# Electronic correlations in magnetized helical edge states coupled to s-wave superconductors

## TL;DR

This paper investigates how electron-electron interactions influence correlation functions and spin transport in magnetized helical edge states coupled to s-wave superconductors, revealing regimes where pairing promotes or suppresses various correlations.

## Contribution

It provides a detailed theoretical analysis of the effects of interactions on correlation functions and spin transport in magnetized helical states with superconductivity, using bosonization and RG techniques.

## Key findings

- Superconducting pairing promotes spin-density-wave correlations in the partially mixed regime.
- Attractive interactions suppress singlet and triplet pairing correlations.
- Zeeman field enhances pairing correlations under repulsive interactions.

## Abstract

We theoretically study the role of electron-electron interactions in one-dimensional magnetized helical states coupled to an s-wave superconductor. We consider a partially mixed helical (superhelical) regime, where the magnetic field (superconductivity) has a dominant contribution. Using bosonization and renormalization group techniques, it is shown how the interactions affect the correlation functions in the system. In the partially mixed helical regime, we find that superconducting pairing promotes spin-density-wave correlations, while singlet and triplet pairing correlations suppress, especially under attractive interactions. In contrast, in the superhelical regime, a perturbative Zeeman field enhances both spin singlet and spin triplet-x pairings under repulsive interactions. We calculate both logarithmic and residual corrections to charge-density-wave, spin-density-wave, and pairing correlations, revealing short- and long-range behaviors. We further investigate spin transport properties supplemented by a renormalization group analysis of the temperature and frequency dependence of spin conductivity. We also analyze the transport of momentum-spin-locked carriers in the presence of Zeeman-induced and pairing-induced gaps, uncovering the effect of interactions and the interplay between the two gaps in helical systems.