Critical magnetic field of very thin superconducting aluminum films

Abstract

We have measured the parallel critical magnetic field $H_{c\parallel }$ of 4-nm-thick Al films. The conductance $\frac{\mathrm{dI}}{\mathrm{dV}}$ of tunnel junctions made on these films was used to obtain for each film the orbital depairing parameter $\zeta$ and spin-orbit scattering parameter $b$ which were then used in the theory of high-field superconductivity to calculate $H_{c\parallel }$. Comparison of the calculated and measured values shows the theory in its traditional form to be quantitatively lacking. When renormalization effects due to the electron-phonon interaction are included, the theory with no adjustable parameters gives a good description of $H_{c\parallel }$ for the Al films. However, if the Al is coated with submonolayer thickness of heavy metal to increase $b$, the theory does not reproduce the measured $H_{c\parallel }$ as well.