Critical magnetic field of very thin superconducting aluminum films

We have measured the parallel critical magnetic field H_c∥ of 4-nm-thick Al films. The conductance dI/dV of tunnel junctions made on these films was used to obtain for each film the orbital depairing parameter ζ and spin-orbit scattering parameter b which were then used in the theory of high-field superconductivity to calculate H_c∥. 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∥ 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∥ as well.