Critical magnetic field of ultrathin superconducting films and interfaces

Abstract

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 $\hat{I}»$ compared with the gap parameter $\hat{I}{”}_0$. We find that at a critical spin-orbit energy $\hat{I}{»}_c$ 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 $\hat{I}»/\hat{I}{”}_0$, the pair formation changes from interband to intraband pairing. For $\hat{I}»>\hat{I}{»}_c$, a dimensional cross-over of the critical field from two to one dimension is taking place.