Effect of Impurities on the Critical Temperature of Superconductors

Abstract

By extending the analysis of Markowitz and Kadanoff, it is shown that in homogeneous, low-concentration tin and indium alloys, impurity-induced changes in the critical temperature $T_c$, arising from all causes other than decreased anisotropy, can be convincingly analyzed into a part due to variations in the electron mean free path and a part due to variations in the number of conduction electrons. A comparison of the latter with direct measurements by Glover and Sherrill of the shift in $T_c$ produced by electrically charging tin and indium films shows excellent agreement for five of the six alloy systems considered, although the sixth system shows poorer agreement. This analysis provides strong support for the theory of Markowitz and Kadanoff, and helps to separate the effect on $T_c$ of changes in the phonon spectrum, the electron-electron coupling constant, and the electron density of states.