The surface impedance of superconductors and normal metals at high frequencies II. The anomalous skin effect in normal metals
Measurements on the skin conductivity of the normal metals silver, gold, and tin show that at low temperatures the skin conductivity tends to become independent of the d. c. conductivity, which is at variance with the predictions of classical skin effect theory. Following a suggestion of H. London that this anomalous behaviour is due to the mean free path of the electrons becoming much greater than the skin depth, an attempt is made to calculate the effect for a semi-classical model of a metal. Although a rigorous solution has not been found, it is shown that the model predicts constancy of skin conductivity when the mean free path becomes very long. Moreover, there is reason to suppose that under these conditions only a small proportion of the conduction electrons contribute effectively to the high-frequency current, and an exact solution is given for a model based on this concept, which also predicts that the skin conductivity should be independent of the d. c. conductivity. A simple dimensional argument may be applied to enable values of the mean free path in copper, gold, aluminium and tin, relative to the value in silver, to be deduced from the experimental results. These values are not in good agreement with theoretical estimates by Mott and Jones. The behaviour of mercury is different from that of the other metals investigated, in that the skin conductivity does not tend to a constant value. It is suggested that the theory based on a crude classical model is inapplicable to a metal such as mercury, in which the anomalous skin effect appears at such temperatures that the ideal resistance is still many times greater than the residual resistance.
