🔬 condensed matter

Visualizing Pair-breaking Scattering Interference in Bulk FeSe

Using scanning tunneling microscopy with superconductive tips, this study identifies subsurface magnetic scatterers in bulk FeSe that generate particle-hole symmetric gap modulations and Josephson current oscillations consistent with pair-breaking scattering interference, establishing PBSI as a viable mechanism for gap modulations in superconductors without preexisting density wave orders.

Original authors: Matthew Toole, Nileema Sharma, James McKenzie, Fangjun Cheng, Sheng Ran, Xiaolong Liu

Published 2026-07-03

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CC BY 4.0

Original authors: Matthew Toole, Nileema Sharma, James McKenzie, Fangjun Cheng, Sheng Ran, Xiaolong Liu

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a superconductor as a perfectly synchronized dance floor where pairs of electrons (the dancers) move in lockstep. Usually, this dance is uniform across the entire floor; everyone is doing the same step at the same time. However, scientists have recently noticed that in some materials, the "dance steps" (the energy gap) seem to ripple and change size in a repeating pattern, like waves on a pond.

For a long time, scientists thought these ripples meant the dancers were forming a new, exotic type of dance called a "Pair Density Wave" (PDW), where the pairs themselves had a specific momentum. But this paper suggests there might be a much simpler explanation: interference caused by a clumsy dancer bumping into a wall.

Here is a breakdown of what the researchers found, using simple analogies:

1. The Setting: A Perfect Dance Floor (FeSe)

The researchers studied a material called FeSe (Iron Selenide). Think of this as a very clean, empty dance floor with no pre-existing obstacles or patterns. Because it's so clean, if they see a ripple in the dance, they know it wasn't caused by a pre-existing pattern in the floor itself.

2. The Culprit: The Magnetic Impurity (The "Bumper")

Inside this clean dance floor, they found tiny, hidden "bumpers" (magnetic impurities) buried just under the surface. When a pair of dancers (electrons) hits one of these bumpers, it doesn't just bounce off; it creates a disturbance.

In the world of quantum physics, this bumper creates a special "echo" state called a Yu-Shiba-Rusinov (YSR) state. You can think of this as a ripple spreading out from where the bumper is located.

3. The Discovery: The Ripple Effect (PBSI)

The team used a super-sensitive microscope (Scanning Tunneling Microscopy) with a special "super-conductive" tip. This tip acts like a high-definition camera that can see the dance steps with incredible clarity, far better than standard cameras.

They discovered that around these hidden bumpers, the size of the dance steps (the superconducting gap) wasn't uniform. Instead, it created a standing wave pattern:

The gap got slightly larger in some spots and slightly smaller in others.
This pattern repeated itself in a straight line, like ripples moving away from a stone dropped in water.

4. The "Aha!" Moment: It's Interference, Not a New Dance

The researchers realized this pattern wasn't a new type of dance (PDW). Instead, it was Pair-Breaking Scattering Interference (PBSI).

The Analogy:
Imagine two people walking in perfect sync (a Cooper pair). If they hit a wall (the magnetic impurity), they scatter. Because they are quantum particles, they act like waves. When these scattered waves meet other waves from the same group, they interfere with each other.

Sometimes the waves add up (making the gap look bigger).
Sometimes they cancel out (making the gap look smaller).

This interference creates the visible ripples in the gap size. The paper shows that the specific direction and spacing of these ripples match exactly what you would expect if the electrons were just bouncing off these magnetic bumpers and interfering with themselves.

5. The Proof: Checking the Rhythm

To be absolutely sure, the researchers didn't just look at the size of the steps; they looked at the rhythm (phase) of the dance at different energy levels.

They checked the dance floor at two different "speeds" (energies).
They found that when the ripples were at a "peak" (high point) at one speed, they were at a "valley" (low point) at the other speed.
This specific "out-of-phase" relationship is the fingerprint of the interference mechanism (PBSI), proving it wasn't a complex new state of matter.

The Main Takeaway

The paper concludes that you don't need a complex, exotic new state of matter (PDW) to explain these ripples. Sometimes, a simple magnetic impurity causing quantum interference (PBSI) is enough to create the same pattern.

This is important because scientists have been seeing these ripples in many different materials and assuming they all mean a new "Pair Density Wave" state exists. This study acts as a "reality check," warning researchers: "Before you claim you found a new exotic state, check if a simple magnetic bump is just causing an interference pattern."

In short: The ripples in the superconducting gap of FeSe are likely just the quantum echo of a magnetic bump, not a sign of a fundamentally new way electrons pair up.

Problem Statement
Recent scanning tunneling microscopy (STM) studies have identified spatially periodic modulations of the superconducting gap ( $\Delta$ ) in various materials. These modulations are frequently attributed to Pair Density Wave (PDW) order, a state where electrons pair with a finite center-of-mass momentum ( $\mathbf{Q}$ ), resulting in particle-hole symmetric gap modulations ( $\Delta(\mathbf{r}) \propto \cos(\mathbf{Q} \cdot \mathbf{r})$ ). However, in superconductors lacking preexisting spin or charge density wave (S/CDW) orders, the attribution of such modulations to fundamental PDWs is contentious. A theoretical mechanism termed Pair-Breaking Scattering Interference (PBSI) has been proposed as an alternative origin. PBSI suggests that scattering off magnetic impurities can induce periodic gap modulations without requiring finite-momentum pairing. Distinguishing between genuine PDW states and PBSI-induced modulations remains a critical challenge, particularly in materials like bulk FeSe where no S/CDW orders exist.

Methodology
The authors investigated bulk FeSe, a nematic $s_{\pm}$ -wave superconductor chosen for its simple structure, well-established Fermi surface, and absence of intrinsic density wave orders. To isolate and characterize potential PBSI signatures, the study employed Scanned Josephson Tunneling Microscopy (SJTM) at 300 mK using superconducting Niobium (Nb) tips. This approach offers enhanced energy resolution beyond the Fermi-Dirac limit, crucial for resolving subtle gap modulations.

The experimental strategy involved three primary techniques:

Gap Mapping: Acquiring $dI/dV$ spectra at each pixel to extract the spatially dependent superconducting gaps ( $\Delta_{0,2}^{\pm}(\mathbf{r})$ and $\Delta_{1,2}^{\pm}(\mathbf{r})$ ) for the $\alpha$ and $\epsilon$ electron/hole pockets. The data was deconvoluted to obtain the Local Density of States (LDOS) of FeSe.
Josephson Current Imaging: Mapping the maximum Josephson tunneling current ( $I_J \propto I_c^2$ ) to visualize superfluid density modulations.
Phase-Referenced Quasiparticle Interference (QPI): Analyzing the phase relationships of differential conductance $g(\mathbf{r}, E)$ at different energies. A generalized phase-referenced signal, $g_{pr}(\mathbf{q}, E', E'') = |g(\mathbf{q}, E')| \cos[\theta(\mathbf{q}, E') - \theta(\mathbf{q}, E'')]$ , was calculated in Fourier space to independently probe the nature of the modulations.

Key Results

Identification of Magnetic Scatterers: The study identified subsurface point defects in FeSe exhibiting Yu-Shiba-Rusinov (YSR) states. These states appeared as sharp, particle-hole symmetric in-gap bound states ( $E \approx \pm 2.47$ meV) with asymmetric peak heights and spatial dispersion, accompanied by a suppression of the Josephson current. These features confirm the presence of magnetic impurities.
Observation of Gap Modulations: Gap mapping revealed periodic spatial modulations of the superconducting gaps around these magnetic impurities. The modulations were particle-hole symmetric and aligned along the $\mathbf{q}_{\Gamma M}$ direction.
Wavevector Consistency: The wavevectors of the observed gap modulations ( $1.3 \text{ nm}^{-1}$ ) matched the intra-pocket scattering vectors ( $\mathbf{Q}_0$ and $\mathbf{Q}_1$ ) connecting the tips of the banana-shaped constant energy contours within the $\alpha$ and $\epsilon$ pockets, respectively.
Symmetry and Phase Analysis:
- Symmetrized gap analysis ( $\Delta^{sym}$ ) showed enhanced modulation intensity at $\mathbf{Q}_0$ , while anti-symmetrized analysis ( $\Delta^{anti}$ ) showed suppression, confirming in-phase spatial modulations of the positive and negative coherence peaks.
- Phase-referenced QPI imaging demonstrated that conductance modulations at energies outside the coherence peaks ( $\pm 3.87$ meV) were in-phase, while those inside ( $\pm 3.23$ meV) were out-of-phase. The sign patterns of the $g_{pr}(\mathbf{q}, E', E'')$ signals at $\mathbf{Q}_0$ were consistent with the theoretical predictions for $s=1$ (sign-preserving) intra-pocket PBSI.
- Josephson current imaging showed faint modulations along the same direction as the gap modulations, consistent with theoretical predictions of simultaneous $I_J(\mathbf{r})$ and $\Delta(\mathbf{r})$ modulations around magnetic impurities.

Significance and Claims
The paper establishes Pair-Breaking Scattering Interference (PBSI) as a viable mechanism for generating periodic gap modulations in superconductors that lack preexisting charge or spin density wave orders. By demonstrating these signatures in bulk FeSe—a material free of composite PDW drivers—the authors provide a benchmark for distinguishing PBSI from fundamental finite-momentum pairing (PDW).

The study highlights that the observed gap modulation amplitude (0.12 meV) is substantially larger than those reported in materials with composite PDWs. Consequently, the authors argue for caution when attributing sizable, periodic gap modulations to PDW states in the absence of other dominant density wave orders. The work also introduces phase-referenced QPI imaging as a direct and independent probe for diagnosing PBSI, offering an alternative to direct gap mapping. Finally, the results motivate further theoretical investigation into PBSI signatures arising from inter-pocket scattering processes involving multiple anisotropic gaps.