Nodeless d-wave pairing in monolayer FeSe revealed by intra-unit-cell Josephson interferometry

Runxin Li; Yuchen Huo; Jiong Mei; Ming-Qiang Ren; Miaomiao Wang; Quanxing Wei; Fengyu Yao; Maowen Zheng; Qing Qu; Cui Ding; Hongtao Yuan; Zhuoyu Chen; Wei-Qiang Chen; Kun Jiang; Qi-Kun Xue; Yu-Jie Sun

AI summary · arXiv: 2610.34382v1 · cond-mat.supr-con

Nodeless d-wave pairing in monolayer FeSe revealed by intra-unit-cell Josephson interferometry

Runxin Li, Yuchen Huo, Jiong Mei, Ming-Qiang Ren, Miaomiao Wang, Quanxing Wei, Fengyu Yao, Maowen Zheng,

and 8 more authors

Qing Qu, Cui Ding, Hongtao Yuan, Zhuoyu Chen, Wei-Qiang Chen, Kun Jiang, Qi-Kun Xue, Yu-Jie Sun

Original paper Submitted to arXiv on 25 Oct. 2026 License: NONEXCLUSIVE-DISTRIB 1.0 Also in: fr

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The essentials

Atomic-scale Josephson imaging reveals a bond-centred response with Fe–Se nodal lines in monolayer FeSe, which calculations identify as a signature of nodeless d-wave pairing.

Question

Can a local, phase-sensitive measurement resolve the microscopic pairing phase in monolayer FeSe, whose quasiparticle spectrum is fully gapped but whose pairing symmetry is disputed? In particular, can intra-unit-cell Josephson interference distinguish nodeless d-wave pairing from competing states?

Method

The authors used a superconducting Nb tip to map zero-bias Josephson conductance across monolayer FeSe/SrTiO3 and compared the spatial response with measurements on conventional s-wave NbSe2. They calculated the local Josephson response by projecting FeSe pair correlations through Wannier functions into the vacuum and coupling them to the tip, testing d-wave and other candidate pairing states.

Findings

Result Monolayer FeSe has a fully gapped quasiparticle spectrum, with characteristic gap energies of approximately 10 and 15 meV.
See the passage in the paper
Tunnelling spectra acquired with a normal-metal tip reveal a fully gapped superconducting state, with characteristic gap energies of ∼ 10 and ∼ 15 meV (Supplementary Fig. 1), consistent with previous STM measurements22,27,32,41.
Result The local Josephson response has maxima near Fe–Fe bond centres and is strongly suppressed along Fe–Se directions.
See the passage in the paper
Using the well-established surface registry22,32,41,45 together with the simultaneously acquired atomic-resolution topography (Fig. 2a), we find that these nodal lines run along the Fe–Se directions (Fig. 2b), enclosing four response maxima centred near the nearest-neighbour Fe–Fe bond.
Result The Fe–Se nodal pattern is not a generic artifact of the tip, lattice corrugation, or vacuum-junction geometry.
See the passage in the paper
This result rules out a generic modulation imposed by the superconducting tip, atomic corrugation or the vacuum tunnelling geometry and identifies the nodal Josephson pattern as an intrinsic property of monolayer FeSe.
Result The calculations reproduce the observed response pattern for nodeless d-wave pairing, with zero response along Fe–Se directions.
See the passage in the paper
It closely reproduces the principal features of the experimental map in Fig. 3a: the response is strongest near the Fe–Fe bond centres and is suppressed to zero along the Fe–Se directions.
Authors’ interpretation The authors explain the nodal lines as destructive interference between opposite-phase pairing components whose tunnelling weights are equal on the Fe–Se mirror lines.
See the passage in the paper
The nodal lines therefore arise from opposite pairing phases combined with mirror-enforced equal tunnelling weights, rather than from accidental minima in the tunnelling matrix element.

Limitations

The inference of pairing symmetry relies on a microscopic tunnelling model and its comparison with the measured spatial pattern.
See the passage in the paper
To test whether this pairing state accounts for the observed real-space structure, we calculate the local Josephson response using a minimal model of monolayer FeSe40.
The relative intensities of the four bond-centred maxima vary between measurements, and the authors cannot determine whether this reflects tip-dependent tunnelling details or intrinsic symmetry breaking.
See the passage in the paper
We note that the four maxima at the Fe–Fe bond centres show some variation in relative intensity between measurements, which may reflect either tip-dependent tunnelling details or intrinsic symmetry breaking, while the nodal-line positions and symmetry remain robust (Supplementary Fig. 4).

Why it matters

The authors argue that intra-unit-cell Josephson interferometry provides a local phase-sensitive method for resolving microscopic pairing structure, beyond probes that primarily measure gap magnitude. In monolayer FeSe, they use it to identify a nodeless d-wave state and propose broader application to competing pairing symmetries in unconventional superconductors.

Written by AI from the paper. Passages are checked word for word against the text we analysed; the rest may contain errors.

AI-generated keywords: Monolayer FeSe Josephson tunnelling d-wave pairing superconducting phase scanning tunnelling microscopy

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Comprehensive Summary
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Original abstract

The paper asks whether monolayer FeSe on SrTiO₃ has sign-changing superconducting pairing, despite its fully gapped quasiparticle spectrum. Conventional spectroscopy can reveal gap magnitudes but is generally insensitive to the relative phase between pairing components. The authors therefore use a local, phase-sensitive technique to distinguish candidate pairing states. They equip a scanning tunnelling microscope with a superconducting niobium tip. The tip forms a movable Josephson junction with the FeSe surface, allowing the local transfer of Cooper pairs to be mapped across the atomic lattice. The Nb tip has a superconducting gap of about 1.4 meV, while normal-tip spectroscopy of FeSe reveals characteristic gap energies of approximately 10 and 15 meV. With the superconducting tip, the authors identify a zero-bias conductance peak and symmetric negative-differential-conductance dips near ±0.4 meV as signatures of Josephson tunnelling. They use the zero-bias response to map the Josephson signal within individual unit cells. The central finding is a strong spatial modulation of the Josephson response, even though the excitation spectrum is fully gapped. The signal peaks near nearest-neighbour Fe–Fe bond centres and nearly vanishes along lines in the Fe–Se directions. Spectra taken at bond-centre positions show the Josephson peak and associated dips, whereas these features are nearly absent at Fe and Se sites. Finite-bias Andreev conductance also varies within the unit cell, increasing near Fe–Fe bonds and decreasing along Fe–Se directions. Measurements on conventional s-wave NbSe₂ show only weak atomic-scale variation and no comparable nodal minima. This comparison argues against the FeSe pattern being a generic effect of the tip, surface corrugation, or tunnelling geometry. To interpret the pattern, the authors calculate the local Josephson response using a microscopic model. In this model, the sample’s pair correlations are projected into the vacuum through FeSe Wannier functions and coupled to the Nb tip. For d-wave pairing proportional to cos kx − cos ky, the calculated map reproduces the bond-centred maxima and Fe–Se nodal lines. The proposed mechanism is destructive interference: the d-wave state has nearest-neighbour Fe–Fe pairing components with opposite signs, and the tip couples to them with position-dependent weights. Along Fe–Se mirror lines, symmetry makes the weights equal, so the opposite-phase contributions cancel. Away from these lines, unequal weights produce a finite Josephson response. Thus, a Josephson node reflects cancellation of tunnelling amplitudes, not a local closing of the superconducting gap. In the one-Fe Brillouin-zone description used in the paper, FeSe’s low-energy electronic structure is dominated by electron pockets near X and Y, while the hole bands near the zone centre lie below the Fermi level. The d-wave nodal directions can therefore miss the electron pockets, allowing the excitation spectrum to remain fully gapped despite a sign change between pocket sectors. Calculations for proposed sign-preserving and sign-changing s-wave alternatives produce modulation but not the observed mirror-related nodal lines. The authors conclude that intra-unit-cell Josephson interferometry can reveal microscopic phase structure and identify monolayer FeSe as a nodeless d-wave superconductor. Their evidence combines spatially resolved measurements with model-dependent calculations; it does not directly measure the momentum-space order parameter or rule out every possible alternative microscopic explanation. The reported variation in the relative intensity of the four maxima may also reflect tip-dependent tunnelling or intrinsic symmetry breaking.

Can a fully gapped superconductor still have sign-changing pairing?

Monolayer iron selenide, or FeSe, grown on strontium titanate (SrTiO₃) presents a superconducting puzzle. Its measured excitation spectrum is fully gapped, yet that alone does not reveal whether the superconducting pair wavefunction changes sign across different parts of the electronic structure. The paper “Nodeless d-wave pairing in monolayer FeSe revealed by intra-unit-cell Josephson interferometry,” by Runxin Li, Yuchen Huo, Jiong Mei, Ming-Qiang Ren, Miaomiao Wang, Quanxing Wei et al., takes on that question with a technique designed to probe superconducting phase locally.

Ordinary spectroscopy can measure the size of an energy gap, but it is generally insensitive to the relative phase of the pairing in different regions of momentum space. To look for that missing information, the researchers turned a scanning tunnelling microscope (STM) into a tiny, movable Josephson junction.

A superconducting tip becomes a phase-sensitive probe

The team used a tip made of superconducting niobium (Nb). When brought close to the FeSe surface, the tip and sample form a junction through which Cooper pairs can tunnel. Moving the tip across the surface lets the researchers map this Josephson response with atomic-scale resolution.

The Nb tip has a superconducting gap of about 1.4 millielectronvolts (meV). With a conventional, non-superconducting tip, the FeSe spectrum shows characteristic gap energies of roughly 10 and 15 meV. With the Nb tip, the researchers identify a conductance peak at zero voltage and symmetric dips in the differential conductance near ±0.4 meV as signatures of Josephson tunnelling.

They then track the zero-bias Josephson signal across individual FeSe unit cells. The result is striking: the superconducting response varies strongly from place to place, even though the excitation spectrum remains fully gapped.

A repeating pattern of peaks and near-zeros

The Josephson signal reaches its strongest values near the centres of nearest-neighbour iron–iron (Fe–Fe) bonds. It nearly vanishes along lines in the iron–selenium (Fe–Se) directions. Spectra measured at Fe–Fe bond centres show the zero-bias peak and accompanying dips clearly; at Fe and Se atomic sites, those features are almost absent.

The researchers also observe spatial variation in finite-bias Andreev conductance, another response associated with superconducting transport. It increases near Fe–Fe bonds and decreases along the Fe–Se directions, echoing the pattern seen in the Josephson signal.

To test whether the pattern might simply come from the probe or from the shape of the surface, the team performed a comparison on conventional s-wave superconductor NbSe₂. There, the atomic-scale variation is weak, with no similar nodal minima. This comparison suggests that the distinctive FeSe pattern is not a generic consequence of the tip, surface corrugation, or tunnelling geometry.

How interference can create a Josephson node

To interpret the map, the authors calculated the local Josephson response using a microscopic model. The calculation projects the sample’s pair correlations into the vacuum through FeSe Wannier functions and couples them to the Nb tip. For d-wave pairing proportional to cos kx − cos ky, the model produces bond-centred maxima and near-zero lines in the Fe–Se directions, closely matching the experiment.

The proposed explanation is destructive interference. In this d-wave state, pairing on neighbouring Fe–Fe bonds has opposite signs. The tip couples to these contributions with weights that depend on its position. Along Fe–Se mirror lines, symmetry makes the weights equal, so the opposite-phase contributions cancel. Away from those lines, the weights differ and the cancellation is incomplete, giving a finite Josephson response.

In this picture, a Josephson node does not mean that the superconducting gap locally closes. Instead, it marks a position where tunnelling amplitudes cancel. That distinction helps reconcile the strong spatial minima with FeSe’s fully gapped excitation spectrum.

Why d-wave pairing can be nodeless here

In the one-Fe Brillouin-zone description used in the paper, the low-energy electronic structure is dominated by electron pockets near the X and Y points. The hole bands near the zone centre lie below the Fermi level. The d-wave nodal directions can therefore miss the electron pockets that host the relevant low-energy states. The pairing can change sign between pocket sectors while the measured excitation spectrum remains fully gapped.

The authors also calculated maps for proposed sign-preserving and sign-changing s-wave alternatives. Those states can produce some spatial modulation, but not the mirror-related nodal lines seen in the experiment. The d-wave model best reproduces the observed pattern among the states considered.

What the result shows—and what it does not

The study presents intra-unit-cell Josephson interferometry as a way to investigate superconducting phase structure that conventional gap spectroscopy cannot readily access. Its combined measurements and model support identifying monolayer FeSe as a nodeless d-wave superconductor.

The conclusion remains grounded in both experiment and interpretation: the spatial pattern is measured directly, while assigning it to a particular pairing state depends on microscopic calculations. The work does not directly measure the momentum-space order parameter or rule out every possible alternative explanation. The varying relative intensity of the four maxima may also reflect tip-dependent tunnelling or intrinsic symmetry breaking. Even with those caveats, the atomic-scale interference pattern offers a distinctive clue to how superconducting pairs are organised in this unusual material.

Created on 02 Nov. 2026

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Weekly letter Presented in "Physics of matter and light this week" of 2 November 2026. Physics of matter and light this week: Hidden order, from atomic bonds to distant clocks

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Nodeless d-wave pairing in monolayer FeSe revealed by intra-unit-cell Josephson interferometry

The essentials

Question

Method

Findings

Limitations

Why it matters

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Definitions

Can a fully gapped superconductor still have sign-changing pairing?

A superconducting tip becomes a phase-sensitive probe

A repeating pattern of peaks and near-zeros

How interference can create a Josephson node

Why d-wave pairing can be nodeless here

What the result shows—and what it does not

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