Visualization of Spontaneous Vortices in a Disordered Superconducting Nanocomposite ✛
Context
Spontaneous symmetry breaking in continuous second-order phase transitions is a universal mechanism leading to the formation of topological defects, such as cosmic strings in the early Universe after the Big Bang or vortices in Bose-Einstein condensates and superconductors. The Kibble–Zurek scenario describes how rapid cooling of a symmetry-broken system inevitably produces defects, as distant regions fail to correlate their phases in time. However, direct observation of the geometric characteristics of such vortices has long remained challenging, especially in highly disordered media where standard notions of coherence may break down.
Methods
The study was conducted on an MgO/MgB₂ nanocomposite fabricated by solid-state synthesis and spark plasma sintering. In this system, the superconducting MgB₂ phase (about 30 vol%) is fractally distributed within an insulating MgO matrix that exhibits metallic conductivity due to oxygen vacancies. Inter-grain coupling occurs via the Josephson effect and Andreev reflection, ensuring macroscopic phase coherence at temperatures below ~37 K. To visualize the vortices, a scanning SQUID microscope with a 10 µm diameter planar pickup loop was used, capable of measuring the vertical magnetic field component to fractions of a flux quantum. The sample was cooled under different protocols: in the presence of an external field (field cooling) and in virtually zero field (less than 0.25 mOe). Measurements were performed at 4 K, and the heating–cooling cycle was repeated many times to check reproducibility.
Results
Under field cooling, standard Abrikosov vortices were observed—round, slightly teardrop-shaped due to the probe’s features, with a characteristic image size around 10 µm, well described by the magnetic monopole model. Each vortex carries one magnetic flux quantum Φ₀ = h/2e. However, in near-zero-field conditions, the picture changed dramatically: extended and tangled vortex structures emerged, with coexisting vortices of opposite polarity. Their number exceeded the possible trapped external flux, indicating a spontaneous origin. Fitting the field profiles with the monopole model yielded anomalously large penetration depth values λ—from ~1 to ~10 µm (compared to an equilibrium value below 100 nm)—pointing to a strong suppression of superfluid density near the core and, consequently, a nonequilibrium, frozen-in nature of these states. Repeated cooling cycles confirmed the stochastic appearance of vortices: their number, polarity, and positions varied from run to run, although preferred nucleation sites coincided, likely due to pinning centers. Numerical simulation of current distributions based on the inverse Biot–Savart law revealed highly branched and tortuous supercurrent paths, correlating with the composite’s fractal morphology. The interferometric principle of SQUID operation enabled high sensitivity in quantum measurements of magnetic flux.
Implications
The findings significantly expand our understanding of the formation and stabilization of topological defects in disordered systems. Contrary to the traditional Kibble–Zurek scenario, which requires ultra-fast cooling to freeze in phases, here vortices form even under slow cooling (~0.2 K/s) thanks to preexisting disconnected superconducting domains with independent phases. This makes the system a unique simulator of phase transitions in complex media—from cosmological inflationary processes to quantum phase transitions in solid-state devices. The observed vortex geometry serves as a direct imprint of local phase fluctuations at the moment global coherence is established, which was previously only a theoretical possibility.
Future development
Future development of the topic involves using a more sensitive technique—SQUID-on-tip with nanometer resolution—to map the structure of individual spontaneous vortices in detail. This will allow direct extraction of the phase correlation length and test the Kibble–Zurek scaling predictions. Additionally, the dynamics of vortices under changing external parameters (temperature, transport current) are of interest, which could shed light on dissipation mechanisms in highly disordered superconducting structures and find applications in cryogenic electronics.
Impact
This work will foster cross-disciplinary exchange between condensed matter physics and cosmology, as the proposed system is a tabletop analog of cosmic string formation processes. It may also influence the development of new superconducting materials with controlled defect topology.
Next steps
Next steps include systematic measurements at various cooling rates to verify universal scaling relations, as well as correlation analysis of the spatial vortex distribution using statistical methods.
Key open problems
The study is directly connected to the unresolved problem of describing phase transitions in disordered and fractal media, where standard mean-field theories break down. It also contributes to understanding the nonequilibrium dynamics of quantum systems under symmetry breaking, including dissipation mechanisms and the formation of topological defects in far-from-equilibrium conditions.
The knowledge machine's view
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
The work visualizes spontaneous vortices in the MgO/MgB₂ nanocomposite using scanning SQUID microscopy upon cooling in a nearly zero field. Extended, tangled vortex structures with opposite polarity were found, appearing stochastically across repeated cycles. Analysis of field profiles points to a nonequilibrium, frozen character of the states with suppressed superfluid density.
Where its strength is
Direct observation of the geometry of spontaneous vortices in a strongly disordered medium provides a rare experimental basis for studying the Kibble–Zurek scenario in mesoscopic superconductors. Particularly valuable is the coexistence of vortices of different polarity and their anchoring to the fractal morphology of the composite.
Where it could go next
- The link between the fractal geometry of current paths and the emergence of spontaneous vortices could be deepened through analysis similar to that performed for defects in graphene, where the role of the disordered network in shaping superconducting order was also studied.based on: Superconducting Web: How Defects in Graphene Weave Quantum Order arXiv:2607.02267
- The stochasticity and frozen nature of states in this system resonates with the idea of nonequilibrium dynamics during phase transitions, considered in the context of cosmic strings, where the cooling rate and correlation length also play a key role.based on: When the Universe Freezes: Gravitational Waves from Cosmic Strings arXiv:2607.20340v1
Worth trying
- Try applying correlation analysis of vortex positions of different polarities to estimate the correlation length, as is done in cosmic string models.
- Check whether the tortuosity of current paths can be described via fractal dimension, similar to approaches to defects in graphene.
- Investigate how the vortex distribution changes with varying cooling rate, to compare with predictions of the Kibble–Zurek scenario.
Why this may matter
Such experiments link condensed matter physics with cosmological models of defect formation, and understanding spontaneous vortices in disordered media may help in developing robust quantum devices, where such structures act as noise or, conversely, as control elements.
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Original abstract
as written by the authors arXiv:2607.14697
Observation of spontaneous symmetry breaking is crucial to our understanding of a continuous second-order phase transition from a disordered system into an ordered one, which often leads to the formation of topological defects. In the case of superconductors, such topological defects are identified as quantized vortices. However, their geometrical characteristics have not been well investigated and understood yet. For the imaging of spontaneous vortices, we employ a proximity-coupled superconducting nanocomposite. Here we show from scanning superconducting quantum interference device microscope measurements that vortices with different polarities, size and shapes are observed stochastically especially under near zero-field conditions. The field distributions of the spontaneous vortices are more extended and intricate than those of the field induced Abrikosov vortices, yielding longer penetration depths ranging from ~1 to ~10 micrometer. The spontaneous vortices are created during cooling as a result of the competition between Josephson coupling and thermal phase fluctuation, both of which are inherently present in this proximity-coupled system. The morphology of the vortices most likely imprints the information that is frozen at the time of vortex formation, providing insights into the local phase differences that are present in the early stage of the phase transition.
The magnetic flux quantum Φ₀ is remarkably small: just 2.07×10⁻¹⁵ V·s. To create a macroscopic field of 1 T, you’d need about 50 million such quanta per square millimeter. And the SQUID microscope used can detect changes as small as a fraction of this quantum!
The idea of cosmic strings, topological defects in spacetime analogous to vortices in superconductors, has repeatedly appeared in science fiction, such as the novel “Cosmic Strings” (author’s collection) or episodes of “Star Trek,” where they serve as sources of exotic energy and portals.
Key numbers
- Transition temperature T_c: ~37 K
- Penetration depth of spontaneous vortices: 1–10 µm
- SQUID pickup loop diameter: 10 µm
- Cooling rate: ~0.2 K/s
- Number of spontaneous vortices in zero field: up to ~10 over an area of 300×300 µm²