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arxiv: 2604.04421 · v1 · submitted 2026-04-06 · ❄️ cond-mat.supr-con · cond-mat.str-el

Recognition: 2 theorem links

· Lean Theorem

Multimodal Terahertz Spectroscopy of the Pairing Symmetry and Normal-State Pseudogap in (La,Pr)₃Ni₂O₇ Films

Shuxiang Xu , Guangdi Zhou , Hao Wang , Tianyi Wu , Wei Wang , Liyu Shi , Dong Wu , Haoliang Huang
show 6 more authors
Xinbo Wang Jinfeng Jia Qi-Kun Xue Zhuoyu Chen Tao Dong Nanlin Wang
Authors on Pith no claims yet

Pith reviewed 2026-05-10 20:00 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con cond-mat.str-el
keywords superconductivitynickelatesterahertz spectroscopypairing symmetrypseudogapthin filmsnonlinear opticsunconventional superconductivity
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The pith

Terahertz measurements show (La,Pr)₃Ni₂O₇ films host bulk superconductivity with disordered s± pairing that coexists with a normal-state pseudogap.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper combines linear terahertz time-domain spectroscopy with third-harmonic generation to examine compressively strained (La,Pr)₃Ni₂O₇ thin films. Linear spectra show low-frequency conductivity suppression below the onset critical temperature, a weak coherence peak, and substantial residual conductivity at low temperature, all consistent with disordered s±-wave pairing. The third-harmonic response rises at the superconducting transition but persists above it, which the authors associate with a pseudogap on the basis of matching temperature scales from photoemission data on similar films. These observations together indicate that superconductivity in this nickelate system is bulk and unconventional while coexisting with a distinct ordered normal state.

Core claim

Multimodal terahertz spectroscopy reveals a bulk superconducting response in (La,Pr)₃Ni₂O₇ films through conductivity suppression below Tc onset, accompanied by a weak coherence peak and residual low-frequency conductivity that together indicate disordered s±-like pairing; the third-harmonic signal persists above Tc onset and is interpreted as arising from a pseudogap in a correlated normal state.

What carries the argument

Multimodal terahertz spectroscopy that combines linear time-domain conductivity measurements with nonlinear third-harmonic generation to track both the superconducting transition and normal-state correlations.

If this is right

  • The superconductivity is intrinsic to the bulk film volume rather than localized at interfaces.
  • The pairing symmetry belongs to the s± class and is influenced by disorder.
  • A distinct ordered state with pseudogap character exists in the normal state and may compete with superconductivity.
  • The nickelate films provide a platform for studying unconventional pairing outside the cuprate and pnictide families.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the pseudogap competes with superconductivity, controlled strain or doping could raise the superconducting transition temperature by suppressing the competing order.
  • Third-harmonic generation could serve as a contact-free probe of pseudogap onset in other nickelate compounds or related layered oxides.
  • The residual low-temperature conductivity implies either gap nodes or strong disorder scattering that future low-temperature scanning probes could map spatially.

Load-bearing premise

The observed conductivity suppression, weak coherence peak, residual low-frequency conductivity, and persisting third-harmonic signal above Tc onset are produced by disordered s± pairing and a pseudogap rather than by inhomogeneity or surface effects.

What would settle it

A complete absence of residual low-frequency conductivity at base temperature together with a sharp, non-persisting third-harmonic signal that vanishes exactly at Tc onset in higher-quality samples would contradict the disordered s± plus pseudogap picture.

Figures

Figures reproduced from arXiv: 2604.04421 by Dong Wu, Guangdi Zhou, Haoliang Huang, Hao Wang, Jinfeng Jia, Liyu Shi, Nanlin Wang, Qi-Kun Xue, Shuxiang Xu, Tao Dong, Tianyi Wu, Wei Wang, Xinbo Wang, Zhuoyu Chen.

Figure 1
Figure 1. Figure 1: The fingerprint of superconductivity observed in the linear THz response of (La,Pr)3Ni2O7 films. (a) Terahertz time domain waveforms transmitted through LPNO/SLAO sample at selected temperatures. The three main peaks are labeled P1, P2 and P3, respectively. The insets show the experimental schematics (top left) and temperature-dependent field |E sam| at the position of peak P3 (top right). |E sam(P3)| decr… view at source ↗
Figure 2
Figure 2. Figure 2: Disordered s±-wave superconductivity evidenced by the THz conductivity of (La,Pr)3Ni2O7 films. (a, b) Frequency-dependent (a) real part σ1 (ω) and (b) imaginary part σ2 (ω) of the THz conductivity at various temperatures. A black dashed line highlights the curve at 40 K, and a bold red line highlights the curve at 2 K. The inset in (a) shows the temperature￾dependent σ1 at the fixed frequency 1.0 THz, with… view at source ↗
Figure 3
Figure 3. Figure 3: Signatures of the anomalous normal state and superconductivity observed in the THG response at 0.5 THz. (a, c) The real-time waveforms of the THG signal after a narrow band￾pass filter (center frequency: 1.5 THz, i.e., 3ω) at selected temperatures, under driving field strengths of (a) 36 kV/cm, (c) 23 kV/cm. The fundamental pulse at 0.5 THz was suppressed by a band-stop filter (0.4–0.6 THz). The shaded ora… view at source ↗
read the original abstract

The discovery of ambient-pressure superconductivity in compressively strained (La,Pr)$_3$Ni$_2$O$_7$ thin films has intensified efforts to identify the pairing mechanism. However, the symmetry of the superconducting order parameter and the character of the normal state remain unsettled. Here we combine bulk-sensitive terahertz (THz) time-domain spectroscopy with THz third-harmonic generation to present spectroscopic insights into these issues. Linear THz spectroscopy reveals a bulk superconducting response in the (La,Pr)$_3$Ni$_2$O$_7$ films, evidenced by the suppression of low-frequency spectral weight below the onset critical temperature, $T_\mathrm{c}^{\mathrm{onset}}$. A weak coherence peak near $T_\mathrm{c}^{\mathrm{onset}}$, together with substantial residual low-frequency conductivity as $T\to 0$, is consistent with disordered $s_{\pm}$-wave pairing. In the nonlinear regime, the third-harmonic signal rises sharply on cooling through $T_\mathrm{c}^{\mathrm{onset}}$, providing an independent signature of the transition. Strikingly, the nonlinear response persists above $T_\mathrm{c}^{\mathrm{onset}}$, pointing to either disorder-enhanced nonlinearity or a distinct correlated normal state. Motivated by angle-resolved photoemission spectroscopy on similarly grown films that identifies a comparable temperature scale, we associate the anomalous normal-state terahertz nonlinearity with a pseudogap. These results establish (La,Pr)$_3$Ni$_2$O$_7$ as a bulk superconductor with $s_{\pm}$-like pairing that coexists with, and may compete with, a distinct ordered state, providing a platform for exploring unconventional superconductivity beyond cuprates and pnictides.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript reports multimodal terahertz spectroscopy (linear time-domain and third-harmonic generation) on compressively strained (La,Pr)₃Ni₂O₇ thin films. It claims a bulk superconducting response below Tc^onset with spectral-weight suppression, a weak coherence peak, and residual low-T conductivity, interpreted as consistent with disordered s±-wave pairing. The third-harmonic signal is observed to rise through Tc^onset and persist above it; the authors associate the anomalous normal-state nonlinearity with a pseudogap on the basis of a matching temperature scale from prior ARPES on similar films, concluding that the material is a bulk superconductor with s±-like pairing that coexists with and may compete with a distinct ordered state.

Significance. If the interpretations are substantiated, the results would provide bulk-sensitive spectroscopic constraints on pairing symmetry and normal-state correlations in this nickelate system, complementing ARPES and transport data and offering a platform for unconventional superconductivity studies. The multimodal THz methodology, combining linear conductivity with nonlinear harmonic generation, is a clear experimental strength that yields independent signatures of the transition and potential normal-state effects.

major comments (2)
  1. [Abstract] Abstract: the persistence of the third-harmonic signal above Tc^onset is associated with a pseudogap solely via temperature-scale agreement with ARPES on similar films. No quantitative modeling (e.g., effective-medium theory for inhomogeneity, vortex-motion contributions, or disorder-enhanced nonlinearity in an s± state) is presented to exclude the alternative explicitly acknowledged in the text, rendering the link to a 'distinct ordered state' that 'may compete' non-unique and load-bearing for the central claim.
  2. [Abstract and linear THz results] Abstract and linear THz results: the assignment of 'disordered s±-wave pairing' rests on qualitative features (weak coherence peak near Tc^onset and substantial residual low-frequency conductivity as T→0). Without explicit comparison to model calculations for alternative symmetries (e.g., d-wave with disorder) or quantitative fits to the conductivity spectra, the specificity of the pairing-symmetry conclusion remains limited.
minor comments (1)
  1. [Abstract] Abstract: the phrase 'bulk-sensitive' for THz measurements on thin films would benefit from a brief statement on penetration depth relative to film thickness to address possible surface contributions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and positive assessment of the multimodal THz methodology and its potential significance. We respond point-by-point to the major comments below, clarifying our interpretations while acknowledging limitations. Revisions have been made to tone down claims and add discussion where appropriate.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the persistence of the third-harmonic signal above Tc^onset is associated with a pseudogap solely via temperature-scale agreement with ARPES on similar films. No quantitative modeling (e.g., effective-medium theory for inhomogeneity, vortex-motion contributions, or disorder-enhanced nonlinearity in an s± state) is presented to exclude the alternative explicitly acknowledged in the text, rendering the link to a 'distinct ordered state' that 'may compete' non-unique and load-bearing for the central claim.

    Authors: We agree that the pseudogap interpretation relies on the matching temperature scale with prior ARPES rather than new quantitative modeling, and the manuscript already notes the alternative of disorder-enhanced nonlinearity. The sharp onset of the nonlinear signal through Tc^onset, together with the independent linear THz evidence for bulk superconductivity, provides supporting context for associating the normal-state response with a distinct correlated state. In revision we have modified the abstract to present the pseudogap link as a motivated interpretation rather than a definitive conclusion, and we have added a short paragraph discussing why vortex-motion or strong inhomogeneity contributions are unlikely under our zero-field, uniform-film conditions. Full effective-medium or microscopic modeling of the nonlinearity lies beyond the scope of this primarily experimental report but would be a natural direction for follow-up work. revision: partial

  2. Referee: [Abstract and linear THz results] Abstract and linear THz results: the assignment of 'disordered s±-wave pairing' rests on qualitative features (weak coherence peak near Tc^onset and substantial residual low-frequency conductivity as T→0). Without explicit comparison to model calculations for alternative symmetries (e.g., d-wave with disorder) or quantitative fits to the conductivity spectra, the specificity of the pairing-symmetry conclusion remains limited.

    Authors: The disordered s± assignment is drawn from the observed combination of a weak coherence peak and substantial residual low-T conductivity, features that align with expectations for s± pairing in the presence of disorder (as documented in iron-pnictide literature) while being inconsistent with a clean full-gap s-wave state. We have added references to theoretical calculations of THz conductivity spectra for disordered s± and d-wave cases in the revised manuscript to make this comparison more explicit. We acknowledge that no new quantitative spectral fits are performed in the present work; accordingly, the text has been revised to state that the data are 'consistent with' disordered s±-wave pairing rather than claiming a unique determination. Detailed modeling of the conductivity spectra would strengthen the conclusion and is noted as desirable for future studies. revision: partial

Circularity Check

0 steps flagged

No significant circularity in experimental interpretations or claims.

full rationale

The manuscript is an experimental THz spectroscopy study reporting direct observations of conductivity suppression, coherence peak, residual conductivity, and third-harmonic generation in (La,Pr)₃Ni₂O₇ films. Interpretations (disordered s± pairing from linear response; pseudogap association from temperature-scale match to cited ARPES) are presented as consistency arguments and motivation rather than derivations. No equations, fitted parameters, or first-principles steps appear that reduce outputs to inputs by construction. The cited ARPES provides an independent temperature benchmark on similar films and does not define or force the THz quantities. All load-bearing claims rest on new measurements, satisfying the criteria for a self-contained experimental paper with no circular reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 3 axioms · 0 invented entities

The central claims rest on standard domain assumptions about THz response in superconductors and the validity of linking nonlinearity to a pseudogap via temperature-scale comparison; no free parameters or new entities are introduced in the abstract.

axioms (3)
  • domain assumption THz time-domain spectroscopy provides a bulk-sensitive probe of the conductivity in thin films.
    Invoked to interpret the suppression of low-frequency spectral weight as a bulk superconducting response.
  • domain assumption A weak coherence peak and residual low-frequency conductivity at T→0 are signatures of disordered s±-wave pairing.
    Used to associate the linear THz data with s± pairing.
  • domain assumption Persisting third-harmonic generation above Tc onset indicates either disorder-enhanced nonlinearity or a distinct correlated normal state (pseudogap).
    Basis for the normal-state interpretation.

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