Critical Magnetic Field and Transition Temperature of Synthetic High-Field Superconductors

Measurements of the critical field ^H and transition temperature ^T of superconducting indium in porous glass have been made using a low-frequency mutual-inductance technique. The pore sizes of the glasses are well characterized, so that 96% of the pore volume is within ±{}10% of the mean pore diameter d. Pore diameters from 65 to 250 {} were used. Below t (≡T^T)=0.5, ^H can be represented approximately by ^H=(3415±40)(1-t²)d^(1.00±0.14),where ^H is in kilo-oersteds and d is in Angstrom units. This is in agreement with the predictions of de Gennes and Maki of Hc2 for type II superconductors in the dirty limit, assuming that the electronic mean free path is proportional to d. Above $t=0.6$, there are deviations from de Gennes's prediction for the d dependence and the t dependence of ^H. For the small pore sizes the temperature dependence of ^H is qualitatively similar to the Abrikosov prediction of Hc2 for type II superconductors; however, near $t=1$ for the largest pore size the temperature dependence of ^H is similar to that for a type I superconductor. The superconducting transition temperature ^T shows a strong dependence upon d, so that ^T(65 ) is 4.23^∘{}K compared with 3.4^∘{}K for the bulk indium. The dependence of ^T on d is conveniently represented by ^T-Tbulk=1-0.0028 d,where d is in Angstrom units. The change in ^T may be due to strain, mean-free-path, or surface effects. The samples are similar to inhomogeneous type II superconductors in their magnetic properties, showing hysteresis and flux jumping.