The transition to superconductivity

Abstract

Magnetic and electrical measurements have been made of the effect of impurity on the transitions to superconductivity in tin. Reproducible results were obtained only with well-annealed monocrystalline specimens. Solution of up to 6 % indium in pure tin decreases the electronic mean free path l from about 3 x 10<super>-3</super> to 3 x 10<super>- 6 </super>cm, and over this range magnetic measurements show that there is only a small depression of the transition temperature T c and a small alteration in the critical field curve of H c and T . Electrical measurements show that if l / > l c , where lc; — 8 x 10<super>-6</super> cm, the resistance transitions are sharp and almost concurrent with the magnetic transitions. However, if l<l c superconducting nucleation apparently occurs, since a state of partial superconductivity exists with zero resistance, but no exclusion of magnetic induction, in fields greater than H c but less than H' c , where it has been found that at any one temperature HJH'C — This relation describes in broad outline the dependence of H' c on l and temperature, although the interpretation of the results is complicated by considerable broadening of the resistance transitions and the appearance of a sensitive non-linear dependence on the measuring current of the temperature of nucleation. These complicating effects may wholly or partly be due to inhomogeneities in indium concentration. The concept of a range of coherence g of the superconducting phase is used in formulating the thermodynamic conditions for the formation in a magnetic field of superconducting nuclei with cylindrical and spherical symmetry. It is shown that the main features of superconducting nucleation in homogeneous tin-indium alloys can be accounted for if g-2 A 0l where t= T/Tc T(i and A0 is the penetration depth at 0°K. The implication that g greatly exceeds / just below is supported by a consideration of the sharpness of resistance transition and the shape of the critical field curve near T c . The formula for g resembles that given in Pippard’s phenomenological theory of superconductivity (1953).