Direct observation of vortex liquid droplets in the iron pnictide superconductor CaKAs$_4$Fe$_4$ at $0.5T$_c$

Using scanning tunneling microscopy, researchers observed localized vortex liquid droplets in the iron pnictide superconductor CaKAs$_4$Fe$_4$ at temperatures as low as 0.5$T_c$, revealing that the onset of local dissipation occurs considerably below the critical temperature where macroscopic melting transitions are typically detected.

The Gist

Imagine a superconductor as a magical, friction-free dance floor where tiny particles called electrons glide together without losing any energy. Usually, this dance floor is perfect. But if you introduce a magnetic field (like a strong wind blowing across the floor), it creates tiny whirlpools in the electron flow. Scientists call these vortices.

In a perfect world, these whirlpools would line up in a neat, rigid grid, like soldiers standing at attention. This is called a "vortex solid." As long as they stay pinned in place, the superconductor remains perfect. But if they start to wiggle, slide, or melt into a chaotic mess, the superconductor starts to lose energy (dissipation).

Here is what this paper discovered, explained simply:

1. The "Melting" Surprise

For a long time, scientists thought these vortex whirlpools only started to melt and become chaotic right near the point where the material stops being a superconductor entirely (called the critical temperature, or $T_c$). It was like thinking ice only melts when it's about to turn into a puddle of water.

However, the researchers looked at a specific iron-based superconductor called CaKFe$_4$As$_4$ using a super-powerful microscope called a Scanning Tunneling Microscope (STM). This microscope is like a camera so sensitive it can see individual whirlpools.

The Discovery: They found that the whirlpools don't wait until the very end to melt. Even when the material is still very cold (only half as hot as its maximum limit), tiny, isolated islands of chaos appear. They call these "vortex liquid droplets."

2. The Analogy: The Frozen Lake with Hot Patches

Imagine a frozen lake (the superconductor) covered in a grid of ice sculptures (the vortices).

• The Old View: You'd think the whole lake stays frozen until the sun gets very hot, and then the ice turns to water all at once.
• The New View: The researchers found that even on a cold day, there are small, localized puddles of water (the "droplets") forming right next to the ice sculptures. The ice sculptures in these puddles are wiggling and sliding around wildly, while the rest of the lake is still frozen solid.

These "puddles" are areas where the thermal energy (heat) is strong enough to break the "pins" holding the whirlpools in place, causing them to move around locally, even though the rest of the material is still behaving like a solid.

3. Why Do They Move? (The Pinning Problem)

Why do some whirlpools stay still while others turn into a liquid droplet? It comes down to pinning.

Think of the material as a bumpy road. The whirlpools like to get stuck in the potholes (defects in the crystal).

• Strong Potholes: If a whirlpool lands in a deep pothole, it stays stuck. It's a "vortex solid."
• Weak Potholes: If the whirlpool is on a flat spot or a shallow bump, the heat makes it wiggle free. It starts hopping around, creating a "vortex liquid droplet."

The researchers found that these droplets form in specific spots where the "potholes" aren't strong enough to hold the whirlpools against the heat. They even tracked individual whirlpools over time and saw some hopping short distances, while others stayed put for hours.

4. What This Means for the "Perfect" State

The big takeaway is that the "perfect" superconducting state isn't as uniform as we thought.

• Macroscopic View: If you look at the whole material with a standard meter, it looks like a perfect superconductor because the "puddles" are so small and scattered that the electricity can still flow around them (like water flowing around small rocks in a stream).
• Microscopic View: But if you zoom in, you see that the material is actually a mix of frozen solid and liquid chaos. The "perfect" state exists in a much smaller temperature range than previously believed.

Summary

The paper shows that in this specific superconductor, the transition from "frozen" to "liquid" isn't a single event that happens all at once when it gets hot. Instead, it's a messy, local process. Tiny islands of chaotic, moving whirlpools appear deep inside the cold material, floating in a sea of frozen, pinned whirlpools. This teaches us that the "perfect" superconducting state is more fragile and complex than we realized, depending heavily on the tiny, local imperfections in the material's structure.

Technical Summary

Technical Summary: Direct Observation of Vortex Liquid Droplets in CaKFe$_4$As$_4$

Problem Statement
In Type-II superconductors, magnetic fields penetrate the material as quantized vortices. While vortices typically form an ordered lattice (vortex solid) pinned by defects, thermal fluctuations can induce a phase transition to a disordered, mobile state (vortex liquid), leading to energy dissipation. Macroscopic experiments and spatially averaged techniques have established that this melting transition generally occurs very close to the critical temperature ($T_c$). However, it remains unclear how the vortex solid responds to thermal fluctuations at the scale of individual vortices at temperatures significantly below $T_c$. Specifically, the local onset of dissipation and the spatial coexistence of solid and liquid phases in the intermediate temperature regime are not well characterized.

Methodology
The authors utilized Scanning Tunneling Microscopy (STM) to directly visualize individual superconducting vortices in the iron pnictide superconductor CaKFe$_4$As$_4$ ($T_c \approx 35$ K) under magnetic fields up to 14 T. This material was selected for its relatively high $T_c$, small coherence length ($\xi < 2$ nm), and well-defined pinning landscape involving intergrown CaFe$_2$As$_2$ and KFe$_2$As$_2$ layers.

The experimental approach involved:

1. Zero-Bias Conductance Mapping: Mapping the tunneling conductance at zero bias, which is proportional to the local density of states (LDOS) at the Fermi level. Vortex cores exhibit a higher LDOS (normal state) compared to the superconducting bulk.
2. Temperature and Field Variation: Conducting measurements at temperatures ranging from 10 K to 30 K (up to $\approx 0.85 T_c$) and magnetic fields from 2 T to 14 T.
3. Time-Resolved Tracking: Acquiring sequential conductance maps over periods of approximately 150 minutes at fixed temperatures and fields to track vortex trajectories and measure thermally induced mobility.
4. Phase Identification: Distinguishing between a "vortex solid" (where individual vortices are resolved), "vortex liquid droplets" (localized regions where vortices fluctuate strongly, appearing as merged patches), and a global "vortex liquid" (spanning the field of view).

Key Contributions and Results
The study provides direct real-space evidence of localized vortex melting well below the macroscopic melting temperature:

• Observation of Vortex Liquid Droplets: The authors identified localized regions, termed "vortex liquid droplets," where vortices strongly fluctuate due to thermal excitation. These droplets appear as areas where individual vortices merge into larger patches, distinct from the surrounding disordered vortex solid where individual vortices remain resolvable.
• Low-Temperature Onset: These liquid droplets were observed at temperatures as low as $0.5 T_c$ (15 K) in a 10 T field. This is significantly lower than the melting transition temperatures typically observed in macroscopic measurements.
• Coexistence of Phases: The results demonstrate a broad crossover region where solid and liquid vortex phases coexist within the same sample. The transition is not uniform; rather, melting initiates locally in areas with enhanced thermal fluctuations.
• Vortex Mobility and Pinning: By tracking vortex trajectories over time, the authors found that vortex mobility is highly dependent on the magnetic field and the local pinning landscape.
  • At low fields (e.g., 2 T), vortices exhibit significant mobility, traveling distances far exceeding the intervortex spacing.
  • At intermediate fields (around 8–10 T), mobility is minimized, and vortices remain largely pinned.
  • The accumulated distance traveled by vortices follows a field dependence consistent with the Dew-Hughes pinning model ($\propto h^p(1-h)^q$), suggesting that the pinning mechanism is governed by surface-like interactions (likely the intergrown layers) rather than point defects alone.
• Correlation with Macroscopic Data: The local observation of liquid droplets extends the vortex liquid phase region in the phase diagram down to $0.5 T_c$, contrasting with macroscopic phase diagrams that typically show a solid phase dominating until much closer to $T_c$.

Significance and Claims
The paper claims that the melting of vortices in superconductors is not a uniform, global transition but a process strongly linked to the local pinning potential landscape. The primary significance of these findings includes:

1. Local Dissipation Onset: The onset of dissipation at the local scale occurs at temperatures considerably below $T_c$ in Type-II superconductors, challenging the view that the vortex solid remains stable until near $T_c$.
2. Implications for Critical Currents: The existence of liquid droplets suggests that even in samples with high critical current densities (where macroscopic voltage drops are zero), local dissipation may be occurring via percolation paths. This is particularly relevant for micron-sized samples or nanostructured superconductors where the formation of such droplets could significantly impact performance.
3. Pinning Landscape Complexity: The study highlights that the interplay between thermal fluctuations and a complex pinning landscape (involving both linear defects and point disorder) governs the formation of liquid droplets. The observation that liquid droplets form preferentially in areas of enhanced fluctuation, even far from $T_c$, underscores the fundamental relevance of enhancing vortex pinning for functional superconducting devices.

The authors conclude that their data reveals a broad coexistence region of solid and liquid phases, indicating that the actual dissipationless superconducting phase has a much smaller temperature range than what is inferred from macroscopic experiments alone.