Upward Curvature of the Temperature Dependence of Upper Critical Magnetic Field Perpendicular to Superconducting Aluminum Films

The temperature dependence of the electrical resistance of thin granular aluminum films shows the maximum far above the superconducting transition temperature due to both effects of thermodynamic fluctuations and electron localization, for the film with large normal-state sheet resistance R N . The temperature dependence of the upper critical field or the film with R N ≃10 3 (\(\)) shows the upward curvature. The results on the upper critical field are explained by a current theory of dirty superconductors including electron localization and electron-electron interactions.