Superconductivity of Microscopic Tin Filaments

An experimental determination has been made of the magnetic fields necessary to induce the superconducting transition in microscopic tin filaments called "whiskers." For temperatures near the zero-field transition temperature, $T_c$, the results are unambiguous, and in this region the critical fields are significantly higher than those of a bulk superconductor. At lower temperatures the critical field curve splits into two parts, the upper curve giving the field for destruction of superconductivity and the lower curve the field for restoration. The temperature dependence of the critical field is compared with the predictions of the London and Ginsburg-Landau theories of superconductivity. It is found that the London theory is inadequate to describe the data over the whole useful range, whereas the Ginsburg-Landau theory provides a satisfactory fit. The disappearance of hysteresis occurs at a temperature for which $2.0\le \frac{h_c}{H_c}\le 2.4$, where $\frac{h_c}{H_c}$ is the ratio of whisker to bulk critical fields. This is in reasonable agreement with the Ginsburg-Landau-Silin condition for the onset of second order transitions. An effective value of ${\lambda }_0$, the penetration depth at 0°K, is derived from the data for each whisker. ${\lambda }_0$ shows a strong dependence on the normal electrical conductivity, as estimated from the change in resistance at the transition. At long mean free path the results are in agreement with those obtained from bulk specimen measurements, but at short mean free path the present ${\lambda }_0$ values are higher.