The surface impedance of superconductors and normal metals at high frequencies III. The relation between impedance and superconducting penetration depth

Abstract

The theory developed in II is extended to cover the case of a superconductor, and a formula is derived relating the r. f. resistivity to the superconducting penetration depth and other parameters of the metal. It is shown how the penetration depth may be deduced directly from measurements of the skin reactance, and a method of measuring reactance is described, based essentially on the variation of the velocity of propagation along a transmission line due to the reactance of the conductors. For technical reasons it is not convenient to measure the reactance absolutely, but a simple extension of the technique described in I enables the change in reactance to be accurately measured when superconductivity is destroyed by a magnetic field. The method has been applied to mercury and tin. In the former case the results are in agreement with Shoenberg’s direct measurements, and confirm that the penetration depth at 0° K is of the order of 7 x 10 –6 cm. The theory developed at the beginning of the paper is used to deduce the variation of penetration depth with temperature from the resistivity measurements of I, and it is shown that agreement with other determinations and with the reactance measurements is fairly good, but not perfect. Some of the assumptions used in developing the theory are critically discussed, and a qualitative account is given to show how Heisenberg’s theory of superconductivity offers an explanation of some of the salient features of superconductivity and inparticular indicates the relation between superconducting and normal electrons.