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 1\ifmmode^\circ\else\textdegree\fi{}K. The electron mean free path $l$ ranged from 18 to 85% of the bulk coherence length ${\ensuremath{\xi}}_{0}$. The Ginzburg-Landau parameter $\ensuremath{\kappa}$ was sufficiently enhanced by the effect of the short mean free path that in the thicker films the the surface sheath region of de Gennes and Saint James was observed. An expression is given for the field dependence of the thermal conductivity in this region, based on theoretical calculations of Caroli and Cyrot and of Maki; this expression, which is strictly valid only in the dirty limit $\frac{l}{{\ensuremath{\xi}}_{0}}\ensuremath{\rightarrow}0$, is in good agreement with our experimental results. The field dependence of the thermal conductivity of the thinner films is compared with theoretical expressions derived by Maki. These expressions are also restricted in validity to the dirty limit. Here the agreement between the theory and the data is not as good as for the thick films, but it improves as the experimental values of $l$ approach the dirty limit.