pressure induced changes on the phonon spectrum F(ω) weighted by the electron-phonon coupling function α^{2}(ω), the dimensionless electron-phonon interaction strength λ, and the average electron-phonon coupling function .<α^{2}> have been determined for the superconducting alloys Pb_{95}In_{5} and Pb_{88}In_{l2}, where the numbers refer to atomic percent. These alloys were selected for study due to their strong-coupling properties and the existence in the phonon spectrum of the "impurity band" modes which arise due to the light indium atoms in the heavy lead lattice. The pressure induced shifts of the predominant phonon frequencies and of the super-conducting energy gap were also determined.

Electron tunneling measurements on Al-Al_{2}0_{3}—PbIn junctions were made at normal pressures and at various pressures ranging up to approximately 36OO bar. The tunneling measurements rely on the fact that an electron, in tunneling through a potential barrier into a superconductor, does so with a probability that is proportional to the density of available states in the superconductor. Measurement of the tunneling current-voltage characteristic then enables one to determine the electron density of states. Since (at T = 0 K) no current can flow until a voltage greater than the energy gap is applied to the junction, tunneling also gives the energy gap. The energy gap and density of states obtained from tunneling were then used as input data to a complex computer program based on the strong-coupling theory of superconductivity developed by W. L. McMillan. McMillan’s program extracts the effective phonon spectrum α^{2}(ω)F(ω) from the Eliashberg self-energy equations. The program also calculates λ and <α^{2}> using α^{2}(ω)F(ω).

The samples were suspended in a beryllium-copper pressure cell and solid helium provided nearly hydrostatic pressure. Pressure was applied with the helium in the gaseous state and solidification took place at constant pressure. Zero pressure data was in good agreement with previously published results.

The energy gap decreases and the phonon frequencies increase with increasing pressure. The impurity band undergoes the smallest relative shift with increasing pressure and the transverse peak exhibits the largest such shift. α^{2}(ω)F(ω) shifts toward higher frequencies and decreases slightly in amplitude. The net result of all these effects is for a shift of the electron-phonon interaction toward weaker-coupling. The best indicators of this trend are the observed decrease of λ and <α^{2}> with increasing pressure.

The quantity Z_{n}(0) = 1 + λ is the enhancement factor due to the electron-phonon interaction of the electronic specific heat co-efficient γ . The value of d1nγ/dP determined in this study is close to the value for lead determined from thermal expansion measurements as well as the value estimated for lead from theoretical considerations.

## Recommended Citation

Hansen, Howard Helge, "A study of superconducting lead-indium alloys subjected to hydrostatic pressure using the electron tunneling technique" (1972). *Graduate Dissertations and Theses*. 175.

https://orb.binghamton.edu/dissertation_and_theses/175