Edge polaritons at metal-insulator boundaries in a phase separated correlated oxide

Adrien Bercher; Alexey B. Kuzmenko; Claribel Dominguez; Javier del Valle; Javier Taboada-Gutierrez; Jeremie Teyssier; Weiwei Luo

REVIEW 3 major objections 4 minor 48 references

Edge polaritons at metal-insulator boundaries in a phase separated correlated oxide

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Edge polaritons of mixed phonon-plasmon character emerge at metal–insulator boundaries in thin NdNiO3 films, appearing as a one-dimensional edge state at sharp edges and as epsilon-near-zero response at smooth edges.

desk verdict Solid near-field observation of an edge phase peak in a phase-separated nickelate, but the 'long-propagating' edge polariton is currently a simulation, not a measured fact. read the letter →

arxiv 2506.03647 v1 pith:SKELXION submitted 2025-06-04 cond-mat.str-el

Weiwei Luo , Adrien Bercher , Claribel Dominguez , Javier del Valle , Jeremie Teyssier , Javier Taboada-Gutierrez , Alexey B. Kuzmenko This is my paper

classification cond-mat.str-el

keywords edgepolaritonsmetal-insulatortransitionphaseseparationNdNiO3correlatedoxidesepsilon-near-zerophonon-plasmonnear-fieldinfrarednanoscopy

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 sets out to explain a sharp phase peak that scattering-type scanning near-field optical microscopy sees exactly at metal–insulator boundaries in thin NdNiO$_3$ films, in a material family usually dismissed as too lossy for plasmonics. It claims the peak is the fingerprint of edge polaritons—hybrid phonon-plasmon modes confined to the boundary—that propagate several microns while keeping their cross-section near 100 nm. The paper further claims that the electromagnetic nature of these modes depends on boundary smoothness: a one-dimensional optical edge state at abrupt edges, and epsilon-near-zero absorption when the boundary is broad. If correct, near-field maps of phase-separated correlated oxides cannot be read as purely local dielectric images, and the same materials become candidates for tunable infrared nanophotonics.

What carries the argument

The load-bearing mechanism is the edge polariton: a quasi-one-dimensional electromagnetic mode that exists only at the metal–insulator boundary, carrying a mixture of phonon and plasmon character because the film's dielectric function combines phonon contributions with the free-carrier response of the metallic phase. In the simulations the boundary is parametrized by a metallicity factor $f$ between insulator and metal, Eq. (1), with a width $w$ that varies from sharp to smooth; the same interpolation places the epsilon-near-zero point at $f \approx 0.16$. The near-field signal is computed with a point-dipole emitter and a probe-point field $E_z$ in a finite-element model, and the dispersion of surface polaritons is obtained from the momentum- and frequency-dependent reflection coefficient $r_p(q,\omega)$. The amplitude–phase correlation curves, where the phase is plotted against the amplitude along a scan, provide the diagnostic that separates tip-excited surface-polariton interference (clockwise rotation) from the edge-polariton anomaly (counterclockwise rotation).

What would settle it

Measure the local dielectric function across a metal–insulator boundary in these films with nano-FTIR at sub-50-nm resolution, and check whether the phase peak survives when the measured permittivity profile across the boundary is used in the simulation; a large mismatch between the measured profile and the linear interpolation, or a phase peak with no corresponding edge-mode field map, would falsify the assignment.

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Extended reading notes

Core claim

On its own terms, the paper's central claim is that the pronounced near-field phase maximum observed at metal-insulator boundaries in phase-separated NdNiO$_3$ films is caused by edge-confined polaritons rather than by a local change in the dielectric function alone. The claim is supported by finite-element simulations in which a dipole source moves across a boundary described by a linear interpolation of the metallic and insulating dielectric functions with a metallicity parameter $f$. For an abrupt boundary the simulations show a narrow one-dimensional edge state that canalizes energy along the boundary for several microns; for a smooth boundary the response is controlled by epsilon-near-zero absorption where $\mathrm{Re}\,\varepsilon$ passes through zero. The two regimes connect continuously as the boundary width is varied, and the observed phase-peak widths (about 115–300 nm in different devices and temperatures) place the experiments between the sharp-edge and intermediate regimes. The paper also attributes the oscillations in the metallic region near boundaries to surface-polariton interference excited by the tip and reflected at the boundary.

Load-bearing premise

The whole interpretation rests on the assumption that the two coexisting phases can be described by the spatially averaged dielectric constants $\varepsilon_{\mathrm{met}} = -230 + 160i$ and $\varepsilon_{\mathrm{ins}} = 30 + 5i$ and that the boundary region is a linear mixture of them; if the local dielectric function at the nanoscale is not that mixture, the simulated edge modes and the phase-peak assignment would not hold.

Editorial extensions

If this is right

If the central claim is right, a s-SNOM phase peak at a metal–insulator boundary is a nonlocal polaritonic effect, and ignoring it will overestimate the actual physical width of the boundary.
The width of the phase peak becomes a usable indicator of the boundary regime: values near the sharp-edge limit (about 170 nm in the experiments) signal a true edge state, while broader peaks (about 300 nm) signal a more smeared epsilon-near-zero-dominated boundary.
Edge polaritons appear whether the metal–insulator transition is reached thermally or by current-induced Joule heating, so the effect does not depend on the particular way the boundary is created.
The propagation length to lateral confinement ratio above 10, together with the fact that much of the field sits in vacuum, points to these oxide edges as usable infrared waveguides despite the material's high losses.

Reading between the lines

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

One consequence the authors leave implicit is that phase maps of other phase-separated metal-insulator-transition materials, such as VO$_2$ or manganites, should be re-examined for the same nonlocal edge contribution before boundary widths are extracted from near-field profiles.
A direct test would be to measure the local dielectric function across a boundary with nano-FTIR at sub-50-nm resolution; if the real profile deviates strongly from the linear metallicity interpolation, the simulated edge-state to epsilon-near-zero crossover would need revision.
Because the edge-state to epsilon-near-zero crossover is continuous in boundary width, strain, current, or defect engineering could tune a single device between the two regimes, effectively making the edge state switchable.
The claim that most of the edge-state field is in vacuum suggests that thinner films or substrates with lower phonon losses could push propagation lengths further, an untested path toward low-loss infrared oxide plasmonics.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The paper reports a clear, reproducible near-field phase maximum at metal-insulator boundaries in phase-separated NdNiO3 films, and attributes it to edge polaritons whose character depends on boundary smoothness. That observation is likely real: it shows up across temperatures, in both spontaneously phase-separated and current-driven filament states, and in multiple devices, with no corresponding topography. The amplitude-phase correlation analysis is careful, and the FEM simulations reproduce the qualitative features, including the crossover from an ENZ-governed response for smooth boundaries to a narrower edge-state-like peak for sharp ones. This is a new system and a new pairing of mechanisms, and it deserves attention from people working on nanophotonics in correlated oxides.

The soft spots are in the gap between the experimental observation and the headline claim. The experiment shows a phase peak, not a propagating mode. The "strongly confined and long-propagating" edge polariton with micron-scale propagation is a simulation result: the field maps in Fig. 4e and the propagation-length figure of merit come from FEM, not from any measured decay length, fringes, or edge-launched standing waves. The paper's own Fig. 4a,b shows that both a smooth ENZ boundary and a sharp edge produce a phase peak, so the peak alone does not discriminate; the discrimination relies on the inferred boundary width w, which is calibrated to the measured peak width. That is a fitted parameter doing real work. The dielectric inputs are also far-field fitted values extrapolated to the nanoscale, with a linear interpolation assumption. None of these are fatal, but they mean the paper's central claim is underdetermined by the current data.

Smaller issues: no error bars on the phase-peak widths, no data or code release, and the discussion sometimes slides from "simulation shows" to what reads like an established property. Those are addressable.

Who is this for: experimentalists and theorists in mid-infrared nanophotonics, near-field optics, and strongly correlated oxides. A serious referee can push for direct propagation evidence—scanning along the boundary to detect decay or fringes—or at least a much clearer separation of the ENZ versus edge-state assignment using an independent measurement of the boundary width. I would not desk-reject this; the observation is solid enough to warrant refereeing, and the interpretation, while partly simulation-dependent, is plausible and worth sharpening.

Recommendation: send to review, with the expectation of major revision requesting either propagation measurements or a significantly toned-down propagation claim.

Referee Report

3 major / 4 minor

Summary. The manuscript reports mid-infrared s-SNOM measurements on 10-nm and 40-nm NdNiO3 films across the metal-insulator transition, either thermally induced or created by Joule-heated filaments. The central observation is a pronounced peak in the near-field phase at metal-insulator boundaries, accompanied by a characteristic flipped-S amplitude-phase correlation. The phase peak is reproduced by FEM simulations in which the local film dielectric function is linearly interpolated between far-field extracted metallic and insulating values with a boundary of variable width w. The simulations show two mechanisms: for smooth boundaries the peak is an ENZ-enhanced surface-polariton response; for sharp boundaries it is a 1D edge state with lateral confinement of about 100 nm and simulated propagation over several micrometers. The paper concludes that ignoring nonlocal polaritonic effects may bias estimates of boundary widths and argues for edge polaritons in correlated oxides.

Significance. If correct, the work would be significant because it extends edge-polariton physics to strongly correlated 'bad metals', a material class not previously considered for such low-loss modes, and it cautions that near-field images of phase-separated oxides should not be interpreted locally. The experimental dataset is a strength: the phase peak is reproduced across temperatures (92-95 K), two film thicknesses, and multiple devices, including electrically written filaments, and topography crosstalk is explicitly excluded. The use of a full 3D Maxwell FEM solver rather than a modal expansion, and the demonstration that smooth and sharp boundaries give distinguishable amplitude-phase correlations, are also strengths. The significance is currently limited by the fact that the headline properties of the mode, namely its propagation length and one-dimensional nature, are demonstrated only in simulation, not in the measured near-field data.

major comments (3)

[Edge polaritons and the nature of the phase peak (Fig. 4)] The discrimination between the ENZ mechanism and the one-dimensional edge state is made through the boundary width w in Eq. (2), but w is not independently measured. The text compares the experimental phase-peak FWHM (115-190 nm) with simulated FWHMs and concludes that the phase-separated state is 'close to the ES limit'; this effectively calibrates w to the very observable that the simulations are meant to explain. Because Fig. 4a and 4b show that both a smooth and a sharp boundary produce a phase peak, the measured peak alone does not identify the mechanism. An independent determination of w (e.g., from the temperature profile of the Joule-heated filament or from a boundary-sensitive probe) or a discrimination criterion that does not use w is needed to support the edge-state assignment.
[Fig. 4e and Discussion] The claim that the edge polaritons are 'long-propagating' over 'several microns' (Fig. 4e, inset of Fig. 4f) and the figure of merit 'well above 10' rest entirely on the FEM simulation. No experimental scan along the boundary, no edge-polariton standing-wave fringes, and no measured decay length are presented in the paper. The experimental observable is a local phase maximum, which cannot by itself distinguish a propagating mode from a localized edge resonance or enhanced absorption at a material step. Given that the abstract states this as a central result, the propagation claim should either be supported by real-space propagation data or explicitly downgraded to a simulated prediction.
[Polariton dispersion and s-SNOM signal far from MI boundaries; Methods] The simulation inputs are the mono-phase dielectric functions epsilon_met = -230 + 160i and epsilon_ins = 30 + 5i at 940 cm-1, obtained by Drude-Lorentz fitting of spatially averaged far-field reflectivity, combined with the linear interpolation of Eq. (1) and the piecewise-linear boundary profile of Eq. (2). The paper does not validate these assumptions at the nanoscale. If the local dielectric functions inside the phase-separated regions differ from the far-field averages, or if the linear mixing rule fails in the mixed region near f = f0, then the simulated field maps and the resulting ENZ/ES assignment could change. A robustness check, such as varying the interpolation rule within effective-medium bounds or using position-dependent spectra, would strengthen the central interpretation.

minor comments (4)

[Discussion] The sentence 'the peak width for the sharp edge (170 nm in Fig. 4a)' appears to refer to Fig. 4b, since Fig. 4a shows the smooth boundary with FWHM = 400 nm; please correct the figure reference.
[Fig. 2 and Fig. 4c] The comparison between the experimental APC curves and the simulated intermediate-width curve (green, w = 100 nm) is only qualitative; overlaying the experimental data on the simulated APC curves would make the claimed resemblance more convincing.
[Eq. (2)] The piecewise definition of f(x) would be clearer if the two constant regions were written explicitly as f(x) = 0 for x < -w/2 and f(x) = 1 for x > w/2, rather than using the Heaviside function in combination with the ramp.
[Introduction] The abstract's phrase 'nonlocal plasmonic effects' may be misleading: the FEM model uses local dielectric functions with a spatially varying metallicity, not a wavevector-dependent material response; consider rephrasing to 'spatially inhomogeneous' or 'boundary-mediated' effects.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the edge-polariton modes emerge from full FEM Maxwell solutions with independently fitted dielectric inputs; the experimental ES/ENZ assignment involves a boundary-width calibration, but this does not reduce the central claim to its inputs.

full rationale

The central derivation is not circular. The mono-phase permittivities ε_met = -230+160i and ε_ins = 30+5i are obtained from Kramers-Kronig-constrained Drude-Lorentz fits to far-field reflectivity in homogeneous states, and Eq. (1)'s linear interpolation plus Eq. (2)'s boundary profile are stated inputs. The FEM simulation then solves the full Maxwell problem and produces both the phase peak and the narrow, several-micron-long edge field pattern (Fig. 4b,e) as outputs; neither quantity is encoded directly in ε(f) or in the boundary profile. The claim that a sharp boundary hosts a one-dimensional edge state is therefore a non-trivial simulation result, not a restatement of the inputs. The main caveat is that the experimental attribution of the phase peak to the ES vs ENZ regime is made by comparing measured peak widths with simulated widths, effectively inferring the boundary width w (Eq. 2) from the same observable it is used to explain; this is a calibration/model-selection step rather than an independent prediction. There is also a minor self-citation (Ref. 30, Luibrand et al., with overlapping authorship) used to support the relation between phase-peak width and physical boundary width, but the central existence and propagation of the edge polariton do not rest on that citation. Overall, no load-bearing step reduces to its own inputs, so the paper is not significantly circular; score 2 reflects the minor self-citation and the inferred-boundary-width calibration.

Assumptions & free parameters 6 free parameters · 4 assumptions · 1 invented entities

The central claim rests on fitted mono-phase dielectric functions, a linear interpolation assumption, and an inferred boundary width. The edge state is a simulation-derived construct without independent experimental confirmation, though the forward Maxwell simulations are well-defined.

free parameters (6)

metallic-state dielectric function ε_met(ω_las) = -230 + 160i
Extracted from Drude-Lorentz fitting of far-field reflectivity of the spatially averaged film; used as input to Fresnel and FEM simulations.
insulating-state dielectric function ε_ins(ω_las) = 30 + 5i
Extracted from the same Drude-Lorentz fitting; used as input to all simulations.
ENZ metallicity f0 = 0.16
Defined by Re(ε(f0)) = 0 from the linear interpolation of the fitted dielectric functions; marks the ENZ regime.
boundary width w = 0, 100 nm, 1 µm (simulation scan); inferred from experiment
The FEM model scans w; the experimental value is inferred from the phase-peak FWHM using the simulation, not measured directly.
tip radius a = 40 nm
Assumed from the experimental tip; sets qtip = 1/a for the Fresnel analysis.
dipole height zd and probe height zp = 200 nm and 25 nm (low), 1.5 µm (high)
Model parameters in the FEM simulations; the low value is chosen to be small compared to the plasmon wavelength but is not precisely matched to the experimental tapping parameters.

assumptions (4)

ad hoc to paper The optical response of the mixed state is a linear interpolation between insulator and metal: ε(f,ω) = (1-f)ε_ins + f ε_met (Eq. 1).
Introduced to describe the gradual MIT with a single metallicity parameter f; ignores possible nanoscale phase coexistence and frequency-dependent mixing beyond a simple average.
ad hoc to paper The boundary profile f(x) is a piecewise linear ramp of width w (Eq. 2).
Simplified model for the order parameter variation across the boundary; smoothness is the key parameter but the exact functional form is not known.
domain assumption The 10 nm film can be replaced by an equivalent 2D conducting layer with the same optical 2D conductivity (Methods).
Valid when film thickness is much smaller than the infrared wavelength, which holds (10 nm versus 10 µm).
domain assumption The s-SNOM signal near edges is approximated by Ez at a probe point below a fixed point dipole (Supplementary Note 3).
Shown to match the complete model far from edges; used to make FEM tractable, but near edges the approximation is not independently validated.

invented entities (1)

One-dimensional optical edge state (ES)
purpose: Explains the phase peak at sharp metal-insulator boundaries as a guided mode along the edge that canalizes electromagnetic energy.
The ES is inferred from FEM simulations, not directly imaged or measured in a separate experiment. The only experimental signature is the phase peak, which could also arise from ENZ absorption for smooth boundaries.

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Cite this review

Pith. "Pith review of Edge polaritons at metal-insulator boundaries in a phase separated correlated oxide." pith.science (2026). https://pith.science/paper/SKELXION

@misc{pith2026250603647,
  author       = {Pith},
  title        = {Pith review of: Edge polaritons at metal-insulator boundaries in a phase separated correlated oxide},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SKELXION}},
  note         = {Machine review of arXiv:2506.03647}
}

abstract

Correlated transition metal oxides, such as cuprates, nickelates, and manganites, are typically considered "bad metals", where high electromagnetic losses suppress the conventional plasmonic effects observed in noble metals, 2D electron gases, and graphene. Nevertheless, using mid-infrared near-field optical nanoscopy, we demonstrate the emergence of strongly confined and long-propagating edge polaritons (EPs) of mixed phonon-plasmon nature at the boundaries between conducting and insulating regions in thin NdNiO$_{3}$ films, fingerprinted as a pronounced peak of the near-field signal phase. Our simulations reveal that the electromagnetic nature of the EPs depends significantly on the edge smoothness, being caused by a one-dimensional optical edge state (ES) at abrupt edges while being governed by the epsilon-near-zero (ENZ) absorption in the case of broad boundaries. Our findings highlight the critical role of nonlocal plasmonic effects in near-field imaging of phase-separated correlated oxides and open new avenues for infrared plasmonics in this family of materials.

Figures

Figures reproduced from arXiv: 2506.03647 by the authors.

**Figure 2.** FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p021_2.png] view at source ↗

**Figure 3.** FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p022_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p023_4.png]

**Figure 5.** Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p024_5.png]

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

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