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Direct real-space imaging of sign-reversal superconducting state by scanning Josephson tunneling

Using scanning Josephson tunneling microscopy, researchers directly imaged half-unit-cell periodic modulations in monolayer Fe(Te,Se) films that confirm a sign-reversal nodeless d-wave pairing symmetry, overcoming previous limitations in determining the complex pairing mechanisms of iron-based superconductors.

Original authors: Tianheng Wei, Yanzhao Liu, Wei Ren, Zhen Liang, Ziqiang Wang, Jian Wang

Published 2026-10-30

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CC BY 4.0

Original authors: Tianheng Wei, Yanzhao Liu, Wei Ren, Zhen Liang, Ziqiang Wang, Jian Wang

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

At the heart of the most mysterious materials in physics lies a simple question: how do electrons pair up to flow without resistance? In many high-temperature superconductors, these pairs are not identical twins; they are more like partners moving in opposite directions, a state known as sign-reversal. Determining the exact shape of this partnership, or its symmetry, is crucial because it reveals the hidden forces that bind the electrons together. For decades, scientists have relied on large-scale experiments to guess at these shapes, but these methods often blur the fine details, much like trying to read a book from a mile away. The challenge has been particularly sharp for iron-based superconductors, a powerful family of materials where the rules of pairing are complex and the signals are often muddled by the presence of multiple electron types.

A team of researchers has now looked at this problem with a microscope so powerful it can see individual atoms, offering a direct view of how these electron pairs behave. By using a specialized technique called scanning Josephson tunneling microscopy, they mapped the superconducting state of a single layer of iron-based material grown on a crystal surface. Instead of seeing a uniform glow of superconductivity, they found a striking pattern of light and dark spots that repeated every half-atom. Most importantly, they discovered that the signal from the electron pairs vanished completely along specific lines connecting the atoms. This "zero line" is not a defect or a gap in the material, but a fundamental signature of the electron pairs canceling each other out. The findings strongly suggest that the electrons in this material are paired in a specific, sign-reversing pattern known as nodeless d-wave, a shape that had been theorized but never directly visualized in this way.

The story begins with a material that has puzzled scientists for years: a single layer of iron, tellurium, and selenium, just one atom thick, sitting on a surface of strontium titanate. This film is famous for becoming a superconductor at relatively high temperatures, yet its internal structure remains a subject of intense debate. To understand what is happening inside, the researchers needed a tool that could probe the quantum phase of the electron pairs, a property that determines how they move and interact. They turned to a scanning tunneling microscope equipped with a tip coated in lead, a conventional superconductor. As this superconducting tip hovers just above the iron-based film, it forms a microscopic bridge, allowing electron pairs to tunnel across the gap. The strength of this tunneling current depends on how the phases of the electron pairs in the tip and the film align.

The researchers did not just measure the current at a single point; they scanned the tip across the surface, atom by atom, recording the strength of the tunneling signal at every location. What they found was a landscape of dramatic contrast. The signal was strongest at the midpoints between neighboring iron atoms, but as the tip moved toward the lines connecting the next-nearest iron atoms, the signal dropped sharply. In fact, along these diagonal lines, the tunneling current almost entirely disappeared. This is a profound observation because the distance between these points is incredibly small, far smaller than the typical size of a superconducting region. If the material were simply uneven or if the superconductivity were patchy, the signal would not vanish so precisely along these specific geometric lines. The vanishing signal indicates that the electron pairs on one side of the line are perfectly out of step with those on the other, causing them to cancel each other out through destructive interference.

This cancellation is the smoking gun for a specific type of pairing symmetry. In the language of quantum mechanics, the researchers found that the electron pairs change their sign when reflected across these diagonal lines. This behavior matches the theoretical prediction for a nodeless d-wave state, where the pairing function has a specific shape that flips its sign under certain rotations and reflections. The team confirmed that this pattern is not an artifact of their equipment or the specific material composition by testing other superconductors. When they performed the same experiment on a conventional superconductor made of lead, the signal remained uniform, showing no such cancellation. When they looked at a bulk version of the iron-based material, which is known to have a different pairing structure, the signal was also uniform. However, when they tested a different iron-based film and a famous copper-based superconductor, both known to have d-wave symmetry, they saw the same vanishing signal along the diagonal lines.

The results provide a clear, real-space picture of the superconducting state in these iron-based films. The researchers argue that the electron pairs in this single-layer material are not following the simple, uniform pattern seen in many other iron-based superconductors. Instead, they are locked into a complex, sign-reversing dance that creates these lines of zero signal. This finding supports the idea that the high-temperature superconductivity in these films arises from a specific type of pairing that was previously only a hypothesis. By visualizing the interference of electron pairs directly on the atomic scale, the study offers a new way to understand the mechanisms behind superconductivity. It suggests that the key to unlocking the secrets of these materials may lie in looking at the subtle cancellations and alignments of electron pairs right where they live, rather than averaging them out over a large area. The work opens a path for exploring other exotic superconductors with the same level of detail, potentially revealing the hidden rules that govern how matter conducts electricity without loss.

Technical Summary: Direct Real-Space Imaging of Sign-Reversal Superconducting State by Scanning Josephson Tunneling

Problem and Motivation
Determining the superconducting pairing symmetry is a fundamental step in identifying the mechanism of unconventional high-temperature superconductivity. While phase-sensitive Josephson tunneling experiments have successfully established $d$ -wave symmetry in high- $T_c$ cuprates, applying these methods to iron-based superconductors (FeSCs) has proven difficult. In FeSCs, the complexity of multiband pairing symmetries and the challenges in fabricating high-quality, homogeneous macroscopic Josephson junctions have limited phase-sensitive studies, particularly for heavily doped systems like monolayer FeSe and Fe(Te,Se) films grown on SrTiO $_3$ (STO). These specific monolayer films possess only electron Fermi pockets and exhibit the highest transition temperatures among FeSCs, yet their pairing symmetry remains debated, with candidates ranging from $s$ -wave to sign-reversal $d$ -wave. Traditional tunneling experiments lack the necessary spatial and momentum resolution to unambiguously distinguish between these candidates in such multiband systems.

Methodology
To address these limitations, the authors employed Scanning Josephson Tunneling Microscopy (SJTM), a technique utilizing a superconducting tip to form a spatially tunable microscopic Josephson junction with the sample. Unlike macroscopic junctions, SJTM avoids inhomogeneity issues and offers sub-atomic spatial resolution. The experiments were conducted on high-quality, one-unit-cell (1-UC) thick Fe(Te,Se)/STO films grown via molecular beam epitaxy (MBE). The measurements were performed at ultralow temperatures (below 150 mK) using a superconducting Pb-coated PtIr tip ( $s$ -wave symmetry).

The study focused on measuring the zero-bias Josephson tunneling conductance ( $g_J$ ), which is proportional to the square of the Josephson critical current ( $I_c^2$ ). By scanning the tip across the atomic lattice, the authors mapped the spatial distribution of $g_J$ and compared it with single-particle tunneling spectra and atomic topography. To validate the robustness of the technique, similar measurements were performed on a diverse set of control samples: monolayer FeSe/STO, bulk Fe(Te,Se), a conventional $s$ -wave Pb film on Si(111), and the high- $T_c$ cuprate Bi $_2$ Sr $_2$ CaCu $_2$ O $_{8+x}$ .

Key Results

Half-Unit-Cell Periodic Modulations: In the 1-UC Fe(Te,Se)/STO film, the Josephson tunneling signal ( $g_J$ ) exhibited a distinct spatial modulation with a period of half the lattice constant ( $a_{Te/Se}/2$ ). The signal was maximized at the midpoints of nearest-neighbor Fe-Fe bonds but almost vanished along the lines connecting next-nearest-neighbor Fe atoms.
Symmetry-Protected Zero Lines: The lines of vanishing $g_J$ coincided precisely with the diagonal mirror planes ( $m_d$ ) of the crystal lattice. This "zero line" phenomenon was observed consistently across different setup conditions and with different tips, indicating it is an intrinsic property of the superconducting state.
Contrast with Control Samples:
- Monolayer FeSe/STO: Showed similar half-unit-cell modulations with zero lines, suggesting a universal pairing symmetry for heavily electron-doped monolayer FeSCs.
- Cuprate Bi $_2$ Sr $_2$ CaCu $_2$ O $_{8+x}$ : Displayed analogous modulations with zero lines along diagonal Cu-Cu lines, consistent with its known $d_{x^2-y^2}$ -wave symmetry.
- Bulk Fe(Te,Se) and Pb/Si(111): Both conventional $s$ -wave superconductors (bulk Fe(Te,Se) with $s_{\pm}$ symmetry and Pb with plain $s$ -wave) exhibited relatively uniform $g_J$ maps without sub-unit-cell modulations or zero lines.
Single-Particle Spectra: Single-particle tunneling spectra measured with a metallic tip revealed a fully opened superconducting gap (>10 meV) at all atomic positions, ruling out the possibility that the zero lines in $g_J$ were caused by local gap closures or inhomogeneous superfluid density.

Interpretation and Theoretical Analysis
The authors interpret the vanishing $g_J$ along the diagonal mirror lines as a result of destructive quantum interference between Josephson tunneling channels originating from different Fermi pockets. Since the tip is an $s$ -wave superconductor, the symmetry of the critical current $I_c$ is determined by the sample's pairing function.

The observation that $I_c$ changes sign under diagonal mirror reflection ( $\sigma_d$ ) but remains even under vertical mirror reflection ( $\sigma_v$ ) is mathematically consistent with a nodeless $d$ -wave pairing symmetry (specifically the $B_{2g}$ representation).
In this scenario, the superconducting order parameters on the two electron Fermi pockets (derived from $xz/xy$ and $yz/xy$ orbitals) have opposite signs. When the tip is positioned on the diagonal mirror plane, the tunneling amplitudes from these two pockets interfere destructively, driving the net critical current to zero.
Theoretical calculations based on tight-binding models and symmetry analysis confirmed that only the nodeless $d$ -wave state reproduces the observed sub-unit-cell modulation pattern and zero lines. Extended $s_{\pm}$ or plain $s$ -wave scenarios were shown to be inconsistent with the data as they lack the necessary symmetry protection to create such zero lines.

Significance
The paper claims to provide the first microscopic, real-space visualization of sign-reversal superconductivity in a monolayer iron-based superconductor. By demonstrating that SJTM can resolve sub-unit-cell phase information and distinguish between $d$ -wave and $s$ -wave symmetries at the atomic scale, the work offers a robust, phase-sensitive experimental approach that does not require the fabrication of complex macroscopic junctions. This technique is presented as a viable method for investigating the pairing mechanisms in other unconventional superconducting systems, including heavily doped FeSCs, cuprates, heavy-fermion systems, and moiré superconductors. The findings support the theoretical prediction that heavily electron-doped monolayer FeSCs host a nodeless $d$ -wave pairing state, distinct from the $s_{\pm}$ state found in their bulk counterparts.

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