Gor'kov-Goodman relation in low-κaluminum films

From measurements of the critical field $H_{c2\mathrm{}}$ in thin films of superconducting aluminum we have been able to verify the Gor'kov-Goodman relation between the Ginzburg-Landau parameter and normal-state resistivity ${\rho }_N$. The proportionality is close to that predicted from the specific heat, however, the intercept at ${\rho }_N=0\mathrm{}$ agrees with nonlocal theory rather than Gor'kov's local calculation. Our work differs from other thin-film measurements in that we use tunneling to determine the transition at $H_{c2\mathrm{}}$ and because we extrapolate against normal-state resistivity rather than film thickness. The temperature dependence of $H_{c2\mathrm{}}$ is found to agree with the calculations of Maki.