Thermal Conductivity of Thick Pure Lead Films for the Study of Surface Superconductivity

Abstract

The differential thermal conductivity of lead films in a magnetic field parallel to the plane of the film has been measured in the temperature range 1.2 to 4.2\ifmmode^\circ\else\textdegree\fi{}K. The thicknesses of the films (from 2500 to 7000 \AA{}) have been selected so that the expected volume of the superconducting surface regions is an appreciable volume fraction of the sample. The fraction of material remaining in the surface superconducting state just above the film's critical field is related to the measured thermal conductivity via a simple phenomenological model. The analysis allows a heuristic determination of the product of the thickness of the superconducting surfaces and the square of the order parameter at the surface. The results are compared with the recent calculations of Fink and Kessinger. Well defined values of ${H}_{c}$ and ${H}_{c3}$ are obtained. Some hysteresis is observed near ${H}_{c}$ in a decreasing magnetic field, and the role of phonons in the heat transport is manifest, but its contributions above ${H}_{c}$ is negligible when compared with the electronic contribution to the thermal conductivity.