Observation of flat-bottom U-shaped energy gap in high-Tc nickelate (La,Pr)3Ni2O7 thin films
Pith reviewed 2026-05-19 19:36 UTC · model grok-4.3
The pith
An energy-symmetric flat-bottom U-shaped gap consistent with nodeless superconductivity is observed in high-Tc nickelate thin films at ambient pressure.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
In (La,Pr)3Ni2O7 thin films, ultra-low temperature STM/S reveals an energy-symmetric, flat-bottom U-shaped gap around the Fermi level with zero residual density of states. This gap, combined with its reduction under 14 T c-axis magnetic field and rapid filling to V-shaped with increasing temperature, matches the expected behavior of a superconducting gap, implying a nodeless gap function at ultra-low temperatures. Electrical transport on the same film shows zero resistance with Tc above 20 K, supporting the superconducting nature.
What carries the argument
The flat-bottom U-shaped tunneling spectrum with zero residual DOS, whose temperature and magnetic field dependence is used to identify it as the superconducting gap.
If this is right
- The observation confirms the presence of superconductivity in the thin film samples at ambient pressure.
- The gap function appears nodeless at ultra-low temperatures.
- The STM method allows detailed study of the superconducting state in these materials.
- Results suggest possibility of local superconductivity with Tc above 77 K in similar systems.
Where Pith is reading between the lines
- If the surface-sensitive STM data truly captures the bulk gap, similar measurements could reveal the pairing symmetry in other nickelate compounds.
- Connecting this to cuprate superconductors might highlight common mechanisms in layered oxides.
- Further experiments varying film thickness or substrate could test if the gap is intrinsic or affected by interfaces.
- Success here encourages ambient-pressure searches for higher-Tc nickelate superconductors.
Load-bearing premise
The tunneling spectra represent the intrinsic bulk superconducting density of states without dominant contributions from surface reconstruction, disorder, or non-superconducting phases.
What would settle it
If future measurements show that the U-shaped gap does not close at the superconducting critical temperature determined by transport or if it appears in non-superconducting regions of the film, the interpretation as a superconducting gap would be falsified.
read the original abstract
The discovery of high transition temperature (high-Tc) superconductivity in Ruddlesden-Popper (R-P) bilayer nickelates under high pressure has stimulated extensive work to understand the underlying mechanism and search for superconductors with higher Tc. The recent realization of superconductivity in R-P bilayer nickelate thin films with onset Tc above 40 K at ambient-pressure enables the use of a wide array of powerful experimental tools to investigate the unconventional high-Tc superconductivity in bilayer nickelates. Here, using ultra-low temperature scanning tunneling microscopy/spectroscopy (STM/S) and electrical transport study, we report the first successful observation of an energy-symmetric, flat-bottom U-shaped gap with zero residual density of states around the Fermi level in the high-Tc nickelate (La,Pr)3Ni2O7 thin film grown on SrLaAlO4 substrate. Before and after STM/S studies, transport measurements on the same sample reveal consistent superconducting behaviors showing zero resistance, with an onset Tc above 40 K and zero resistance Tc above 20 K. The tunneling spectra exhibit highly unconventional temperature evolution, characterized by a rapid filling of the U-shaped energy gap to a V-shaped gap as the temperature increases. Furthermore, the U-shaped energy gap is reduced under a c-axis magnetic field of 14 T. The energy-symmetric U-shaped gap, taken together with its dependence on magnetic field and temperature, is consistent with the behavior of a superconducting gap, suggesting a nodeless gap function at ultra-low temperatures. Our findings shed new lights on the nature of high-Tc superconductivity and provide an encouraging and thought-provoking hint for a local superconductivity with Tc above liquid nitrogen boiling temperature in nickelate superconductors at ambient or zero pressure.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript reports ultra-low temperature STM/S measurements on (La,Pr)3Ni2O7 thin films on SrLaAlO4 substrates, observing an energy-symmetric flat-bottom U-shaped gap with zero residual DOS at the Fermi level. Transport measurements on the same sample show consistent superconductivity with onset Tc above 40 K and zero-resistance Tc above 20 K. The gap fills rapidly into a V-shape with increasing temperature and is suppressed by a 14 T c-axis field; the authors interpret these features as evidence for a nodeless superconducting gap function.
Significance. If the STM spectra are shown to reflect the bulk superconducting DOS, the result would supply the first direct tunneling evidence for gap symmetry in ambient-pressure bilayer nickelate films. This could help discriminate among pairing mechanisms and support the possibility of local superconductivity above liquid-nitrogen temperature, thereby advancing the understanding of high-Tc nickelates.
major comments (2)
- [Results and Discussion (STM/S spectra and interpretation)] The central claim that the flat-bottom U-shaped gap indicates a nodeless bulk superconducting gap rests on the premise that the STM/S spectra map the intrinsic quasiparticle DOS. Because STM is confined to the topmost layers, the manuscript must address possible surface reconstruction, apical-oxygen loss, or substrate-induced strain that could produce analogous gaps unrelated to bulk superconductivity. No spatial correlation between STM locations and transport-defined superconducting regions, nor checks for phase separation or competing surface orders (CDW, magnetic), are described.
- [Temperature and magnetic-field dependence paragraphs] The temperature evolution (rapid filling of U-shape to V-shape) and 14 T field suppression are presented as consistent with superconductivity, yet the text provides no quantitative gap extraction, error bars, or model fits (e.g., to BCS or d-wave forms) that would allow readers to assess whether the data exclude small residual DOS or alternative gap-like features within experimental noise.
minor comments (2)
- The base temperature of the STM measurements and the numerical value of the gap edge (with uncertainty) should be stated explicitly in the abstract and main text.
- [Methods] Figure captions and methods should specify tunneling setpoint conditions, tip material, and any spatial homogeneity maps to aid reproducibility.
Simulated Author's Rebuttal
We thank the referee for the careful and constructive review of our manuscript. The comments highlight important aspects of data interpretation and analysis that we address point by point below. We will revise the manuscript to strengthen the presentation where feasible while maintaining scientific accuracy.
read point-by-point responses
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Referee: [Results and Discussion (STM/S spectra and interpretation)] The central claim that the flat-bottom U-shaped gap indicates a nodeless bulk superconducting gap rests on the premise that the STM/S spectra map the intrinsic quasiparticle DOS. Because STM is confined to the topmost layers, the manuscript must address possible surface reconstruction, apical-oxygen loss, or substrate-induced strain that could produce analogous gaps unrelated to bulk superconductivity. No spatial correlation between STM locations and transport-defined superconducting regions, nor checks for phase separation or competing surface orders (CDW, magnetic), are described.
Authors: We agree that STM/S is inherently surface-sensitive and that the manuscript would benefit from a more explicit discussion of this point. Transport data were acquired on the same film before and after STM measurements, showing reproducible superconductivity with onset Tc above 40 K and zero-resistance Tc above 20 K; this macroscopic consistency provides indirect support that the gap is not an isolated surface artifact. In the revised manuscript we will add a dedicated paragraph addressing possible surface reconstruction, apical-oxygen loss, and substrate strain, referencing the structural characterization (XRD, AFM) already present in the methods. We note that the observed gap is energy-symmetric with strictly zero residual DOS and is suppressed by a 14 T c-axis field—features difficult to reconcile with typical CDW or magnetic surface orders, which usually produce asymmetric or gapped spectra with finite residual DOS. While we did not perform spatially resolved STM-transport correlations (transport being a global probe), spectra acquired at multiple locations on the film were reproducible; we will clarify this limitation and its implications. revision: partial
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Referee: [Temperature and magnetic-field dependence paragraphs] The temperature evolution (rapid filling of U-shape to V-shape) and 14 T field suppression are presented as consistent with superconductivity, yet the text provides no quantitative gap extraction, error bars, or model fits (e.g., to BCS or d-wave forms) that would allow readers to assess whether the data exclude small residual DOS or alternative gap-like features within experimental noise.
Authors: We concur that quantitative fitting and error analysis would improve the ability of readers to evaluate the claims. In the revised version we will extract the gap magnitude versus temperature and magnetic field, report the associated uncertainties, and overlay BCS nodeless s-wave fits to the lowest-temperature spectra. These fits will be used to demonstrate that the residual DOS at the Fermi level is consistent with zero within experimental noise and that the temperature-induced evolution from U- to V-shape is inconsistent with a simple nodal gap. The 14 T field suppression will likewise be compared to the expected pair-breaking behavior for a nodeless gap. revision: yes
Circularity Check
No circularity: direct experimental observation with no derivation chain
full rationale
This is a purely observational experimental paper reporting STM/S tunneling spectra on (La,Pr)3Ni2O7 thin films. The flat-bottom U-shaped gap with zero residual DOS is extracted directly from raw differential conductance data, and its consistency with a nodeless superconducting gap is stated as an empirical interpretation based on observed temperature filling to V-shape and suppression under 14 T field. No equations, fitted parameters, predictions, or first-principles derivations are presented that could reduce to inputs by construction. No self-citations are invoked as load-bearing uniqueness theorems or ansatze. The central claim rests on experimental measurements and transport corroboration rather than any self-referential loop.
Axiom & Free-Parameter Ledger
axioms (1)
- domain assumption STM tunneling spectra reflect the local electronic density of states near the Fermi level.
Lean theorems connected to this paper
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IndisputableMonolith/Cost/FunctionalEquation.leanwashburn_uniqueness_aczel unclear?
unclearRelation between the paper passage and the cited Recognition theorem.
energy-symmetric, flat-bottom U-shaped gap with zero residual density of states... consistent with the behavior of a superconducting gap, suggesting a nodeless gap function
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IndisputableMonolith/Foundation/BlackBodyRadiationDeep.leanBlackBodyRadiationDeepCert unclear?
unclearRelation between the paper passage and the cited Recognition theorem.
The U-shaped energy gap is reduced under a c-axis magnetic field of 14 T... rapid filling of the U-shaped energy gap to a V-shaped gap
What do these tags mean?
- matches
- The paper's claim is directly supported by a theorem in the formal canon.
- supports
- The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
- extends
- The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
- uses
- The paper appears to rely on the theorem as machinery.
- contradicts
- The paper's claim conflicts with a theorem or certificate in the canon.
- unclear
- Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.
Reference graph
Works this paper leans on
-
[1]
Sun, H. et al. Signatures of superconductivity near 80 K in a nickelate under high pressure. Nature 621, 493–498 (2023)
work page 2023
-
[2]
Zhang, Y . et al. High-temperature superconductivity with zero resistance and strange-metal behaviour in La3Ni2O7−δ. Nature Physics 20, 1269–1273 (2024)
work page 2024
-
[3]
Wang, N. et al. Bulk high-temperature superconductivity in pressurized tetragonal La2PrNi2O7. Nature 634, 579–584 (2024)
work page 2024
-
[4]
Yang, J. et al. Orbital-dependent electron correlation in double-layer nickelate La3Ni2O7. Nature Communications 15, 4373 (2024)
work page 2024
-
[5]
Luo, Z., Hu, X., Wang, M., Wú, W. & Yao, D.-X. Bilayer Two-Orbital Model of La3Ni2O7 under Pressure. Physical Review Letters 131, 126001 (2023)
work page 2023
-
[6]
Luo, Z., Lv, B., Wang, M., Wú, W. & Yao, D.-X. High-TC superconductivity in La3Ni2O7 based on the bilayer two-orbital t-J model. npj Quantum Materials 9, 61 (2024)
work page 2024
-
[7]
Lechermann, F., Gondolf, J., Bötzel, S. & Eremin, I. M. Electronic correlations and superconducting instability in La3Ni2O7 under high pressure. Physical Review B 108, L201121 (2023)
work page 2023
-
[8]
Shen, Y ., Qin, M. & Zhang, G.-M. Effective Bi-Layer Model Hamiltonian and Density-Matrix Renormalization Group Study for the High-Tc Superconductivity in La3Ni2O7 under High Pressure. Chinese Physics Letters 40, 127401 (2023)
work page 2023
-
[9]
Sakakibara, H., Kitamine, N., Ochi, M. & Kuroki, K. Possible High Tc Superconductivity in La3Ni2O7 under High Pressure through Manifestation of a Nearly Half-Filled Bilayer Hubbard Model. Physical Review Letters 132, 106002 (2024)
work page 2024
-
[10]
Liao, Z. et al. Electron correlations and superconductivity in La3Ni2O7 under pressure tuning. Physical Review B 108, 214522 (2023)
work page 2023
-
[11]
Yang, Y ., Zhang, G.-M. & Zhang, F.-C. Interlayer valence bonds and two-component theory for high-Tc superconductivity of La3Ni2O7 under pressure. Physical Review B 108, L201108 (2023)
work page 2023
-
[12]
Jiang, K.-Y ., Cao, Y .-H., Yang, Q.-G., Lu, H.-Y . & Wang, Q.-H. Theory of Pressure Dependence of Superconductivity in Bilayer Nickelate La3Ni2O7. Physical Review Letters 134, 076001 (2025)
work page 2025
-
[13]
Li, Q. et al. Signature of Superconductivity in Pressurized La4Ni3O10. Chinese Physics Letters 41, 017401 (2024)
work page 2024
-
[14]
Zhu, Y . et al. Superconductivity in pressurized trilayer La4Ni3O10−δ single crystals. Nature 631, 531–536 (2024)
work page 2024
-
[15]
Shi, M. et al. Spin density wave rather than tetragonal structure is prerequisite for superconductivity in La3Ni2O7-δ. Nature Communications 16, 9141 (2025)
work page 2025
-
[16]
Zhang, Y ., Lin, L.-F., Moreo, A., Maier, T. A. & Dagotto, E. Trends in electronic structures and s±-wave pairing for the rare-earth series in bilayer nickelate superconductor R3Ni2O7. Physical Review B 108, 165141 (2023). 14
work page 2023
-
[17]
Fan, S. et al. Tunneling spectra with gaplike features observed in nickelate La3Ni2O7 at ambient pressure. Physical Review B 110, 134520 (2024)
work page 2024
-
[18]
Liu, Z. et al. Electronic correlations and partial gap in the bilayer nickelate La3Ni2O7. Nature Communications 15, 7570 (2024)
work page 2024
-
[19]
Geisler, B., Hamlin, J. J., Stewart, G. R., Hennig, R. G. & Hirschfeld, P. J. Structural transitions, octahedral rotations, and electronic properties of A3Ni2O7 rare-earth nickelates under high pressure. npj Quantum Materials 9, 38 (2024)
work page 2024
-
[20]
Chen, X. et al. Electronic and magnetic excitations in La3Ni2O7. Nature Communications 15, 9597 (2024)
work page 2024
-
[21]
Li, F. et al. Bulk superconductivity up to 96 K in pressurized nickelate single crystals. Nature 649, 871–878 (2026)
work page 2026
-
[22]
Shi, M. et al. Pressure induced superconductivity in hybrid Ruddlesden‒Popper La5Ni3O11 single crystals. Nature Physics 21, 1780–1786 (2025)
work page 2025
-
[23]
Ko, E. K. et al. Signatures of ambient pressure superconductivity in thin film La3Ni2O7. Nature 638, 935–940 (2025)
work page 2025
-
[24]
Zhou, G. et al. Ambient-pressure superconductivity onset above 40 K in (La,Pr)3Ni2O7 films. Nature 640, 641–646 (2025)
work page 2025
-
[25]
Liu, Y . et al. Superconductivity and normal-state transport in compressively strained La2PrNi2O7 thin films. Nature Materials 24, 1221–1227 (2025)
work page 2025
-
[26]
Hao, B. et al. Superconductivity in Sr-doped La3Ni2O7 thin films. Nature Materials 24, 1756–1762 (2025)
work page 2025
-
[27]
Bardeen, J., Cooper, L. N. & Schrieffer, J. R. Theory of Superconductivity. Physical Review 108, 1175–1204 (1957)
work page 1957
-
[28]
McMillan, W. L. Transition Temperature of Strong-Coupled Superconductors. Physical Review 167, 331–344 (1968)
work page 1968
-
[29]
Fischer, Ø., Kugler, M., Maggio-Aprile, I., Berthod, C. & Renner, C. Scanning tunneling spectroscopy of high-temperature superconductors. Reviews of Modern Physics 79, 353–419 (2007)
work page 2007
- [30]
-
[31]
Fernandes, R. M. et al. Iron pnictides and chalcogenides: a new paradigm for superconductivity. Nature 601, 35–44 (2022)
work page 2022
-
[32]
Wilson, S. D. & Ortiz, B. R. A V3Sb5 kagome superconductors. Nature Reviews Materials 9, 420–432 (2024)
work page 2024
-
[33]
Jiao, L. et al. Chiral superconductivity in heavy-fermion metal UTe2. Nature 579, 523–527 (2020)
work page 2020
-
[34]
Energy Gap in Superconductors Measured by Electron Tunneling
Giaever, I. Energy Gap in Superconductors Measured by Electron Tunneling. Physical Review Letters 5, 147–148 (1960)
work page 1960
-
[35]
Zhou, G. et al. Gigantic-oxidative atomic-layer-by-layer epitaxy for artificially designed complex oxides. National Science Review 12, nwae429 (2025)
work page 2025
- [36]
-
[37]
Matsuura, S. et al. Reproducible superconducting gap on clean surfaces of BiSrCaCuO prepared by etching with a scanning tunneling microscope tip. Physica C 300, 26–32 (1998)
work page 1998
-
[38]
Gu, Q. et al. Single particle tunneling spectrum of superconducting Nd1-xSrxNiO2 thin films. Nature Communications 11, 6027 (2020)
work page 2020
-
[39]
Zhao, K. et al. Disorder-induced multifractal superconductivity in monolayer niobium dichalcogenides. Nature Physics 15, 904–910 (2019)
work page 2019
- [40]
-
[41]
Dessau, D. S. et al. Anomalous spectral weight transfer at the superconducting transition of Bi2Sr2CaCu2O8+δ. Physical Review Letters 66, 2160–2163 (1991)
work page 1991
-
[42]
Renner, C., Revaz, B., Genoud, J.-Y ., Kadowaki, K. & Fischer, Ø. Pseudogap Precursor of the Superconducting Gap in Under- and Overdoped Bi2Sr2CaCu2O8+δ. Physical Review Letters 80, 149–152 (1998)
work page 1998
-
[43]
Kivelson, S. A. & Spivak, B. Macroscopic character of composite high-temperature superconducting wires. Physical Review B 92, 184502 (2015)
work page 2015
-
[44]
Giaever, I. & Zeller, H. R. Superconductivity of Small Tin Particles Measured by Tunneling. Physical Review Letters 20, 1504–1507 (1968)
work page 1968
-
[45]
Wang, R.-F. et al. Observation of Coulomb blockade and Coulomb staircases in superconducting Pr0.8Sr0.2NiO2 films. Physical Review B 107, 115411 (2023)
work page 2023
-
[46]
Liu, C. et al. Dynamical Coulomb blockade as a signature of the sign-reversing Cooper pairing potential. Physical Review B 110, 014514 (2024)
work page 2024
-
[47]
Hanna, A. E. & Tinkham, M. Variation of the Coulomb staircase in a two-junction system by fractional electron charge. Physical Review B 44, 5919–5922 (1991)
work page 1991
- [48]
-
[49]
Lee, Y . et al. High-temperature superconductivity in Nd0.85Sr0.15NiO2 membranes under pressure. Preprint at https://arxiv.org/abs/2604.09525 (2026)
work page internal anchor Pith review Pith/arXiv arXiv 2026
- [50]
-
[51]
Zhang, Y . et al. Nodeless superconducting gap in AxFe2Se2 (A=K,Cs) revealed by angle-resolved photoemission spectroscopy. Nature Materials 10, 273–277 (2011)
work page 2011
-
[52]
Zhang, W. et al. Interface charge doping effects on superconductivity of single-unit-cell FeSe films on SrTiO3 substrates. Physical Review B 89, 060506 (2014)
work page 2014
- [53]
-
[54]
Tunnelling from a Many-Particle Point of View
Bardeen, J. Tunnelling from a Many-Particle Point of View. Physical Review 16 Letters 6, 57–59 (1961)
work page 1961
-
[55]
Tersoff, J. & Hamann, D. R. Theory and Application for the Scanning Tunneling Microscope. Physical Review Letters 50, 1998–2001 (1983)
work page 1998
-
[56]
Tersoff, J. & Hamann, D. R. Theory of the scanning tunneling microscope. Physical Review B 31, 805–813 (1985)
work page 1985
-
[57]
Chatterjee, K. et al. Visualization of the interplay between high-temperature superconductivity, the pseudogap and impurity resonances. Nature Physics 4, 108–111 (2008)
work page 2008
-
[58]
Hanaguri, T. et al. Scanning tunneling microscopy/spectroscopy of vortices in LiFeAs. Physical Review B 85, 214505 (2012)
work page 2012
-
[59]
Stühler, R. et al. Tomonaga–Luttinger liquid in the edge channels of a quantum spin Hall insulator. Nature Physics 16, 47–51 (2020)
work page 2020
-
[60]
Liu, C. et al. Zero-energy bound states in the high-temperature superconductors at the two-dimensional limit. Science Advances 6, eaax7547 (2020)
work page 2020
-
[61]
Chen, C. et al. Atomic line defects and zero-energy end states in monolayer Fe(Te,Se) high-temperature superconductors. Nature Physics 16, 536–540 (2020). 17 Extended Data Fig. 1 | More tunneling spectra measured in Region 1. a-f, Tunneling spectra measured at different positions in Region 1 (Vs = 100 mV , Is = 500 pA, Vmod = 2 mV). Measurement temperatur...
work page 2020
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