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

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Measurements of the critical field $\stackrel{^}{H}$ and transition temperature $\stackrel{^}{T}$ 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 \ifmmode\pm\else\textpm\fi{}10% of the mean pore diameter $d$. Pore diameters from 65 to 250 \AA{} were used. Below $t (\ensuremath{\equiv}\frac{T}{\stackrel{^}{T}})=0.5$, $\stackrel{^}{H}$ can be represented approximately by $\stackrel{^}{H}=\frac{(3415\ifmmode\pm\else\textpm\fi{}40)(1\ensuremath{-}{t}^{2})}{{d}^{(1.00\ifmmode\pm\else\textpm\fi{}0.14)}},$where $\stackrel{^}{H}$ is in kilo-oersteds and $d$ is in Angstrom units. This is in agreement with the predictions of de Gennes and Maki of ${H}_{c2}$ 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 $\stackrel{^}{H}$. For the small pore sizes the temperature dependence of $\stackrel{^}{H}$ is qualitatively similar to the Abrikosov prediction of ${H}_{c2}$ for type II superconductors; however, near $t=1$ for the largest pore size the temperature dependence of $\stackrel{^}{H}$ is similar to that for a type I superconductor. The superconducting transition temperature $\stackrel{^}{T}$ shows a strong dependence upon $d$, so that $\stackrel{^}{T}(65 \AA{})$ is 4.23\ifmmode^\circ\else\textdegree\fi{}K compared with 3.4\ifmmode^\circ\else\textdegree\fi{}K for the bulk indium. The dependence of $\stackrel{^}{T}$ on $d$ is conveniently represented by $\stackrel{^}{T}\ensuremath{-}{T}_{\mathrm{bulk}}=1\ensuremath{-}0.0028 d,$where $d$ is in Angstrom units. The change in $\stackrel{^}{T}$ 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.