Observation of a gel of quantum vortices in a superconductor at very low magnetic fields

José Benito Llorens,Lior Embon,Alexandre Correa,Roberto F Luccas,Hermann Suderow,Federico J Mompeán,Milorad V Milošević,Jon Azpeitia,Isabel Guillamón,Mar García-Hernández,Jesús David González,Jazmín Aragón Sánchez,Yonathan Anahory,Yanina Fasano,Edwin Herrera,Carmen Munuera

doi:10.1103/physrevresearch.2.013329

Abstract

A gel consists of a network of particles or molecules formed for example using the sol-gel process, by which a solution transforms into a porous solid. Particles or molecules in a gel are mainly organized on a scaffold that makes up a porous system. Quantized vortices in type II superconductors mostly form spatially homogeneous ordered or amorphous solids. Here we present high-resolution imaging of the vortex lattice displaying dense vortex clusters separated by sparse or entirely vortex-free regions in $\beta$-Bi$_2$Pd superconductor. We find that the intervortex distance diverges upon decreasing the magnetic field and that vortex lattice images follow a multifractal behavior. These properties, characteristic of gels, establish the presence of a novel vortex distribution, distinctly different from the well-studied disordered and glassy phases observed in high-temperature and conventional superconductors. The observed behavior is caused by a scaffold of one-dimensional structural defects with enhanced stress close to the defects. The vortex gel might often occur in type-II superconductors at low magnetic fields. Such vortex distributions should allow to considerably simplify control over vortex positions and manipulation of quantum vortex states.

Highlights

Quantized vortices in superconductors arrange spatially in structures that bear some similarities with atomic or molecular arrangements
Experiments made in superconductors at low magnetic fields have until now unveiled vortex clustering in hexagonal lattices due to attractive interactions or the intermediate mixed state in single crystals or polycrystalline vortex arrangements and glassy phases in presence of disorder [5,6,7,8,9,10,11,12,13,14,15,16]
Our measurements illuminate the interplay of geometric defects and crystalline stress at very low magnetic fields in superconductors, which turns out to be much more varied than previously thought

Summary

Introduction

Quantized vortices in superconductors arrange spatially in structures that bear some similarities with atomic or molecular arrangements. The main difference is that vortices consist of single quantized fluxes with repulsive interactions, whereas atoms and molecules have numerous degrees of freedom and allow for bonding. Experiments made in superconductors at low magnetic fields have until now unveiled vortex clustering in hexagonal lattices due to attractive interactions or the intermediate mixed state in single crystals or polycrystalline vortex arrangements and glassy phases in presence of disorder [5,6,7,8,9,10,11,12,13,14,15,16]. We find vortex clusters whose distribution has characteristics specific to gels, such as a wide distribution of intervortex separation, covering widely different distances that diverges when decreasing the magnetic field and is characterized by multiple fractal exponents

Results

Discussion

Conclusion