Fluctuation Effects in the Complex Impedance of Superconducting Tin-Whisker Crystals nearTc

An extensive experimental study of fluctuation effects in the complex ac impedance $Z_W(\omega ,T)$ of one-dimensional tin-whisker crystals near the superconducting transition temperature $T_c$ is described. The behavior of $Z_W(\omega ,T)$ in whiskers with cross-sectional areas 2 × ${10}^{-10\mathrm{}}$-3 × ${10}^{-9\mathrm{}}$ ${\mathrm{cm}}^2$ was measured at 60 MHz, 1 kHz, and dc from below $T_c$ in the mean-field temperature range up through $T_c$ and slightly above. Paraconductivity data were not obtained. By correlating high-frequency reactance data with resistance data from dc or low-frequency ac measurements, a more stringent test was made of the theory of fluctuation effects than is possible with dc measurements alone. We find that the theory of Langer and Ambegaokar (LA) as completed by McCumber and Halperin (MH) for the onset of resistance is inconsistent with our results unless the LA barrier height is reduced by a factor of approximately 0.55. If this is done, the LA-MH prediction agrees with resistance data over the full whisker size range. The MH result for the onset of fluctuation effects in the reactance agrees with our data without modification. No theory exists which can explain the behavior of $Z_W(\omega ,T)$ as $T$ passes through $T_c$. Our data are presented in a form to facilitate comparison with future theories. Reactance data in the mean-field region yield a direct measurement of the penetration depth. We find an interesting size effect in this quantity, and a new value is reported for the London penetration depth in pure tin, ${\lambda }_L=289\mathrm{}\pm 20$ Å.