Thermal conductivity of superconducting tin films in a magnetic field

Abstract

We have measured the magnetic field dependence of the thermal conductivity of superconducting tin films in a parallel field ranging from zero to above the critical fields, and at temperatures from 0.3 to 10 K. They had electron mean free paths which were from 18% to 85% of the bulk coherence 1ength Eo. The Landau-Ginzburg parameter x o was sufficiently enhanced by the effect of the.short mean free paths that in our thicker films we were able to observe the surface. sheath region of de Gennes and Saint James. We have derived an expression for the field dependence of the thermal conductivity in this region, based upon theoretical calculations of Caroli and Cyrot and of Maki; this expression, which is strictly valid only in the limit l/Eo -> 0, is in good agreement with our experimental results. We have compared the experimental results for our thinner films with theoretical calcu lations of the field dependence of the thermal conductivity by Maki. These expressions are also restricted in validity to the limit l/Eo -> O. Here the agreement between the theory and the data is not so good as in the thick film case, but it improve as the experimental values of l approach the limit l/Eo -> O.