Distinguishing impurity-induced bound states from Majorana-like zero-energy peaks in strained CsCa2Fe4As4F2 by scanning tunneling microscopy

This study utilizes scanning tunneling microscopy under local strain to demonstrate that while CsCa2Fe4F2 exhibits zero-energy conductance peaks on specific defects that mimic Majorana zero modes, these features actually originate from nearly degenerate Yu-Shiba-Rusinov states, thereby clarifying the material's sign-changing multiband superconductivity and establishing robust methods to distinguish impurity-induced states from topological signatures.

The Gist

The Big Picture: Hunting for "Quantum Ghosts" in a Crystal

Imagine you are a detective trying to find a very specific, elusive ghost in a haunted house. In the world of physics, this "ghost" is called a Majorana Zero Mode (MZM). Scientists believe these particles are special because they could be the building blocks for super-fast, unbreakable quantum computers.

The researchers in this paper were looking for these ghosts inside a crystal called CsCa₂Fe₄As₄F₂. This crystal is a type of "iron-based superconductor," which means it conducts electricity with zero resistance at very low temperatures. It's a promising house for finding these ghosts, but it's a tricky one.

The Setup: Stretching the Crystal

To make the house more interesting, the scientists didn't just look at the crystal as it was; they gave it a little "stretch." They applied local strain (like gently bending a piece of metal) to the crystal.

• The Analogy: Think of the crystal as a trampoline. When it's flat, the springs (electrons) move in a predictable way. But when you stretch one side of the trampoline, the springs get tighter or looser in different spots.
• The Result: This stretching revealed that the crystal has a "fully gapped" superconducting state. Imagine a smooth, solid floor with no holes (nodes) in it. The stretching also made the different layers of the crystal's internal structure "speak up," allowing the scientists to see multiple distinct energy gaps that were previously hidden.

The Suspects: Defects in the Crystal

No crystal is perfect; they all have tiny flaws or "defects." The scientists looked at different types of these flaws to see how they affected the superconducting floor.

1. The "Harmless" Defect (Cs-site vacancy): This is like a missing brick on the outer wall of the house. It didn't disturb the floor much.
2. The "Troublemakers" (Defects II, III, and IV): These are flaws deep inside the house, near the floor itself. When the scientists looked at these, they saw "bound states"—little pockets of energy trapped inside the superconducting gap.
   • The Analogy: If the superconducting floor is a calm lake, these defects are like rocks sticking out of the water, creating small ripples (bound states) around them.

The Big Discovery: The "Zero-Energy Peak"

Here is where the plot thickens. On one specific type of defect (Defect IV), the scientists saw a very sharp spike in their measurements right at zero energy. They called this a Zero-Energy Conductance Peak (ZECP).

• The Suspicion: In previous experiments with similar materials, a spike like this was the "smoking gun" for a Majorana ghost (MZM). It looked exactly like what a quantum ghost should look like. The team thought, "Bingo! We found it!"

The Twist: It's Not a Ghost, It's a Twin

But the scientists didn't stop there. They decided to play "interrogation" with this spike to see if it was really a ghost or just an imposter. They used three different tests:

1. The "Super-Sharp Glasses" Test: They used a special "superconducting tip" (like putting on high-definition glasses) to look at the spike more closely.

   • What they found: The spike wasn't actually exactly at zero energy. It was slightly off-center. A real Majorana ghost must be perfectly centered.
   • The Real Culprit: The spike was actually two very close spikes (nearly degenerate states) that looked like one because their glasses weren't sharp enough before. It's like seeing two twins standing so close together they look like one person from a distance.

2. The "Magnetic Storm" Test: They turned on a strong magnetic field.

   • What they found: The spike got weaker and wider.
   • The Verdict: Real Majorana ghosts are tough; they ignore magnetic fields. This spike was weak and easily disturbed. It wasn't a ghost.

3. The "Tug-of-War" Test: They changed how close their measuring tool was to the crystal (tunneling transmissivity).

   • What they found: As they got closer, the single spike split into two separate peaks that moved apart.
   • The Verdict: This is exactly what happens with ordinary impurity states (the twins mentioned earlier). A real Majorana ghost would stay put and not split.

The Conclusion

The scientists concluded that while the crystal is a fascinating place with a complex, sign-changing superconducting structure (which is great news for understanding how these materials work), they did not find the Majorana ghosts.

The "Zero-Energy Peak" they saw was actually a Yu-Shiba-Rusinov state—a fancy name for a pair of ordinary quantum states that happen to be very close in energy, mimicking a ghost.

Why Does This Matter?

Even though they didn't find the ghost, this paper is a huge success for two reasons:

1. It teaches us how to be better detectives: The paper provides a strict checklist (using superconducting tips, magnetic fields, and distance tests) to prove whether a "ghost" is real or just a trick of the light. This will save other scientists from making false claims in the future.
2. It reveals the crystal's secrets: They learned that stretching the crystal changes its superconducting properties in cool ways, which helps us understand how to control these materials for future technology.

In short: They went looking for a unicorn, found a very convincing horse instead, and wrote a manual on how to tell the difference so everyone else doesn't get fooled.

Technical Summary

1. Problem Statement

Iron-based superconductors are promising platforms for exploring topological superconductivity and Majorana Zero Modes (MZMs). While MZMs have been observed in materials like Fe(Te,Se) and (Li,Fe)OHFeSe, their existence in other families, such as the 1111 and 122 families, remains unconfirmed.

• Specific Challenge: The 1111 and 122 families typically exhibit polar surfaces after cleavage, leading to trivial surface states that suppress the superconducting gap, hindering intrinsic property measurements.
• Material of Interest: $CsCa_2Fe_4As_4F_2$ (a member of the 122 family) offers a non-polar Cs-terminated cleavage plane with a high $T_c$ (~28–33 K). However, its superconducting pairing symmetry (nodal vs. fully gapped) is controversial, and the potential for topological superconductivity under local strain is unclear.
• Key Ambiguity: A sharp Zero-Energy Conductance Peak (ZECP) is often a signature of MZMs. However, distinguishing true MZMs from impurity-induced Yu-Shiba-Rusinov (YSR) states or other bound states is a persistent experimental challenge, particularly when ZECPs appear on specific defects.

2. Methodology

The researchers employed Scanning Tunneling Microscopy/Spectroscopy (STM/STS) under ultra-high vacuum and cryogenic conditions ($T = 80$ mK) to investigate $CsCa_2Fe_4As_4F_2$ single crystals.

• Sample Preparation: Crystals were mechanically cleaved at ~80 K to expose the non-polar Cs layer. The study focused on regions exhibiting unidirectional local strain (visible as surface wrinkles), which breaks the fourfold rotational symmetry.
• Tip Technology:
  • Metallic Tips: Standard PtIr tips were used for initial topography and spectroscopy.
  • Superconducting Tips: To achieve higher energy resolution, PtIr tips were coated with Lead (Pb) by indenting them into a clean Pb(111) surface. This allows for the detection of delicate in-gap states that might be obscured by thermal broadening or tip density of states (DOS) effects.
• Advanced Analysis:
  • Deconvolution: A numerical deconvolution method was applied to spectra taken with the superconducting tip to extract the intrinsic DOS of the sample, removing the convolution effects of the tip's own superconducting gap.
  • Parameter Variation: The team systematically varied the magnetic field (up to 5 T) and tunneling transmissivity (by adjusting tip-sample distance) to test the stability and evolution of observed zero-energy peaks.

3. Key Contributions

1. Strain-Induced Gap Modulation: Demonstrated that unidirectional local strain significantly modulates superconducting gap sizes and reveals multiple coherence peaks that are often hidden in strain-free regions, supporting a fully gapped multiband scenario.
2. Defect Characterization: Identified and classified four distinct types of defects (including Cs-site vacancies and subsurface defects) and mapped their specific in-gap bound state signatures.
3. Pairing Symmetry Confirmation: Provided strong evidence for sign-changing $s_{\pm}$ pairing symmetry by observing pair-breaking effects (in-gap bound states) induced by both magnetic and non-magnetic (Cs-site) impurities.
4. MZM vs. YSR Distinction: Established a rigorous experimental protocol to distinguish MZMs from impurity-induced bound states. The study conclusively proved that the observed sharp ZECPs in this system are not MZMs but rather nearly degenerate Yu-Shiba-Rusinov states.

4. Key Results

A. Superconducting Gap and Strain Effects

• Multiband Gap: STM spectra revealed a fully developed superconducting gap with four pairs of coherence peaks (3–10 meV), consistent with ARPES data.
• Strain Impact: Local strain (wrinkles) modulates the gap sizes differently for different bands ($\Delta_1$ to $\Delta_4$). Strain also breaks the $C_4$ symmetry, inducing electronic nematicity and making in-plane orbitals (like $d_{xy}$) detectable via STM due to $z$-axis orbital mixing.

B. Impurity Effects and Pairing Symmetry

• Cs-Site Vacancies (Non-magnetic): Even non-magnetic defects at the Cs site (outside the FeAs planes) induce in-gap bound states when probed with high-resolution superconducting tips.
• Subsurface Defects (II-IV): Defects II, III, and IV (likely Fe/As site or interstitial) induce strong pair-breaking effects with bound states at specific energies ($\approx \pm 2$ meV and 0 meV).
• Conclusion: The fact that non-magnetic impurities break Cooper pairs strongly supports a sign-changing pairing symmetry ($s_{\pm}$), as non-magnetic scattering is pair-breaking only if the order parameter changes sign between Fermi surface sheets.

C. The Nature of the Zero-Energy Conductance Peak (ZECP)

A sharp ZECP was observed on "Defect IV," initially resembling MZMs seen in Fe(Te,Se). However, systematic tests ruled out the MZM hypothesis:

1. Energy Resolution (Superconducting Tip): High-resolution spectra revealed that the "ZECP" is actually asymmetric and slightly shifted from zero energy. Deconvolution showed it consists of two pairs of nearly degenerate bound states (one pair very close to zero, another slightly further away) that merge into a single peak with lower-resolution metallic tips.
2. Magnetic Field Response: The peak intensity was strongly suppressed and broadened at 5 T. True MZMs are topologically protected and should be robust against magnetic fields (until the critical field is reached).
3. Tunneling Transmissivity: As the tip-sample distance decreased (increasing coupling), the single zero-energy peak split into two energy-symmetric branches moving away from $E_F$. This is characteristic of impurity-induced bound states shifting with coupling strength, whereas MZMs are predicted to remain pinned at zero energy and evolve toward quantized conductance ($2e^2/h$) without splitting.

5. Significance

• Material Physics: The study clarifies the superconducting mechanism in $CsCa_2Fe_4As_4F_2$, confirming it as a fully gapped, sign-changing multiband superconductor where local strain acts as a powerful tuning knob for electronic states.
• Methodological Advance: It provides a critical "rulebook" for distinguishing false positives in the search for Majorana modes. The authors demonstrate that sharp zero-energy peaks alone are insufficient evidence; one must verify particle-hole symmetry, magnetic field robustness, and transmissivity evolution to rule out nearly degenerate YSR states.
• Future Directions: The work establishes a systematic approach for identifying weak impurity signals and offers a new perspective for exploring topological properties in unconventional superconductors under local strain, guiding future searches for genuine topological superconductivity in iron-based materials.