Upper critical field in noncentrosymmetric superconductors

TL;DR

This paper calculates the upper critical magnetic field in noncentrosymmetric superconductors considering impurities and both orbital and paramagnetic effects, revealing a stable helical vortex state with specific conditions for its appearance.

Contribution

It introduces a comprehensive calculation of the upper critical field in noncentrosymmetric superconductors, including impurity effects and the stability of the helical vortex state.

Findings

Helical vortex state is stable against disorder.

Order parameter modulation occurs only at low temperatures in certain conditions.

The state resembles the LOFF state in centrosymmetric superconductors.

Abstract

We calculate the upper critical field in superconductors without inversion symmetry at arbitrary temperatures, in the presence of scalar impurities. Both orbital and spin (paramagnetic) mechanisms of pair breaking are considered. The superconducting phase transition at nonzero field occurs into a helical vortex state, in which the order parameter is modulated along the applied field (in a cubic crystal). The helical state is stable with respect to disorder. However, if the difference between the densities of states in the electron bands split by spin-orbit coupling is neglected, then the order parameter modulation is present only at low temperatures, and only if the system is sufficiently clean and paramagnetically limited. This state resembles the Larkin-Ovchinnikov-Fulde-Ferrell state in centrosymmetric superconductors.