memory devices [@padurariu_theoretical_2010].

Acknowledgements
================

The authors thank F. S. Bergeret for useful discussions and fruitful remarks and suggestions. This work was supported by EU Network COST CA16218 (NANOCOHYBRI) and the French ANR project OPTOFLUXONICS (A.B. and J.C.). J. B. acknowledges the financial support from the Initiative d’Excellence (IDEX) of the Université de Bordeaux and the funding by the Spanish Ministerio de Economía y Competitividad (MINECO) (Projects No. FIS2014-55987-P and No. FIS2017-82804-P). Computer time for this study was provided by the computing facilities MCIA (Mésocentre de Calcul Intensif Aquitain) of the Université de Bordeaux and of the Université de Pau et des Pays de l’Adour.\

[**Author contribution statement**]{}

All the authors have contributed to the derivation of the analytical results. Moreover Julie Baumard has also implemented the numerical calculations for the various phase diagrams. All the authors have contributed to the redaction of the manuscript and approved its final version.

\[app:hamiltonian\] Normal state Hamiltonian in the helical basis
=================================================================

Here we provide details concerning the derivation of the diagonal Hamiltonian Eq. (\[hamiltonian\_diag\]). In Nambu space, the Hamiltonian describing the wire in the absence of superconductivity may be written: $$\hat{h}_\text{N} = \left(\xi + \alpha\,p\,\sigma_z\right)\,\tau_z + \vec{h}\cdot\vec{\sigma} \;,$$ where $\sigma_{x,y,z}$ and $\tau_{x,y,z}$ 