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Direct Visualization of an Incommensurate Unidirectional Charge Density Wave in La$_4$Ni$_3$O$_{10}$

T0 review · 4 major / 5 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read Scanning tunneling microscopy images La4Ni3O10 at ambient pressure and finds an incommensurate, unidirectional charge density wave with qCDW ≈ 0.76 qb that opens a partial gap of 2Δ ≈ 71 meV near the Fermi level.

desk verdict A competent STM study: the real-space CDW claim is credible and useful, but the 71 meV gap assignment is under-supported and should be treated as tentative. read the letter →

arxiv 2501.18885 v1 pith:UN7FZBND submitted 2025-01-31 cond-mat.supr-con cond-mat.str-el

Mingzhe Li , Jiashuo Gong , Yinghao Zhu , Ziyuan Chen , Jiakang Zhang , Enkang Zhang , Yuanji Li , Ruotong Yin
show 5 more authors
Shiyuan Wang Jun Zhao Dong-Lai Feng Zengyi Du Ya-Jun Yan
This is my paper · ORCID
classification cond-mat.supr-concond-mat.str-el
keywords chargedensitywaveLa4Ni3O10trilayernickelatescanningtunnelingmicroscopyFermisurfacenestingdensity-wavegapRuddlesden-Poppernickelatesunidirectionalorder
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper reports the first direct real-space visualization of an incommensurate, unidirectional charge density wave in the trilayer nickelate La4Ni3O10 at ambient pressure. Using scanning tunneling microscopy and spectroscopy on the cleaved LaO-I surface, the authors see a charge modulation with wave vector $q_{\mathrm{CDW}} \approx 0.76\,q_{b}$ running along the b-axis, together with a density-of-states depletion between -32 meV and +39 meV that they identify as the two edges of a CDW gap of $2\Delta \approx 71$ meV. The result matters because La4Ni3O10 and its bilayer relative La3Ni2O7 become superconducting under pressure only after their density-wave order is suppressed, so the size, symmetry, and origin of the ambient-pressure density wave constrain why the two compounds have very different critical temperatures. The paper argues the CDW is electronic in origin, likely produced by Fermi surface nesting, and is probably a subsidiary order accompanying a spin density wave with $q_{\mathrm{SDW}} = q_{\mathrm{CDW}}/2$.

What carries the argument

The central object is the real-space charge modulation measured by scanning tunneling microscopy and spectroscopy on the cleaved LaO-I surface of La4Ni3O10. The argument is carried by two measurements: (i) dI/dV conductance maps whose fast Fourier transforms show a nondispersive diffraction spot at $q_{\mathrm{CDW}} \approx 0.76\,q_{b}$ along the b-axis, and (ii) a multi-component cosine fit of the spatial DOS oscillations along the b-axis that separates the CDW component (period $1.316\,b$) from surface lattice reconstructions (periods $b$, $2b$, $4b$). The CDW gap is identified through a phase reversal of the CDW component between the peaks at -32 meV and +39 meV, which mark where the density of states begins its rapid depletion. These observations are tied to the bulk density-wave transition at $T_{\mathrm{DW}} \approx 138$ K by comparing the gap size with earlier bulk measurements rather than by a direct temperature-dependent STM control.

What would settle it

Measure the same LaO-I surface with STM/STS as a function of temperature through T_DW ≈ 138 K: if the q ≈ 0.76 qb conductance modulation and the -32/+39 meV gap edges both vanish at T_DW and reappear on cooling, the assignment is confirmed; if the modulation persists above T_DW or the gap edges do not track the transition, the bulk-CDW interpretation fails. A momentum-resolved check would be to observe the gap on the specific α and β Fermi-surface patches connected by qSDW ≈ 0.38 qb with ARPES, which would certify or rule out the proposed nesting scenario.

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Extended reading notes

Core claim

The central claim is that in La4Ni3O10 at ambient pressure, the electronic density of states is organized by a unidirectional, incommensurate charge density wave with $q_{\mathrm{CDW}} \approx 0.76\,q_{b}$, directed along the b-axis, and that this order opens a roughly symmetric gap of $2\Delta \approx 71$ meV centered near the Fermi level. The evidence is a combination of dI/dV maps that show charge stripes along the a-axis with a nondispersive diffraction peak at $q_{\mathrm{CDW}}$ in the Fourier transforms, and spatial spectra along the b-axis that are fit with four cosine components whose CDW component reverses phase between the -32 meV and +39 meV gap edges. The paper further proposes that the CDW is a subsidiary phase of a spin density wave with $q_{\mathrm{SDW}} = q_{\mathrm{CDW}}/2 \approx 0.38\,q_{b}$, based on two Fermi-surface nesting connections between the $\alpha$ and $\beta$ bands measured by ARPES. Because the gap is large relative to the 138 K transition temperature, the authors conclude the density wave depletes the Fermi surface severely enough to prevent superconductivity at ambient pressure, and they attribute the lower $T_c$ of pressurized La4Ni3O10 compared with La3Ni2O7 to weaker electronic correlations in the trilayer compound.

Load-bearing premise

The load-bearing premise is that the 0.76 qb modulation and the -32/+39 meV gap-like feature seen on the cleaved LaO-I surface are the bulk electronic charge-density wave of La4Ni3O10 and its gap, rather than a surface-specific reconstruction or a spectroscopic artifact.

Editorial extensions

If this is right

  • The ambient-pressure ground state of La4Ni3O10 is a partially gapped metal with $2\Delta \approx 71$ meV, so superconductivity at ambient pressure is blocked by a heavily depleted Fermi surface; this supports the competition between density waves and superconductivity in the phase diagram.
  • The CDW is incommensurate and unidirectional along the b-axis, so any microscopic model of the trilayer nickelate density wave must reproduce a single-axis order tied to the tilt direction of the NiO6 octahedra rather than an isotropic or biaxial pattern.
  • If the CDW is a subsidiary phase of an SDW with $q_{\mathrm{SDW}} \approx 0.38\,q_{b}$, then the magnetism of La4Ni3O10 is best described as itinerant and Fermi-surface-driven, a picture distinct from the local-moment spin stripes proposed for La3Ni2O7.
  • The spread of reported gap values (71 meV by STM, 60 meV by optics, 50 meV by NMR, 12-20 meV by ARPES) means the gap location on the Fermi surface is not yet settled by any single technique, so a momentum-resolved measurement of the gap on the $\alpha$ and $\beta$ bands would be the decisive next test.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper, a temperature-dependent STM/STS run across $T_{\mathrm{DW}}$ would test whether the $q \approx 0.76\,q_{b}$ modulation and the -32/+39 meV gap edges vanish together; their correlated disappearance is the cleanest confirmation that both belong to the same bulk order.
  • The paper's $q_{\mathrm{CDW}} = 2q_{\mathrm{SDW}}$ relation fits a pattern seen in chromium and other metals, which suggests the nickelate's density wave is itinerant; a testable extension is to search for the SDW nesting vector with neutron scattering on the same crystals used here.
  • Because the four-period cosine fit separates lattice reconstruction from charge order, the same analysis could be applied to other cleaved nickelate surfaces, including La3Ni2O7, to determine whether a CDW exists there in real space despite its weak amplitude.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper reports scanning tunneling microscopy/spectroscopy (STM/STS) measurements on the cleaved LaO-I surface of La4Ni3O10 at low temperature. The authors observe a unidirectional, incommensurate modulation along the b-axis with wave vector qCDW ≈ 0.76 qb, which they identify as a charge density wave (CDW) based on comparison with bulk x-ray diffraction. In dI/dV spectra, they find strong DOS depletion between approximately -32 meV and +39 meV and assign the peaks P3 and P4 as the CDW gap edges, yielding 2Δ ≈ 71 meV. They propose that the CDW arises from Fermi surface nesting and is a subsidiary phase of a spin density wave with qSDW = 1/2 qCDW, and they discuss implications for the difference in Tc between La4Ni3O10 and La3Ni2O7.

Significance. If the claims hold, this is the first real-space visualization of a CDW in La4Ni3O10, providing a direct microscopic counterpart to the bulk density-wave order inferred from XRD and neutron scattering. The measured qCDW matching the bulk value is a concrete strength, as is the explicit comparison with earlier optical, NMR, and ARPES gap estimates. The proposed nesting scenario, though borrowed from prior work, gives a falsifiable framework. However, the central quantitative claim—the 71 meV CDW gap—is not yet supported to the standard required by the paper's conclusions, because the gap-edge assignment rests on a two-energy phase comparison without controls or uncertainties.

major comments (4)
  1. [§3, Table I] The identification of the -32 meV and +39 meV peaks (P3 and P4) as CDW gap edges is not established by the data as presented. The phase-reversal argument compares only two energies: φCDW(P3) = 0.41π versus φCDW(P4) = 1.46π. However, P2 at -44 meV has the largest CDW amplitude (ACDW = 0.644) with φCDW = 0.33π, and P1 at -130 meV has φCDW = 1.25π, so no clean two-edge phase jump across the gap is demonstrated; no energy-dependent phase plot is shown. No error bars are given for any fitted amplitude or phase, so the statistical significance of the 1.05π difference cannot be assessed. Furthermore, no spectrum above T_DW ≈ 138 K is presented, so the depletion between -32 meV and +39 meV is not directly tied to the density-wave transition. This is load-bearing because the 2Δ ≈ 71 meV value is the basis for comparing with optical/NMR/ARPES gaps and for the claim that the partial gap suppresses ambient-pressure superconductivity.
  2. [§2, Fig. 2(c)] The quoted qCDW ≈ 0.76 qb is given without an uncertainty and without a discussion of the FFT peak calibration, which matters because the surface is reconstructed and the qCDW period enters the fitting model as 1.316b in Eq. (1). A 1% error in q would shift the period noticeably, and since the gap-phase analysis depends on the fitted φCDW, the precision of q must be quantified. A temperature-dependent measurement showing that the qCDW spots disappear above T_DW would also directly connect the observed modulation to the bulk transition; without it, the assignment relies entirely on consistency with prior XRD.
  3. [§3, Eq. (1)] The four-cosine fitting model is asserted rather than validated. The fits are applied to a single spatial line cut at each energy (cut #3 in Fig. 3), with no residuals, goodness-of-fit measures, or comparison of alternative models such as a continuum of q or additional harmonics. Because the CDW phase φCDW is the central evidence for the gap-edge assignment, the fit should be shown to be stable and unique, including a test of whether the 1.316b component is distinguishable from neighboring periods given the line-cut length and noise.
  4. [§1, Fig. 1(g) and §2] The paper states that the 2b and 4b lattice distortion exists solely on the cleaved surface, yet both this surface reconstruction and the CDW modulation are measured on the same LaO-I surface. Although qCDW matches the bulk XRD wave vector, the possibility that the observed modulation and the associated gap are surface-specific or surface-enhanced is not directly addressed. Since the paper's title claims direct visualization of a CDW in La4Ni3O10, the surface-versus-bulk issue should be discussed explicitly, for example by noting the degree of coupling between the surface reconstruction and the CDW or by comparing with any bulk-sensitive measurements on the same crystals.
minor comments (5)
  1. [Abstract and main text] There is a typo 'APRES' in the paragraph discussing ARPES measurements by two groups; this should read 'ARPES'.
  2. [Table I] The table uses a Roman numeral 'Ⅰ' in the caption; standard formatting with 'Table 1' would be clearer.
  3. [§3, text after Eq. (1)] The statement that 2Δ ≈ 71 meV 'aligns well' with T_DW = 138 K is not quantified; the BCS mean-field ratio 2Δ/kBT_DW ≈ 6 is notably larger than the weak-coupling value of 3.52, so the phrase needs either a strong-coupling justification or a softer wording.
  4. [Fig. 2(c)] The FFT intensity profiles are said to be taken at different energies, but the specific energies are not listed in the caption or text; including the energies would make the nondispersive character of the CDW peak easier to verify.
  5. [References] Several cited works are arXiv preprints (e.g., [25], [35]-[37], [40], [42], [43], [55]); this is acceptable in a fast-moving field, but the authors should ensure the published versions are cited where available at the time of revision.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: STM observations and fits are not constructed from the claimed conclusions.

full rationale

The paper's central results are the real-space qCDW≈0.76qb modulation and the 2Δ≈71 meV depletion. Both are extracted from raw STM/STS data: qCDW is read from FFT spots in dI/dV maps and checked against an external XRD value (ref 27), and the gap interval is identified from the measured dI/dV spectrum plus free fits of cosine components whose phases were not constrained to reverse. The phase reversal between P3 and P4 is a fitted output, not an input, so calling P3/P4 the gap edges is an interpretive inference, not a definitional reduction. The nesting scenario borrows qSDW=1/2qCDW from prior bulk work (ref 27) and the Fermi surface from ARPES (ref 36); borrowing external inputs is not circular. Self-citations (refs 51-53) are used only as an analogy for intertwined SDW/CDW orders and do not carry the derivation. The absence of a normal-state control and the absence of error bars on fitted phases are legitimate correctness concerns but are explicitly not circularity under the review criteria.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central claim rests mainly on the STM measurement and three interpretive assumptions: the decomposition into four cosine periods, the identification of the FFT peak as an electronic CDW, and the assignment of the gap edges by phase reversal. No new physical entities are introduced; the nesting scenario borrows qSDW and the Fermi surface from prior work.

free parameters (2)
  • Cosine-component amplitudes (A_b, A_CDW, A_2b, A_4b) at P1-P5 = Values in Table I
    Fit parameters used to separate the CDW component from lattice and reconstruction periods; no error bars or cross-validation are given.
  • Cosine-component phases (φ_b, φ_CDW, φ_2b, φ_4b) at P1-P5 = Values in Table I
    Used to infer the CDW phase reversal between P3 and P4, which underpins the gap-edge assignment.
assumptions (5)
  • ad hoc to paper The dI/dV spatial modulation is the sum of four independent cosine components with periods b, 1.316b, 2b and 4b plus a linear background (Eq. 1).
    This decomposition is chosen after the FFT spots are identified; the paper does not test alternative models or provide statistical justification.
  • domain assumption The 0.76 qb FFT peak in dI/dV maps reflects an electronic CDW, not a surface reconstruction or artifact.
    The paper argues the q value matches bulk XRD [27], but also finds a surface-only lattice distortion, so the electronic origin is inferred rather than proven.
  • ad hoc to paper The peaks at -32 meV and +39 meV are the edges of the CDW gap because the extracted CDW phase is nearly reversed between them.
    This is a phase-consistency argument from the fitted cosine model, without temperature dependence or momentum-resolved data.
  • domain assumption The ARPES Fermi surface from ref. [36] can be used to evaluate nesting on the distorted LaO-I surface measured by STM.
    The STM surface has a lattice distortion that the bulk ARPES surface does not, and the FS is C4 symmetric while the CDW is unidirectional.
  • domain assumption The relation qCDW = 2 qSDW and the dominance of SDW over CDW from refs. [27,37] apply to the measured surface.
    The paper uses these prior results to propose FS nesting at qSDW = 0.38 qb and 0.62 qb, but does not measure the SDW itself.

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Cite this review

Pith. "Pith review of Direct Visualization of an Incommensurate Unidirectional Charge Density Wave in La$_4$Ni$_3$O$_{10}$." pith.science (2026). https://pith.science/paper/UN7FZBND

@misc{pith2026250118885,
  author       = {Pith},
  title        = {Pith review of: Direct Visualization of an Incommensurate Unidirectional Charge Density Wave in La$_4$Ni$_3$O$_10$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UN7FZBND}},
  note         = {Machine review of arXiv:2501.18885}
}
abstract

Superconductivity emerges in both La$_3$Ni$_2$O$_7$ and La$_4$Ni$_3$O$_{10}$ under high pressure by suppressing their density-wave transitions, but critical temperature (Tc) differs significantly between these two compounds. To gain deeper insights into the distinct superconducting states, it is essential to unravel the nature of the density-wave states at ambient pressure, a topic that remains largely unexplored. Here, using scanning tunneling microscopy/spectroscopy (STM/STS), we report the direct visualization of an incommensurate unidirectional charge density wave (CDW) in La$_4$Ni$_3$O$_{10}$ in real space. The density of states (DOS) is strongly depleted near $E_F$, indicating the opening of a CDW gap of $2{\Delta} \approx 71$ meV, which is unfavorable for the formation of superconductivity at ambient pressure. We propose that the CDW arises from Fermi surface nesting, and is likely a subsidiary phase of a spin density wave. Compared to La$_3$Ni$_2$O$_7$, the weaker electronic correlation in La$_4$Ni$_3$O$_{10}$ is likely one reason for the lower $T_c$.

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Forward citations

Cited by 3 Pith papers

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  1. Multiorbital character of the density wave in trilayer nickelate superconductors

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    Polarized Raman scattering on trilayer nickelate La4Ni3O10 identifies 114 meV as the density wave gap, with a multiorbital origin involving both Ni-3d orbitals.

  2. Suppression of Intertwined Density Waves in La$_4$Ni$_{3-x}$Cu$_x$O$_{10+\delta}$

    cond-mat.str-el 2025-07 accept novelty 5.0 of 10

    Copper substitution linearly suppresses the density wave transition in La4Ni3O10 and releases mobile holes, but does not by itself induce superconductivity.

  3. Recent progress in nickelate superconductors

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    A comprehensive review of nickelate superconductors that surveys the 112, 327, and 43(10) families and frames the key open questions about their pairing mechanisms.

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Reviewed August 9, 2026 · model on record in the stance chip above.