Ghost Josephson plasmon in bilayer superconductors

Lara Benfatto; Niccol\`o Sellati

REVIEW 3 major objections 4 minor 1 cited by

Ghost Josephson plasmon in bilayer superconductors

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The lower Josephson plasmon in a bilayer superconductor carries zero density-response weight at $q_c=0$ because it is a staggered, $c$-axis-polarized mode that stays transverse until the out-of-plane momentum grows.

desk verdict The q_c=0 ghost mechanism is real, but the finite-q_c predictions and the RIXS assignment rest on a density probe that omits the sublattice phase. read the letter →

arxiv 2412.14927 v1 pith:C7YELWJK submitted 2024-12-19 cond-mat.supr-con

Niccolò Sellati , Lara Benfatto This is my paper · ORCID

classification cond-mat.supr-con

keywords Josephsonplasmonbilayersuperconductorghostmodedensity-densityresponsephase-onlyactionpolarizationRIXScuprate

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 explains why one of the two Josephson plasmons in a bilayer superconductor is a ghost: it has zero weight in the density response at zero out-of-plane momentum $q_c=0$, even though the mode genuinely exists. Working with a phase-only action for the superconducting order parameter, the authors derive the full density-density response and show that the lower mode's spectral weight vanishes at $q_c=0$ for every in-plane momentum. The reason is that the lower mode is built from counterflowing currents polarized along the $c$-axis, so at small $q_c$ it is virtually transverse and cannot be excited by a longitudinal density probe. As $q_c$ grows, the mode acquires a longitudinal projection and becomes visible, which the authors use to argue that a RIXS branch in a bilayer cuprate is this lower plasmon.

What carries the argument

The machinery is a Gaussian, phase-only action for superconducting phase fluctuations, promoted to a $2\times2$ matrix form for the two layers per unit cell and dressed with the Coulomb interaction through the scalar potential, Eqs. (15)-(16). The density-density response, Eq. (20), is rearranged so the two Josephson-mode poles $\omega_\pm(q)$ appear explicitly, giving the spectral weights $W_\pm(q)$ in Eqs. (23)-(24). To expose the physical mechanism, the authors introduce gauge-invariant current fields $\psi_a,\psi_c$ and the normalized longitudinal projection $\psi^\pm_L(q)$; this is the object that shows the upper mode is longitudinal for all momenta while the lower mode is transverse at small $q_c$ and becomes longitudinal only at large $q_c$.

What would settle it

A momentum-resolved density probe on a clean bilayer superconductor, sweeping $q_c$ through zero at small fixed $q_a$, would falsify the claim if it resolved a lower-branch peak at $q_c=0$ or if the spectral weight $W_-(q)$ computed from the microscopic parameters stayed finite as $q_c\to 0$.

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Extended reading notes

Core claim

The central claim is that in a bilayer superconductor with two inequivalent interlayer Josephson couplings, the lower Josephson plasmon is invisible to density probes at $q_c=0$ because it is a staggered, $c$-axis-polarized mode. When the two layers per unit cell break the translational symmetry along $c$, the single-layer plasmon dispersion backfolds from the zone boundary to $q_c=0$; the folded branch keeps the polarization it had at the boundary, namely currents perpendicular to the planes that counterflow between the intrabilayer and interbilayer spacings. Such a mode is transverse at small $q_c$, so its spectral weight $W_-(q)$ in Eq. (24) vanishes identically at $q_c=0$ for all $q_a$, while the upper mode remains fully longitudinal. For larger $q_c$ the lower mode develops a longitudinal projection and reappears in the density response, with opposite-sign density fluctuations in the two layers.

Load-bearing premise

The argument assumes that retardation effects are negligible, so the superconducting phase couples only to the scalar potential; if the neglected phase-vector-potential coupling matters at the smallest probed $q_c$, the lower mode could acquire a small density response and would not be strictly ghost.

Editorial extensions

If this is right

At $q_c=0$ the density response contains only the upper Josephson plasmon; the lower branch cannot be detected by RIXS or EELS at that momentum, regardless of in-plane momentum.
The spectral weight of the lower branch is not periodic in $q_c$ with period $2\pi/d$: the mode reappears when $q_c$ approaches the zone boundary, so a measurement at $q_c=1.8\pi/d$ can see the branch that is invisible at $q_c=0.2\pi/d$.
For the bilayer cuprate Ca-YBCO, the RIXS-measured dispersion is most plausibly the lower Josephson plasmon, with the upper branch overdamped in the quasiparticle continuum.
In the region where it becomes visible, the lower plasmon's density fluctuations in the two layers have opposite signs and its dispersion is approximately linear, resembling the acoustic demon-like mode discussed for multiband metals.

Reading between the lines

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

An extension of the mechanism suggests that any multicomponent superconductor whose unit cell contains several layers should show similar ghost branches whenever a dispersion folded from the zone boundary is polarized transverse to the density-probe direction; artificial bilayer and superlattice systems could test this directly.
The distinction between a ghost mode and a truly neutral mode matters experimentally: a transverse mode should still appear in optical conductivity or transverse current probes at small $q_c$, offering a separation between the two explanations that the paper does not work out.
The analogy with the acoustic demon mode raises a broader question the paper leaves open: whether out-of-phase density oscillations generically produce acoustic dispersions in multicomponent metals and superconductors, independent of the folding mechanism that creates them.
Because the spectral weight is not periodic in $q_c$, analyses that fold experimental momenta into the first Brillouin zone should assign branch intensities carefully, since the same physical mode can appear bright or dark depending on which zone image is measured.

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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 core idea here is good, and at q_c=0 it holds up: the lower Josephson plasmon is a counterflowing, c-axis-polarized mode whose density spectral weight vanishes because it is effectively transverse and staggered. That result follows from the matrix structure, reproduces earlier RPA calculations, and the backfolding picture plus gauge-invariant current analysis are genuinely new. Worth a serious look.

But the stress-test note is correct, and it matters. The response matrix in Eq. (20) is built in the two-layer basis, and a physical density probe at finite q_c couples to the layers with phase factors 1 and e^{-iq_c d1}. The paper instead sums all matrix elements of the response, which is only valid at q_c=0. This is not a harmless approximation: it is exactly what generates the claimed 2π/d non-periodicity of the spectral weights. A physical response in a periodic crystal must be periodic. Once the sublattice phases are included, the lower-branch weight at q_c=1.8π/d equals the weight at q_c=-0.2π/d (equivalently 0.2π/d), which is small. So the central prediction—that the lower branch becomes visible at the RIXS momentum—and the fit to the Ca-YBCO data in Sec. III.C rest on an unphysical density operator. The q_c=0 ghost survives; the finite-q_c story does not.

Other caveats are minor by comparison: the alpha=0 closed forms and neglect of retardation are acknowledged and do not affect the q_c=0 result. The paper is internally consistent and honest about its own limitations, which is why I would send it to a referee: the flaw is specific and fixable in principle, and the q_c=0 mechanism could still be a useful contribution if the finite-q_c analysis is redone with the correct probe coupling.

In current form, I would not cite it for the experimental claim, and I would not trust the visibility criterion at large q_c. But the physical picture of the ghost at q_c=0 is a real step forward.

Referee Report

3 major / 4 minor

Summary. The manuscript develops a phase-only action description of collective plasma modes in bilayer superconductors and derives the density-density response matrix. Its central claim is that the lower Josephson plasmon has zero spectral weight in the density response at out-of-plane momentum q_c=0 because it is a staggered, c-axis-polarized counterflow mode that is virtually transverse at small q_c. The authors further claim that this mode becomes visible at large q_c, that the spectral weights are not periodic in q_c, and that the RIXS branch observed in Ca-YBCO at q_c=1.8π/d should be assigned to this lower plasmon. The derivation reproduces earlier RPA results and offers a physically appealing backfolding picture.

Significance. If the ghost mechanism is correct, the paper provides a valuable analytical and physical explanation for the invisibility of the lower Josephson plasmon in bilayer cuprates: the mode's polarization is transverse to the density probe at small q_c, unlike the in-phase upper mode. The closed forms for the spectral weights in the α→0 limit, the explicit connection to current polarizations via the gauge-invariant ψ fields, and the cross-checks against independent RPA calculations (refs. 22, 46, 47) are useful contributions. The analogy with the Pines' demon is stimulating. However, the finite-q_c visibility and the RIXS assignment rest on a questionable definition of the physical density operator, which is a load-bearing issue for the paper's experimental claims.

major comments (3)

[Sec. III.A, Eq. (22)] The charge response is defined as -Im Σ_{αβ}[χ̂_{ρρ}]_{αβ}. For a periodic bilayer with layer positions r_1=R and r_2=R+d_1, a physical plane-wave scalar potential δφ(r)=δφ_q e^{iq·r} couples to the two sublattices with amplitudes (1, e^{-iq_c d_1}) (up to a global phase). The physical density response is therefore e(q)^T χ̂(q) e(q), not the unweighted sum over all matrix elements. The unweighted sum corresponds to a probe that is identical on both layers of every unit cell, i.e., a staggered potential rather than a plane wave. Consequently, the finite-q_c spectral weights in Eqs. (23)-(24), the claimed non-periodicity, and the visibility of the lower branch at q_c=1.8π/d are not established. The vanishing at q_c=0 survives because the phase factor reduces to unity there, but the crucial finite-q_c prediction is an artifact of the probe definition.
[Sec. III.A, after Eq. (24)] The statement that the spectral weights of the density-density response are not 2π/d periodic is unphysical for a periodic crystal: any observable response function must be periodic under q_c→q_c+2π/d. The non-periodicity of W_±(q) follows directly from the use of the unweighted matrix sum. With the correct sublattice-coherent probe, the response at q_c=1.8π/d is equal to that at q_c=-0.2π/d (and hence, by inversion symmetry, to that at q_c=0.2π/d). The authors should either justify an alternative Fourier convention that makes their sum the physical response or remove the non-periodicity claim and recompute the spectral weights.
[Sec. III.C and Fig. 7] The RIXS comparison relies on a large lower-branch spectral weight at q_c=1.8π/d. Since the physical spectral weight at this momentum is the same as at q_c=-0.2π/d, where the lower branch has small weight according to the authors' own Fig. 3(b), the assignment of the measured mode to the lower plasmon is not supported unless additional q-dependent matrix elements (e.g., form factors or the RIXS scattering cross-section) are explicitly modeled. The authors should re-evaluate the comparison with Ref. [22] and discuss which physical ingredients could lead to a difference between q_c=1.8π/d and q_c=0.2π/d in the measured intensity.

minor comments (4)

[Sec. III.A, Fig. 2] The symbol d_2 is used throughout but never defined; please define d_2 = d - d_1 explicitly.
[Secs. II.B and III.A, Eqs. (12) and (22)] The delta-function spectral weights in Eqs. (12) and (22) are stated without the phenomenological damping γ; the figures use Lorentzian broadening, so the relationship between the analytic expressions and the plotted intensities should be clarified.
[Sec. III.B and Fig. 6] The layer-resolved responses χ_c^(1) and χ_c^(2) are introduced only in the text near Fig. 6; please give explicit definitions in the main text and specify the probe convention used for these quantities.
[Abstract] The phrase 'two layers per unit cells' contains a minor grammatical error; it should read 'two layers per unit cell'.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the ghost-plasmon mechanism is derived from the phase-only action and checked against independent RPA results; the finite-q_c Bloch-phase objection is a correctness issue, not a circular step.

full rationale

The central claim is derived, not assumed. Equation (24) gives W_-(q) explicitly, and its vanishing at q_c = 0 follows from algebraic facts in the same equation: omega_+(q_a,0) = omega_ab and the sin(q_c d_lambda/2) factors. No fitted parameter or target observable enters this step. The transverse/counterflow polarization picture is obtained from the eigenvectors of the gauge-invariant action in Appendix C, so it too is a derived property rather than an ansatz. The paper is heavily self-citing: the phase-only formalism comes largely from Refs. 42 and 50-52 by the same group. However, that prior work is a parameter-free effective-action scheme and is explicitly benchmarked against independent RPA computations (Refs. 22, 46, 47), so the self-citation is not load-bearing. The RIXS comparison in Sec. III.C is a fit of material parameters to data, not a prediction that is statistically forced by those same fitted parameters; the branch assignment is an interpretation of the fitted curves. The skeptical Bloch-phase objection to Eq. (22) -- that the physical density probe should carry e^{-iq_c d_1} phase factors for the two sublattices, making the physical response periodic -- is a substantive correctness concern about the finite-q_c observable, but it is not a circularity: the finite-q_c spectral weights may be artifacts of the unweighted sum, yet they are not obtained by defining the target answer into the premises or by fitting the conclusion. The stated retardation cutoff qbar is also an explicit regime limitation, not a hidden input. I therefore find no circular step; the moderately heavy reliance on the authors' own earlier formalism justifies a score of 2 rather than 0.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central mechanism is derived from a phase-only action with standard RPA dressing. No new particles or fields are introduced. The free parameters are material inputs and fit parameters; the zero of the lower-branch spectral weight does not depend on their specific values. The main axioms are the phase-only model, the neglect of retardation, the two-coupling bilayer model, and the alpha = 0 simplification.

free parameters (6)

omega_ab/2pi = 1.24 eV = 1.24 eV
In-plane plasma frequency fitted to RIXS data of Ref. [22] in Sec. III.C; affects the experimental branch assignment but not the central zero of W_-.
omega_c1/2pi = 330 meV = 330 meV
Intrabilayer Josephson plasma frequency fitted to RIXS data in Sec. III.C.
omega_c2/2pi = 4.96 meV = 4.96 meV
Interbilayer Josephson plasma frequency fitted to RIXS data in Sec. III.C.
alpha = 2.07 Angstrom^2 = 2.07 Angstrom^2
Debye screening length squared fitted to RIXS data in Sec. III.C.
gamma/2pi = 0.248 meV = 0.248 meV
Phenomenological damping fitted in Sec. III.C to match the RIXS peak width.
Figure parameters (omega_ab/omega_c2 = 200, omega_c1/omega_c2 = 12, d1/d = 0.3, a/d = 0.35, alpha/d^2 = 0.08)
Representative cuprate values chosen by hand for Figs. 2, 3, 5, 6. The central zero of W_- does not depend on these values.

assumptions (5)

domain assumption Phase-only Gaussian action for layered superconductors (Eq. 1) describes SC phase fluctuations below Tc.
Starting point of the derivation; assumes the phase of the order parameter is the only low-energy degree of freedom and that gradient expansion is valid.
domain assumption Minimal coupling plus RPA dressing via the scalar potential captures longitudinal plasmons.
Standard RPA treatment used to promote the sound-like phase mode to a plasmon; neglects vertex corrections beyond RPA.
domain assumption Neglect of the theta-A coupling (retardation) is valid at probed momenta.
Invoked after Eq. (4) and in Sec. III.B; justified by the statement that retardation matters only below a momentum scale of order micrometer^-1.
domain assumption The bilayer is described by two different Josephson couplings D_c1 and D_c2 with lattice spacings d1 and d2.
Central model assumption for bilayer cuprates, introduced in Sec. III.A, that creates the two-mode structure.
ad hoc to paper The alpha = 0 (infinite compressibility) limit does not change the qualitative behavior of the spectral weights.
Used in Sec. III.A to obtain the compact closed forms for W_+ and W_- in Eqs. (23) and (24); the paper argues finite alpha does not change the overall response.

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Cite this review

Pith. "Pith review of Ghost Josephson plasmon in bilayer superconductors." pith.science (2026). https://pith.science/paper/C7YELWJK

@misc{pith2026241214927,
  author       = {Pith},
  title        = {Pith review of: Ghost Josephson plasmon in bilayer superconductors},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/C7YELWJK}},
  note         = {Machine review of arXiv:2412.14927}
}

read the original abstract

The experimental measurement of collective charge fluctuations in metals and superconductors is a preferential tool to benchmark fundamental interactions in solids. Recent experiments in multicomponent systems, from superconducting layered cuprates to multiband metals, highlighted striking effects due to the interplay between different degrees of freedom. In this paper we provide a physical explanation for the existence of a "ghost" Josephson plasmon in bilayer superconductors, layered systems with two layers per unit cells that interact with two different Josephson couplings. We show that one of the two plasmons that emerge after the breaking of the translational symmetry along the out-of-plane direction is connected to counterflowing current fluctuations polarized perpendicularly to the planes. This effect makes it a staggered mode that is virtually transverse at small out-of-plane momenta qc, explaining why it is hidden in the density response at small qc. Our work offers an additional perspective on the understanding of collective excitations in systems with multiple intertwined degrees of freedom.

Figures

Figures reproduced from arXiv: 2412.14927 by the authors.

**Figure 1.** (a) Josephson plasma mode dispersion ωRPA(q) according to Eq. (7) as a function of qa for some fixed qc. Dashed lines are ωL(q) according to Eq. (8). (b) Intensity map of χc(q, ω) of a single-layer superconductor according to Eq. (12) as a function of qa for fixed qc = 0.2π/d. The response function is normalized to its maximum value. White dashed line represents ωRPA(q). In the plots, ωab/ωc = 200, a/d = 0.6, α/d2 =… view at source ↗

**Figure 2.** (a) Schematic representation of two subsequent bi [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Intensity map of χc(q, ω) of a bilayer superconductor according to Eq. (22) as a function of qa for fixed (a) qc = 0, (b) qc = 0.2π/d, (c) qc = 1.8π/d, or (d) as a function of qc for fixed qa = 0.05π/a. Every intensity map is normalized to its maximum value. White dashed lines represent the RPA dispersions ω+(q) and ω−(q). In the plot we used ωab/ωc2 = 200, ωc1/ωc2 = 12, d1/d = 0.3, a/d = 0.35, α/d2 = 0.08 and γ/ωc2… view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: Sketch of the backfolding mechanism that leads to [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 5.** Figure 5: (a) Schematic representation of the polarization [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

**Figure 6.** Figure 6: Intensity map of χ (λ) c (q, ω) for (a,c) λ = 1 and (b,d) λ = 2. In the plots we used the same parameters as in [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

**Figure 7.** Figure 7: Comparison between χc(q, ω) (color map) as in Eq. (22) and experimental points (red squares) extracted from Ref. [22]. The response function is normalized to its maximum value. Lattice parameters are a = 3.83 Å, d1 = 3.37 Å, d = 11.74 Å [69]. Fit parameters are ωab/2π …

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Works this paper leans on

70 extracted references · 50 canonical work pages · cited by 1 Pith paper

[22]

A. A. Husain, E. W. Huang, M. Mitrano, M. S. Rak, S. I. Rubeck, X. Guo, H. Yang, C. Sow, Y. Maeno, B. Uchoa, T. C. Chiang, P. E. Batson, P. W. Phillips, and P. Abba- monte, Pines’ demon observed as a 3d acoustic plasmon in sr2ruo4, Nature621, 66 (2023)

work page 2023
[1]

S. A. Maieret al., Plasmonics: fundamentals and appli- cations, Vol. 1 (Springer, New York, NY, 2007)

work page 2007
[2]

L. J. P. Ament, M. van Veenendaal, T. P. Devereaux, J. P. Hill, and J. van den Brink, Resonant inelastic x-ray scattering studies of elementary excitations, Rev. Mod. Phys. 83, 705 (2011)

2011
[3]

branch separately vanishes in each layer for smallqc, due to the fact that the current fluctuations are transverse and do not induce density fluctuations

Color bars are in logarithmic scale, saturated with blue for values between −10−5 and 10−5 and normalized to the maximum absolute value. branch separately vanishes in each layer for smallqc, due to the fact that the current fluctuations are transverse and do not induce density fluctuations. On the other hand for largeqc, see Fig. 6(c,d), the currents asso...

work page 2022
[4]

F. J. García de Abajo, Optical excitations in electron microscopy, Rev. Mod. Phys.82, 209 (2010)

2010
[5]

D. N. Basov, R. D. Averitt, D. van der Marel, M. Dres- sel, and K. Haule, Electrodynamics of correlated electron materials, Rev. Mod. Phys.83, 471 (2011)

2011
[6]

D. N. Basov, M. M. Fogler, and F. J. G. de Abajo, Po- laritons in van der waals materials, Science354, aag1992 (2016)

work page 2016
[7]

Nücker, H

N. Nücker, H. Romberg, S. Nakai, B. Scheerer, J. Fink, Y. F. Yan, and Z. X. Zhao, Plasmons and interband tran- sitions in bi2sr2cacu2o8, Phys. Rev. B39, 12379 (1989)

work page 1989

Show all 70 references

[8]

Nücker, U

N. Nücker, U. Eckern, J. Fink, and P. Müller, Long- wavelength collective excitations of charge carriers in high-tc superconductors, Phys. Rev. B44, 7155 (1991)

1991
[9]

R. S. Markiewicz, M. Z. Hasan, and A. Bansil, Acoustic plasmons and doping evolution of mott physics in res- onant inelastic x-ray scattering from cuprate supercon- ductors, Phys. Rev. B77, 094518 (2008)

2008
[10]

Greco, H

A. Greco, H. Yamase, and M. Bejas, Plasmon excitations in layered high-Tc cuprates, Phys. Rev. B 94, 075139 (2016)

2016
[11]

S. Vig, A. Kogar, M. Mitrano, A. A. Husain, V. Mishra, M. S. Rak, L. Venema, P. D. Johnson, G. D. Gu, E. Frad- kin, M. R. Norman, and P. Abbamonte, Measurement of the dynamic charge response of materials using low- energy, momentum-resolved electron energy-loss spec- troscopy ...

2017
[12]

Hepting, L

M. Hepting, L. Chaix, E. W. Huang, R. Fumagalli, Y. Y. Peng, B. Moritz, K. Kummer, N. B. Brookes, W. C. Lee, M. Hashimoto, T. Sarkar, J. F. He, C. R. Rotundu, Y. S. Lee, R. L. Greene, L. Braicovich, G. Ghiringhelli, Z. X. Shen, T.P.Devereaux,andW.S.Lee,Three-dimensional collec...

2018
[13]

Mitrano, A

M. Mitrano, A. A. Husain, S. Vig, A. Kogar, M. S. Rak, S. I. Rubeck, J. Schmalian, B. Uchoa, J. Schneeloch, R. Zhong, G. D. Gu, and P. Abbamonte, Anomalous den- sity fluctuations in a strange metal, Proceedings of the National Academy of Sciences115, 5392 (2018)

2018
[14]

A. A. Husain, M. Mitrano, M. S. Rak, S. Rubeck, B. Uchoa, K. March, C. Dwyer, J. Schneeloch, R. Zhong, G. D. Gu, and P. Abbamonte, Crossover of charge fluc- tuations across the strange metal phase diagram, Phys. Rev. X9, 041062 (2019)

2019
[15]

J. Lin, J. Yuan, K. Jin, Z. Yin, G. Li, K.-J. Zhou, X. Lu, M. Dantz, T. Schmitt, H. Ding, H. Guo, M. P. M. Dean, and X. Liu, Doping evolution of the charge ex- citations and electron correlations in electron-doped su- perconducting la2-xcexcuo4, npj Quantum Materials5, 4 (2020)

2020
[16]

B. Yu, W. Tabis, I. Bialo, F. Yakhou, N. B. Brookes, Z. Anderson, Y. Tang, G. Yu, and M. Greven, Un- usual dynamic charge correlations in simple-tetragonal hgba2cuo4+δ, Phys. Rev. X10, 021059 (2020)

2020
[17]

A. Nag, M. Zhu, M. Bejas, J. Li, H. C. Robarts, H. Ya- mase, A. N. Petsch, D. Song, H. Eisaki, A. C. Walters, M. García-Fernández, A. Greco, S. M. Hayden, and K.- J. Zhou, Detection of acoustic plasmons in hole-doped lanthanum and bismuth cuprate superconductors using resonant...

2020
[18]

Singh, H

A. Singh, H. Y. Huang, C. Lane, J. H. Li, J. Okamoto, S. Komiya, R. S. Markiewicz, A. Bansil, T. K. Lee, A. Fu- jimori, C. T. Chen, and D. J. Huang, Acoustic plasmons and conducting carriers in hole-doped cuprate supercon- ductors, Phys. Rev. B105, 235105 (2022)

2022
[19]

Hepting, M

M. Hepting, M. Bejas, A. Nag, H. Yamase, N. Coppola, D. Betto, C. Falter, M. Garcia-Fernandez, S. Agrestini, K.-J. Zhou, M. Minola, C. Sacco, L. Maritato, P. Or- giani, H. I. Wei, K. M. Shen, D. G. Schlom, A. Galdi, A. Greco, and B. Keimer, Gapped collective charge ex- citatio...

2022
[20]

C. Boyd, L. Yeo, and P. W. Phillips, Probing the bulk plasmon continuum of layered materials through electron energy loss spectroscopy in a reflection geometry, Phys. Rev. B106, 155152 (2022)

2022
[21]

S. J. Thornton, D. B. Liarte, P. Abbamonte, J. P. Sethna, and D. Chowdhury, Jamming and unusual charge density fluctuations of strange metals, Nature Communications 14, 3919 (2023)

2023
[23]

Bejas, V

M. Bejas, V. Zimmermann, D. Betto, T. D. Boyko, R. J. Green, T. Loew, N. B. Brookes, G. Cristiani, G. Logvenov, M. Minola, B. Keimer, H. Yamase, A. Greco, and M. Hepting, Plasmon dispersion in bi- layer cuprate superconductors, Phys. Rev. B109, 144516 (2024)

2024
[24]

A. Nag, L. Zinni, J. Choi, J. Li, S. Tu, A. C. Walters, S. Agrestini, S. M. Hayden, M. Bejas, Z. Lin, H. Yamase, K. Jin, M. García-Fernández, J. Fink, A. Greco, and K.- J. Zhou, Impact of electron correlations on two-particle charge response in electron- and hole-doped cuprate...

2024 arXiv
[25]

Schultz, A

J. Schultz, A. Lubk, F. Jerzembeck, N. Kikugawa, M. Knupfer, D. Wolf, B. Büchner, and J. Fink, Opti- cal and acoustic plasmons in the layered material sr2ruo4 (2024), arXiv:2401.05880 [cond-mat.str-el]

2024 arXiv
[26]

Abbamonte and J

P. Abbamonte and J. Fink, Collective charge excita- tions studied by electron energy-loss spectroscopy (2024), arXiv:2404.04670 [cond-mat.str-el]

2024 arXiv
[27]

J. Chen, X. Guo, C. Boyd, S. Bettler, C. Kengle, D. Chaudhuri, F. Hoveyda, A. Husain, J. Schneeloch, G. Gu, P. Phillips, B. Uchoa, T.-C. Chiang, and P. Ab- bamonte, Consistency between reflection momentum- resolved electron energy loss spectroscopy and optical spectroscopy mea...

2024
[28]

D.Pines,Electroninteractioninsolids,CanadianJournal of Physics34, 1379 (1956). 13

1956
[29]

Rajasekaran, E

S. Rajasekaran, E. Casandruc, Y. Laplace, D. Nicoletti, G. D. Gu, S. R. Clark, D. Jaksch, and A. Cavalleri, Para- metric amplification of a superconducting plasma wave, Nature Physics12, 1012 (2016)

2016
[30]

Rajasekaran, J

S. Rajasekaran, J. Okamoto, L. Mathey, M. Fechner, V. Thampy, G. D. Gu, and A. Cavalleri, Probing op- tically silent superfluid stripes in cuprates, Science359, 575 (2018)

2018
[31]

K. A. Cremin, J. Zhang, C. C. Homes, G. D. Gu, Z. Sun, M. M. Fogler, A. J. Millis, D. N. Basov, and R. D. Averitt, Photoenhanced metastable c-axis electrodynam- ics in stripe-ordered cuprate la1.885ba0.115cuo4, Pro- ceedings of the National Academy of Sciences116, 19875 (2019)

2019
[32]

D. Fu, D. Nicoletti, M. Fechner, M. Buzzi, G. D. Gu, and A. Cavalleri, Terahertz phase slips in striped la2−xbaxCuo4, Phys. Rev. B105, L020502 (2022)

2022
[33]

K. Kaj, K. A. Cremin, I. Hammock, J. Schalch, D. N. Basov, and R. D. Averitt, Terahertz third harmonic generation in c-axis la1.85sr0.15cuo4, Phys. Rev. B107, L140504 (2023)

2023
[34]

Katsumi, M

K. Katsumi, M. Nishida, S. Kaiser, S. Miyasaka, S. Tajima, and R. Shimano, Near-infrared light-induced superconducting-like state in underdoped Yba2cu3oy studied by c-axis terahertz third-harmonic generation, Phys. Rev. B107, 214506 (2023)

2023
[35]

von Hoegen, M

A. von Hoegen, M. Fechner, M. Först, N. Taherian, E. Rowe, A. Ribak, J. Porras, B. Keimer, M. Michael, E. Demler, and A. Cavalleri, Amplification of supercon- ducting fluctuations in driven yba2cu3o6+x, Phys. Rev. X 12, 031008 (2022)

2022
[36]

H. Hu, S. Kaiser, D. Nicoletti, C. R. Hunt, I. Gierz, M. C. Hoffmann, M. Le Tacon, T. Loew, B. Keimer, and A. Cavalleri, Optically enhanced coherent transport in yba2cu3o6.5 by ultrafast redistribution of interlayer cou- pling, Nature Materials13, 705 (2014)

2014
[37]

J. Yuan, L. Shi, L. Yue, B. Li, Z. Wang, S. Xu, T. Xu, Y. Wang, Z. Gan, F. Chen, Z. Lin, X. Wang, K. Jin, X. Wang, J. Luo, S. Zhang, Q. Wu, Q. Liu, T. Hu, R. Li, X. Zhou, D. Wu, T. Dong, and N. Wang, Dynamical interplay between superconductivity and pseudogap in cuprates as re...

2024 doi
[38]

Savel’ev, A

S. Savel’ev, A. L. Rakhmanov, V. A. Yampol’skii, and F. Nori, Analogues of nonlinear optics using terahertz josephson plasma waves in layered superconductors, Na- ture Physics2, 521 (2006)

2006
[39]

Savel’ev, V

S. Savel’ev, V. A. Yampol’skii, A. L. Rakhmanov, and F. Nori, Terahertz josephson plasma waves in layered superconductors: spectrum, generation, nonlinear and quantum phenomena, Reports on Progress in Physics73, 026501 (2010)

2010
[40]

M. H. Michael, A. von Hoegen, M. Fechner, M. Först, A. Cavalleri, and E. Demler, Parametric resonance of josephson plasma waves: A theory for optically ampli- fied interlayer superconductivity inYBa2Cu3O6+x, Phys. Rev. B102, 174505 (2020)

2020
[41]

Gabriele, M

F. Gabriele, M. Udina, and L. Benfatto, Non-linear tera- hertz driving of plasma waves in layered cuprates, Nature Communications 12, 752 (2021)

2021
[42]

P. E. Dolgirev, A. Zong, M. H. Michael, J. B. Curtis, D. Podolsky, A. Cavalleri, and E. Demler, Periodic dy- namics in superconductors induced by an impulsive op- tical quench, Communications Physics5, 234 (2022)

2022
[43]

Fiore, N

J. Fiore, N. Sellati, F. Gabriele, C. Castellani, G. Sei- bold, M. Udina, and L. Benfatto, Investigating joseph- son plasmons in layered cuprates via nonlinear terahertz spectroscopy, Phys. Rev. B110, L060504 (2024)

2024
[44]

van der Marel and A

D. van der Marel and A. Tsvetkov, Transverse optical plasmons in layered superconductors, Czech. J. of Phys. 46, 3165 (1996)

1996
[45]

C. C. Homes, T. Timusk, R. Liang, D. A. Bonn, and W. N. Hardy, Optical conductivity of c axis oriented YBa2Cu3O6.70: Evidence for a pseudogap, Phys. Rev. Lett. 71, 1645 (1993)

1993
[46]

A.Dubroka, M.Rössle, K.W.Kim, V.K.Malik, D.Mun- zar, D. N. Basov, A. A. Schafgans, S. J. Moon, C. T. Lin, D. Haug, V. Hinkov, B. Keimer, T. Wolf, J. G. Storey, J. L. Tallon, and C. Bernhard, Evidence of a precursor superconducting phase at temperatures as high as 180 k in rba2...

2011
[47]

S. T. Van den Eede, T. J. N. van Stralen, C. F. J. Flipse, and H. T. C. Stoof, Plasmons in a layered strange metal using the gauge-gravity duality, Phys. Rev. B109, 085119 (2024)

2024
[48]

Yamase, Theory of charge dynamics in bilayer elec- tron system with long-range coulomb interaction (2024), arXiv:2411.13650 [cond-mat.str-el]

H. Yamase, Theory of charge dynamics in bilayer elec- tron system with long-range coulomb interaction (2024), arXiv:2411.13650 [cond-mat.str-el]

2024 arXiv
[49]

Benfatto, S

L. Benfatto, S. Caprara, C. Castellani, A. Paramekanti, and M. Randeria, Phase fluctuations, dissipation, and su- perfluid stiffness in d-wave superconductors, Phys. Rev. B 63, 174513 (2001)

2001
[50]

Benfatto, A

L. Benfatto, A. Toschi, and S. Caprara, Low-energy phase-only action in a superconductor: A comparison with the XY model, Phys. Rev. B69, 184510 (2004)

2004
[51]

Gabriele, C

F. Gabriele, C. Castellani, and L. Benfatto, Generalized plasma waves in layered superconductors: A unified ap- proach, Phys. Rev. Res.4, 023112 (2022)

2022
[52]

Sellati, F

N. Sellati, F. Gabriele, C. Castellani, and L. Benfatto, Generalized josephson plasmons in bilayer superconduc- tors, Phys. Rev. B108, 014503 (2023)

2023
[53]

Sellati, J

N. Sellati, J. Fiore, C. Castellani, and L. Benfatto, Opti- calabsorptionintiltedgeometriesasanindirectmeasure- ment of longitudinal plasma waves in layered cuprates, Nanomaterials 14, 10.3390/nano14121021 (2024)

2024 doi
[54]

Nagaosa and S

N. Nagaosa and S. Heusler, Quantum Field Theory in Condensed Matter Physics, Texts and monographs in physics (Springer, New York, NY, 1999)

1999
[55]

H. A. Fertig and S. Das Sarma, Collective modes in lay- ered superconductors, Phys. Rev. Lett.65, 1482 (1990)

1990
[56]

H. A. Fertig and S. Das Sarma, Collective excitations and mode coupling in layered superconductors, Phys. Rev. B 44, 4480 (1991)

1991
[57]

E. H. Hwang and S. Das Sarma, Collective modes and their coupling to pair-breaking excitations in layered d- wave superconductors, Phys. Rev. B52, R7010 (1995)

1995
[58]

De Palo, C

S. De Palo, C. Castellani, C. Di Castro, and B. K. Chakraverty, Effective action for superconductors and bcs-bose crossover, Phys. Rev. B60, 564 (1999)

1999
[59]

Paramekanti, M

A. Paramekanti, M. Randeria, T. V. Ramakrishnan, and S. S. Mandal, Effective actions and phase fluctuations in d-wave superconductors, Phys. Rev. B62, 6786 (2000)

2000
[60]

Z. Sun, M. M. Fogler, D. N. Basov, and A. J. Millis, Collective modes and terahertz near-field response of su- perconductors, Phys. Rev. Research2, 023413 (2020). 14

2020
[61]

P. W. Anderson, Random-phase approximation in the theoryofsuperconductivity,Phys.Rev. 112,1900(1958)

1958
[62]

T. Cea, C. Castellani, and L. Benfatto, Nonlinear op- tical effects and third-harmonic generation in supercon- ductors: Cooper pairs versus higgs mode contribution, Phys. Rev. B93, 180507 (2016)

2016
[63]

T. P. Devereaux and D. Einzel, Electronic raman scatter- ing in superconductors as a probe of anisotropic electron pairing, Phys. Rev. B51, 16336 (1995)

1995
[64]

Coleman,Introduction to Many-Body Physics(Cam- bridge University Press, 2015)

P. Coleman,Introduction to Many-Body Physics(Cam- bridge University Press, 2015)

2015
[65]

van der Marel and A

D. van der Marel and A. A. Tsvetkov, Transverse-optical josephson plasmons: Equations of motion, Phys. Rev. B 64, 024530 (2001)

2001
[66]

Fazio and H

R. Fazio and H. van der Zant, Quantum phase transi- tions and vortex dynamics in superconducting networks, Physics Reports355, 235 (2001)

2001
[67]

Homann, J

G. Homann, J. G. Cosme, and L. Mathey, Higgs time crystal in a high-Tc superconductor, Phys. Rev. Res.2, 043214 (2020)

2020
[68]

Homann, J

G. Homann, J. G. Cosme, J. Okamoto, and L. Mathey, Higgs mode mediated enhancement of interlayer trans- port in high-Tc cuprate superconductors, Phys. Rev. B 103, 224503 (2021)

2021
[69]

Gabriele, R

F. Gabriele, R. Senese, C. Castellani, and L. Benfatto, Charge-density response in layered metals: Retardation effects, generalized plasma waves, and their spectroscopic signatures, Phys. Rev. B109, 045137 (2024)

2024
[70]

Mohan, K

R. Mohan, K. Singh, N. Kaur, S. Bhattacharya, M. Dixit, N. Gaur, V. Shelke, S. Gupta, and R. Singh, Calcium and oxygen doping in y ba2cu3oy, Solid State Communi- cations 141, 605 (2007)

2007

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [22]

A. A. Husain, E. W. Huang, M. Mitrano, M. S. Rak, S. I. Rubeck, X. Guo, H. Yang, C. Sow, Y. Maeno, B. Uchoa, T. C. Chiang, P. E. Batson, P. W. Phillips, and P. Abba- monte, Pines’ demon observed as a 3d acoustic plasmon in sr2ruo4, Nature621, 66 (2023)

work page 2023

[2] [1]

S. A. Maieret al., Plasmonics: fundamentals and appli- cations, Vol. 1 (Springer, New York, NY, 2007)

work page 2007

[3] [2]

L. J. P. Ament, M. van Veenendaal, T. P. Devereaux, J. P. Hill, and J. van den Brink, Resonant inelastic x-ray scattering studies of elementary excitations, Rev. Mod. Phys. 83, 705 (2011)

2011

[4] [3]

branch separately vanishes in each layer for smallqc, due to the fact that the current fluctuations are transverse and do not induce density fluctuations

Color bars are in logarithmic scale, saturated with blue for values between −10−5 and 10−5 and normalized to the maximum absolute value. branch separately vanishes in each layer for smallqc, due to the fact that the current fluctuations are transverse and do not induce density fluctuations. On the other hand for largeqc, see Fig. 6(c,d), the currents asso...

work page 2022

[5] [4]

F. J. García de Abajo, Optical excitations in electron microscopy, Rev. Mod. Phys.82, 209 (2010)

2010

[6] [5]

D. N. Basov, R. D. Averitt, D. van der Marel, M. Dres- sel, and K. Haule, Electrodynamics of correlated electron materials, Rev. Mod. Phys.83, 471 (2011)

2011

[7] [6]

D. N. Basov, M. M. Fogler, and F. J. G. de Abajo, Po- laritons in van der waals materials, Science354, aag1992 (2016)

work page 2016

[8] [7]

Nücker, H

N. Nücker, H. Romberg, S. Nakai, B. Scheerer, J. Fink, Y. F. Yan, and Z. X. Zhao, Plasmons and interband tran- sitions in bi2sr2cacu2o8, Phys. Rev. B39, 12379 (1989)

work page 1989