# Topological superconductivity at finite temperatures in proximitized magnetic nanowires

## TL;DR

This study uses Monte Carlo simulations to explore how temperature affects magnetic order and topological superconductivity in proximitized nanowires, revealing the critical temperature for Majorana modes.

## Contribution

It provides a non-perturbative analysis of temperature effects on topological phases in magnetic nanowires, including the correlation length and critical temperature for Majorana modes.

## Key findings

- Helical magnetic order induces topological superconductivity.
- Thermal fluctuations reduce spiral order and topological gap.
- Critical temperature limits the existence of Majorana quasiparticles.

## Abstract

Performing Monte Carlo simulations we study the temperature dependent self--organization of magnetic moments coupled to itinerant electrons in a finite--size one--dimensional nanostructure proximitized to a superconducting reservoir. At low temperature an effective interaction between the localized magnetic moments, that is mediated by itinerant electrons, leads to their helical ordering. This ordering, in turn, affects the itinerant electrons, inducing the topologically nontrivial superconducting phase that hosts the Majorana modes. In a~wide range of system parameters, the spatial periodicity of a spiral order that minimizes the ground state energy turns out to promote the topological phase. We determine the correlation length of such spiral order and study how it is reduced by thermal fluctuations. This reduction is accompanied by suppression of the topological gap (which separates the zero-energy mode from continuum), setting the upper (critical) temperature for existence of the Majorana quasiparticles. Monte Carlo simulations do not rely on any ansatz for configurations of the localized moments, therefore they can be performed for arbitrary model parameters, also beyond the perturbative regime.