On the Author Correction to "Magnetic flux trapping in hydrogen-rich high-temperature superconductors", Nat Phys. 19, 1293 (2023), arXiv:2206.14108

This commentary paper refutes the claim that sulfur hydride (H$_3$S) exhibits high-temperature superconductivity via magnetic flux trapping, arguing that the experimental protocol used to generate the supporting time-dependent magnetic moment data is invalid and that an alternative protocol demonstrates the original evidence for vortex pinning is unfounded.

The Gist

Imagine a scientific detective story where a researcher is checking the work of a famous team that claimed to have discovered a "super-powerful" material.

The Original Claim
A group of scientists (Minkov and colleagues) published a paper claiming they found a way to trap magnetic fields inside a material called sulfur hydride ($H_3S$) under high pressure. They said this material acts like a "superconductor" (a material with zero electrical resistance) that works at very high temperatures.

Their main piece of evidence was a graph showing how the magnetic field inside the material changed over time. They argued that the field was slowly "creeping" or leaking out, which is a behavior expected in superconductors. They said, "Look, the field is changing exactly how we predicted!"

The Detective's Critique
N. Zen, the author of this paper, acts as the detective. He says, "Hold on. The way you measured this is flawed, and your conclusion doesn't hold up."

Here is the breakdown of his argument using simple analogies:

1. The "Stopwatch" Problem (The Delay)

To see if a magnetic field is slowly leaking (creeping), you have to start your stopwatch after you turn off the external magnet.

• The Flaw: The original team waited a very long time (38 hours) before they started their stopwatch.
• The Analogy: Imagine you are trying to prove a cup of hot coffee is cooling down. But you wait 38 hours before you even look at the thermometer. By the time you start watching, the coffee might already be cold, or the change might be so tiny you can't see it. You missed the most interesting part of the story.
• The Standard: Zen looked at hundreds of other successful experiments with known superconductors. He found that scientists usually start their "stopwatch" much sooner. The original team's method was like using a stopwatch that was set to start 38 hours late, making their data useless for proving the specific phenomenon they claimed.

2. The "Wrong Script" Problem

The original team tried to defend their long delay by saying, "We followed a standard protocol used by other scientists."

• The Flaw: Zen points out that the "standard protocol" they cited was published after the original team had already finished their experiment.
• The Analogy: It's like a chef saying, "I followed the recipe from a cookbook that wasn't published until next year." It's a logical impossibility. You can't follow a rule that didn't exist yet.

3. The "Zoomed-In" Photo Problem

The original team showed a graph (Figure 4c) that looked like a flat line, suggesting the magnetic field was stable or decaying very slowly.

• The Flaw: Zen argues they only showed a tiny, zoomed-in slice of the data.
• The Analogy: Imagine a movie of a car driving down a hill. The original team showed you a single frame where the car looks like it's stopped. Zen says, "If you zoom out and show the whole movie (a longer time scale), you might see the car is actually speeding up, or the data is just too short to tell what's happening."
• The Result: When Zen re-plotted the data with the correct "zoom level" (a longer time scale), the evidence for the "magnetic creep" disappeared. The data was too short to prove anything.

4. The Missing "Smoking Gun"

Zen points out that for a material to be a true superconductor, it needs to show two things:

1. The Meissner Effect: It should push magnetic fields away (like a magnet repelling another magnet).
2. Magnetic Hysteresis: It should trap magnetic fields in a specific, repeatable way.

The original team has never successfully shown these two things for sulfur hydride. They have only shown electrical resistance dropping to zero. Zen argues that zero resistance alone isn't enough proof; it could be a mix of metal and insulator acting weird, not a true superconductor.

The Conclusion

Zen concludes that the claim that sulfur hydride is a high-temperature superconductor is invalid based on the evidence provided.

• The measurement method was too short and started too late.
• The data doesn't actually show the "creeping" behavior they claimed.
• Without proof of the "Meissner effect" (pushing away magnets), the claim of superconductivity remains unproven.

In short: The paper argues that the "proof" of this super-powerful material is like a blurry, incomplete photo. When you look at the whole picture with the right tools, the evidence simply isn't there.

Technical Summary

Technical Summary: Commentary on "Magnetic flux trapping in hydrogen-rich high-temperature superconductors"

Problem Statement
This commentary addresses the validity of the experimental evidence presented by Minkov et al. in Nature Physics (2023) and its subsequent Author Correction (2025), which claim to observe magnetic flux trapping and thermally activated motion of vortices (TAMV) in hydrogen-rich high-temperature superconductors, specifically sulfur hydride (H$_3$S) under high pressure. The original claim relies on time-dependent magnetic moment data (flux creep) measured at 165 K, 180 K, and 185 K. The author argues that the experimental protocol used to collect this data is fundamentally flawed and inapplicable to the conditions of high-pressure H$_3$S, rendering the conclusion that H$_3$S traps magnetic flux invalid. Furthermore, the commentary highlights that the Author Correction contains a justification based on a protocol (Guven et al., 2024) that was published more than a year after the original experiments were conducted, creating a factual inconsistency.

Methodology
The author employs a comparative statistical analysis and a re-evaluation of the experimental timeline and scaling parameters:

1. Protocol Analysis: The commentary scrutinizes the "delay time" ($t_{delay}$), defined as the interval between turning off the external magnetic field and starting the measurement. It introduces a "measurement period index" ($p$) defined as $p \equiv \log(t_{end}/t_{delay})$, where $t_{end}$ is the end time of the measurement. This index quantifies the duration over which phenomena are observed relative to the delay.
2. Statistical Benchmarking: Using the review article by Yeshurun et al. (1996) and its 546 cited experimental data points, the author constructs a distribution of $t_{delay}$ and $p$ values from established flux creep experiments. The median $p$ value for these established studies is found to be 2.0.
3. Re-evaluation of Minkov et al. Data: The author calculates the $p$ values for the data reported by Minkov et al. (165 K, 180 K, and 185 K). These values are found to be significantly lower (0.38, <0.1, and <0.1, respectively) than the median of established studies and even lower than the $p \approx 0.78$ used in the Guven et al. (2024) protocol, which Minkov et al. claimed to follow.
4. Scaling and Visualization: The author re-plots the Minkov et al. data using the appropriate time scale required to achieve a $p$ value of 2.0 (the benchmark for valid TAMV claims). This involves extending the observation window to $1368 \times 10^4$ seconds for the 165 K data, and even longer for higher temperatures.
5. Contextual Verification: The paper cross-references the existence of the cited protocols against submission and publication dates to highlight chronological inconsistencies in the Author Correction.

Key Contributions and Results

• Invalidation of the Protocol: The study demonstrates that the $p$ values used by Minkov et al. are insufficient to claim the observation of flux creep. The data provided covers only a negligible fraction of the time scale required to distinguish between decay-free behavior and logarithmic decay.
• Chronological Inconsistency: The commentary points out that the protocol cited in the Author Correction (Guven et al., 2024) did not exist at the time Minkov et al. submitted their work (September 2022), undermining the claim that they followed an established "applied superconductivity" protocol.
• Re-plotted Data: When the Minkov et al. data is scaled to the appropriate $p=2$ boundary, the resulting plot (Fig. 2b) shows no data points sufficient to claim TAMV. The data is essentially "blank" regarding the long-term decay required to prove flux trapping.
• Lack of Supporting Evidence: The author reiterates that H$_3$S has not demonstrated the Meissner effect (field expulsion) or reproducible magnetic hysteresis loops, which are prerequisites for claiming superconductivity via magnetic evidence. The reliance on electrical zero-resistance data alone is deemed insufficient, as it can be mimicked by inhomogeneous granular mixtures of semiconducting and metallic phases.

Significance and Claims
The paper concludes that the claim by Minkov et al. that H$_3$S exhibits magnetic flux trapping and is a high-temperature superconductor is unsupported by the presented magnetic data. The author asserts that:

• The time-dependent magnetic moment data in Refs. [1, 2] represents only a "single scene" of a film stretched to appear as the whole, failing to capture the necessary long-term dynamics.
• Without a valid observation of TAMV or the Meissner effect, the ground state of "hydride superconductivity" cannot be regarded as superconducting based on current magnetic evidence.
• The most plausible scenario for the observed phenomena is an inhomogeneous granular mixture of phases rather than a true superconducting state.
• The study serves as a reminder that scientific truth must be built upon measured facts and rigorous protocols, rather than optimistic theoretical calculations or premature conclusions.

The author explicitly states that while no data manipulation is tolerated, the current evidence for hydride superconductivity is premature and requires a more objective and careful examination, particularly given recent theoretical studies suggesting lower transition temperatures for metallic hydrogen.