Critical Magnetic Field of Ultra-Thin Superconducting Films and Interfaces

We derive an analytic expression for the temperature dependent critical magnetic field parallel to ultra-thin superconducting films with Rashba spin-orbit interaction. Thereby we cover the range from small to large spin-orbit interactions. 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 inter-band to intra-band pairing. For lambda > lambda(c) a dimensional cross-over of the critical field from two to one dimension is taking place.