# Critical magnetic field of ultrathin superconducting films and interfaces

## TL;DR

This paper derives an analytic expression for the temperature-dependent critical magnetic field in ultrathin superconducting films with Rashba spin-orbit interaction, revealing a first-order phase transition and a dimensional crossover at a critical spin-orbit energy.

## Contribution

It provides a new analytic model covering a range of spin-orbit interactions and predicts a first-order phase transition and dimensional crossover in the critical magnetic field behavior.

## Key findings

- First-order phase transition at critical spin-orbit energy λ_c.
- Change from interband to intraband pairing with increasing λ.
- Dimensional crossover of the critical field from 2D to 1D for λ > λ_c.

## 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 $\lambda$ 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.