Phase diagram of a surface superconductor in parallel magnetic field

TL;DR

This paper presents a detailed theoretical phase diagram of a 2D surface superconductor under parallel magnetic field, revealing transitions between homogeneous, LOFF-like, and helical states influenced by Rashba spin-orbit interaction and impurities.

Contribution

It introduces the effects of strong Rashba spin-orbit coupling on the phase transitions and states in a 2D superconductor under magnetic field, including the emergence of a helical state.

Findings

LOFF-like state exists at high magnetic fields and low temperatures.

A new helical state appears at higher temperatures between BCS and LOFF states.

Impurities suppress inhomogeneous states and can eliminate them at certain levels.

Abstract

Detailed theory of phase diagram of clean 2D surface superconductor in a parallel magnetic field is presented. Regular spin-orbital interaction of the Rashba type is known to produce inhomogeneous superconductive state similar to the Larkin-Ovchinnikov-Fulde-Ferrel (LOFF) state with $\Delta({\bf r})\propto \cos({\bf Qr})$ at high magnetic fields, with $Q \sim g\mu_B h/v_F$. We consider the case of relatively strong Rashba interaction and show that at low temperatures $T\leq 0.4 T_{c0}$ the LOFF-type state is separated from the usual homogeneous state by the first-order phase transition line. At higher temperatures new "helical" state with $\Delta({\bf r}) \propto \exp(i{\bf Qr})$ intervene between uniform BCS state and LOFF-like state. One component of superfluid density tensor $n_s$ vanishes on the second-order transition line between BCS state and helical state. Nonmagnetic impurities suppresses both inhomogeneous states, and eliminate them completely at $T_{c0}\tau \leq 0.11$.