# Reentrant Phase Coherence in Superconducting Nanowire Composites

## TL;DR

This paper demonstrates that inhomogeneous nanofilament composites can exhibit reentrant phase coherence, overcoming phase fluctuation issues in low-dimensional superconductors, with potential for more resilient superconducting materials.

## Contribution

It introduces a new approach using nanofilament composites to achieve reentrant phase coherence in low-dimensional superconductors, enhancing their stability against fluctuations.

## Key findings

- Reentrant phase coherence observed upon increasing temperature, magnetic field, or current.
- Peak in Josephson energy correlates with reentrant phase coherence.
- Na$_{2- ext{delta}}$Mo$_6$Se$_6$ serves as a blueprint for resilient nanofilamentary superconductors.

## Abstract

The short coherence lengths characteristic of low-dimensional superconductors are associated with usefully high critical fields or temperatures. Unfortunately, such materials are often sensitive to disorder and suffer from phase fluctuations in the superconducting order parameter which diverge with temperature $T$, magnetic field $H$ or current $I$. We propose an approach to overcome synthesis and fluctuation problems: building superconductors from inhomogeneous composites of nanofilaments. Macroscopic crystals of quasi-one-dimensional Na$_{2-\delta}$Mo$_6$Se$_6$ featuring Na vacancy disorder ($\delta\approx$~0.2) are shown to behave as percolative networks of superconducting nanowires. Long range order is established via transverse coupling between individual one-dimensional filaments, yet phase coherence remains unstable to fluctuations and localization in the zero-($T$,$H$,$I$) limit. However, a region of reentrant phase coherence develops upon raising ($T$,$H$,$I$). We attribute this phenomenon to an enhancement of the transverse coupling due to electron delocalization. Our observations of reentrant phase coherence coincide with a peak in the Josephson energy $E_J$ at non-zero ($T$,$H$,$I$), which we estimate using a simple analytical model for a disordered anisotropic superconductor. Na$_{2-\delta}$Mo$_6$Se$_6$ is therefore a blueprint for a future generation of nanofilamentary superconductors with inbuilt resilience to phase fluctuations at elevated ($T$,$H$,$I$).