Critical magnetic field of ultrathin superconducting films and interfaces

We derive an analytic expression for the temperature dependent critical magnetic field parallel to ultrathin superconducting films with Rashba spin-orbit interaction. Thereby we cover the range from small to large spin-orbit interactions $\lambda$ compared with the gap parameter $\Delta_0$. We find that at a critical spin-orbit energy $\lambda_c$ a first-order phase transition takes place at which the pairing momentum of the Cooper pairs changes discontinuously. We speculate that this might give raise to new phenomena. With increasing $\lambda/\Delta_0$, the pair formation changes from interband to intraband pairing. For $\lambda>\lambda_c$, a dimensional cross-over of the critical field from two to one dimension is taking place.