Limitations of detecting structural changes and time-reversal symmetry breaking in scanning tunneling microscopy experiments

This paper argues that the reported magnetic field-induced changes in the lattice structure and charge density wave intensity of RbV$_3$Sb$_5$, previously interpreted as evidence of piezomagnetism, are actually artifacts caused by STM tip reconfiguration and instrumental distortions rather than intrinsic sample properties.

The Gist

Imagine you are trying to take a perfect, high-resolution photograph of a tiny, intricate mosaic floor (the atoms in a superconductor) to see if the pattern changes when you turn on a magnetic light or shine a laser on it.

This paper is essentially a forensic investigation into a recent scientific claim that said, "Hey, when we shine this light or turn on this magnet, the floor tiles actually stretch and the pattern changes!"

The authors of this paper, Christopher Candelora and Ilija Zeljkovic, are saying: "Stop the press. The floor didn't change. Your camera just glitched."

Here is the breakdown using simple analogies:

1. The "Camera Lens" Problem (The STM Tip)

In Scanning Tunneling Microscopy (STM), the "camera" is actually a needle so sharp it's only one atom wide. This needle drags across the surface to take a picture.

• The Claim: The original researchers thought the needle was just a passive observer. They believed that when the magnetic field changed, the floor (the sample) changed its shape.
• The Reality: The authors show that the needle itself is like a fickle paintbrush. Sometimes the tip gets a little bit of dirt on it, or a single atom on the very end of the needle falls off or moves.
• The Analogy: Imagine trying to trace a drawing with a pencil. If you accidentally drop a tiny piece of eraser on the tip of your pencil, your lines will look thicker or blurrier. If you then say, "Look! The drawing got thicker!" you are wrong. The drawing didn't change; your pencil tip did.
• The Evidence: The authors show that the "atomic fingerprints" (Bragg peaks) in the data change wildly—sometimes by 500%—between scans. If the floor were stable, these fingerprints should look identical every time. The fact that they change proves the "pencil tip" (the STM needle) was changing, not the floor.

2. The "Wobbly Tripod" Problem (Drift and Creep)

Even if your camera is perfect, the tripod it sits on might be wobbly. In these experiments, the "tripod" is the machine holding the sample, which uses piezoelectric crystals (materials that move when electricity is applied).

• The Claim: The original paper claimed the atoms moved by about 1% (a tiny amount, but huge in physics) when the magnetic field flipped.
• The Reality: The machine suffers from thermal drift (the room gets slightly warmer, expanding the metal) and piezo creep (the machine "creeps" or stretches slowly over time, like a rubber band that hasn't fully snapped back).
• The Analogy: Imagine you are measuring the distance between two trees with a tape measure. But, every time you take a measurement, the ground beneath you slowly sinks, or the tape measure itself stretches because it's hot. You might conclude the trees moved apart, but really, your measuring tape just got sloppy.
• The Evidence: The authors looked at the data and saw that the "trees" (atoms) seemed to move in random directions. Sometimes they moved left, sometimes right, with no logical pattern. If the magnetic field were the cause, the trees should move in a consistent, predictable way every time the field flipped. Instead, the movement looked like random noise caused by a wobbly tripod.

3. The "Forward vs. Backward" Glitch

The authors found a smoking gun in the data. When an STM scans a surface, it usually goes left-to-right (Forward), then right-to-left (Backward).

• The Logic: If the floor actually changed because of a magnet, the "Forward" picture and the "Backward" picture should tell the same story.
• The Glitch: The authors found that the Forward scans showed a "zig-zag" pattern that looked like a discovery, but the Backward scans showed the exact opposite.
• The Analogy: It's like taking a photo of a clock, then taking another photo of the same clock a second later. If the first photo says the time is 12:00 and the second says 6:00, you don't conclude the clock is broken; you conclude you made a mistake in how you took the photos. The inconsistency proves the "change" was an illusion created by the machine's movement, not the sample.

The Verdict

The original researchers claimed they discovered a rare phenomenon called piezomagnetism (where a magnetic field physically stretches a material).

Candelora and Zeljkovic argue that this is a false alarm. The "stretching" and "pattern changes" they saw were just:

1. Dirty or changing camera lenses (STM tip reconfiguration).
2. A wobbly, expanding tripod (thermal drift and piezo creep).

In short: The superconductor floor stayed perfectly still. The scientists just thought it moved because their microscope was having a bad day. This paper is a call to be much more careful with how we measure these tiny, delicate changes in the future.

Technical Summary

1. Problem Statement

The paper addresses a controversial claim made in a recent Nature study (Xing et al., 2024) regarding the kagome superconductor RbV$_3$Sb$_5$. The original study reported:

• Piezomagnetism: A rare phenomenon where an external magnetic field induces a $\sim$1% change in the in-plane lattice constants.
• Field-Dependent CDW: A modification of the $2 \times 2$ charge density wave (CDW) intensity and chirality controlled by the direction of the magnetic field.
• Optical Manipulation: Similar field-induced effects driven by electric fields (light).

Candelora and Zeljkovic argue that these conclusions are artifacts resulting from uncontrolled experimental variables in Scanning Tunneling Microscopy (STM), specifically STM tip reconfiguration and instrumental drift (piezo creep, hysteresis, and thermal drift), rather than intrinsic physical changes in the sample.

2. Methodology

The authors performed a rigorous re-analysis of the raw data and supplementary files provided in the original Xing et al. paper. Their methodology included:

• Tip Stability Analysis: Visual inspection of raw STM topographs to identify "tip changes" (reconfiguration of atoms at the tip apex). They compared the sharpness, anisotropy, and defect appearance across different scans.
• Fourier Transform (FT) Analysis:
  • Extracted intensities of atomic Bragg peaks ($I_B$) and CDW peaks ($I_{CDW}$) using the same "single pixel" method as the original authors.
  • Analyzed the consistency of peak intensities across different scan directions (Forward/FWD vs. Backward/BWD).
• Lattice Constant Measurement:
  • Calculated atomic Bragg peak lengths ($Q_{B,i}$) using a center-of-mass (COM) fitting method with a $5 \times 5$ pixel window.
  • Compared consecutive scans taken at the same magnetic field to establish a baseline for experimental error.
  • Analyzed the ratio $Q_{B,1}/Q_{B,3}$ to test for systematic trends versus random noise.
• Artifact Simulation: Used simulated topographies to demonstrate how piezo creep and thermal drift distort lattice images and shift Bragg peaks in a manner identical to the reported "piezomagnetic" effects.
• Data Consistency Checks: Specifically compared Forward (FWD) and Backward (BWD) scan data, which should yield identical physical results if the sample is stable, to expose non-self-consistent trends.

3. Key Contributions

The paper provides a critical rebuttal to the piezomagnetism claim by isolating specific experimental flaws:

1. Identification of Tip-Induced Artifacts: The authors demonstrate that the apparent changes in CDW intensity are caused by the STM tip changing shape (becoming sharper or duller) between scans. This alters the tunneling probability anisotropically, changing the apparent amplitude of modulations without any change in the sample.
2. Quantification of Instrumental Drift: They show that thermal drift and piezo creep can artificially distort measured lattice constants by several percent—magnitudes comparable to or larger than the reported $\sim$1% effect.
3. Exposure of Data Inconsistency: By analyzing FWD and BWD scans, they reveal that the reported "systematic" trends are absent or contradictory when both scan directions are considered.
4. Baseline Error Estimation: They establish that consecutive scans at the same field show variations in Bragg peak lengths of up to 2%, indicating that the reported 1% effect is indistinguishable from experimental noise.

4. Key Results

• Tip Changes Dominate CDW Intensity:
  • In the magnetic field dataset, atomic Bragg peak intensities varied by as much as five-fold between scans. Since atomic lattice structure should be invariant, this proves the tip changed significantly.
  • The CDW intensity ($I_{CDW}$) showed no systematic trend with magnetic field; it fluctuated randomly (e.g., becoming dimmer then brighter under identical field changes), correlating instead with the quality of the tip.
• Lack of Systematic Lattice Change:
  • The ratio of Bragg peak lengths ($Q_{B,1}/Q_{B,3}$) showed no consistent pattern upon magnetic field reversal.
  • FWD vs. BWD Contradiction: While Forward scans appeared to show a "zig-zag" trend consistent with piezomagnetism, Backward scans showed the opposite trend for the majority of data points. This proves the trend is an artifact of the scanning process (drift), not the sample.
• Consecutive Scan Variability:
  • Under a constant magnetic field ($B = -2$ T), individual Bragg peak lengths varied by up to 2% between consecutive scans. This establishes that the experimental error margin is larger than the claimed physical effect.
• Optical/Light Manipulation Data:
  • Similar analysis of the electric field (light) dataset revealed indiscriminate variations in Bragg peak intensities and CDW signals, along with visible tip changes (e.g., defects appearing different, QPI rings disappearing).
  • The authors conclude that no evidence exists for electric-field-induced effects in this dataset either.

5. Significance

• Refutation of Piezomagnetism: The paper concludes that there is no evidence supporting the claim that magnetic fields induce intrinsic lattice distortions or piezomagnetism in RbV$_3$Sb$_5$. The reported effects are fully explainable by standard STM artifacts.
• Methodological Warning: It serves as a critical case study for the STM community, highlighting the necessity of:
  • Monitoring tip stability rigorously.
  • Comparing Forward and Backward scans to detect drift.
  • Taking multiple consecutive scans at fixed conditions to quantify noise floors.
  • Avoiding the interpretation of single-scan comparisons as physical phenomena.
• Impact on Kagome Physics: By challenging the existence of field-induced structural changes, the paper suggests that the time-reversal symmetry breaking and chiral charge order in kagome superconductors may not be driven by the piezomagnetic mechanism proposed in the original study, necessitating a re-evaluation of the underlying physics of these materials.

In summary, Candelora and Zeljkovic demonstrate that the original findings were likely misinterpretations of instrumental noise, urging a more rigorous approach to data analysis in high-precision STM experiments.