pith. sign in

arxiv: 2511.03829 · v2 · submitted 2025-11-05 · ❄️ cond-mat.mes-hall · physics.optics

Unconventional quantization of 2D plasmons in cavities formed by gate slots

Ilia Moiseenko , Zhanna Devizorova , Olga Polischuk , Viacheslav Muravev , Dmitry Svintsov This is my paper

Pith reviewed 2026-05-18 00:41 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall physics.optics
keywords 2D plasmonsplasmonic cavitygate slotsquantization conditionreflection phase shiftabsorption cross-section2D electron system
0
0 comments X

The pith

A slot between parallel metal gates forms a plasmon cavity where modes resonate at L = λ/8 + nλ/2 because the wave picks up a -π/4 phase shift on reflection from the gate edge.

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

The paper shows that a narrow gap between two metal gates over a two-dimensional electron system creates an unconventional plasmon resonator. Resonances occur when slot width L satisfies L = λ/8 plus integer multiples of λ/2. This rule follows from the plasmon acquiring a phase shift of -π/4 upon reflection at the gate edge. The fundamental mode therefore fits into a cavity only one-eighth the plasmon wavelength, far smaller than standard half-wavelength resonators. The modes leak only weakly into the gated regions and absorb up to half the maximum dipole cross-section through field concentration at the edges.

Core claim

We demonstrate that the slot between parallel metal gates placed above two-dimensional electron system (2DES) forms a plasmonic cavity with unconventional mode quantization. The resonant plasmon modes are excited when the slot width L and the plasmon wavelength λ satisfy the condition L = λ/8 +n × λ/2, where n=0, 1, 2 …. This unique quantization rule arises from a non-trivial phase shift of −π/4 acquired by the 2D plasmon upon reflection from the edge of the gate. The slot plasmon modes exhibit weak decay into the gated 2DES region, with the decay rate being proportional to the square root of the separation between the gate and the 2DES. Absorption cross-section by such slots reaches ∼50 %of

What carries the argument

The non-trivial phase shift of −π/4 acquired by the 2D plasmon upon reflection from the edge of the gate, which fixes the quantization condition L = λ/8 + nλ/2 for the cavity modes.

If this is right

  • The lowest resonance occurs at a cavity size of only one eighth of the plasmon wavelength.
  • Plasmon modes decay weakly into the gated region at a rate proportional to the square root of the gate-2DES separation.
  • Absorption cross-section reaches about 50 percent of the fundamental dipole limit due to field enhancement at the metal edges.
  • Higher-order modes follow the same offset rule for n = 1, 2, and beyond.

Where Pith is reading between the lines

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

  • These gate slots could enable compact plasmonic resonators for terahertz circuits in 2D materials without additional matching structures.
  • Changing gate height or dielectric environment might alter the exact phase shift and thereby tune the quantization offset.
  • Analogous reflection phases could produce unconventional quantization rules in other confined 2D waves such as exciton polaritons.

Load-bearing premise

The plasmon wave acquires a reflection phase shift of exactly -π/4 at the gate edge under the modeled boundary conditions.

What would settle it

Measure absorption or transmission spectra for varying slot widths L at fixed plasmon wavelength λ and check whether resonance peaks occur precisely at L = λ/8 + nλ/2 for successive integers n.

Figures

Figures reproduced from arXiv: 2511.03829 by Dmitry Svintsov, Ilia Moiseenko, Olga Polischuk, Viacheslav Muravev, Zhanna Devizorova.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Schematic illustration of a slot-induced resona [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Reflection of the 2D plasmon at a single gate edge. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) The spectrum of absorption cross section [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The spectrum of absorption cross section [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
read the original abstract

We demonstrate that the slot between parallel metal gates placed above two-dimensional electron system (2DES) forms a plasmonic cavity with unconventional mode quantization. The resonant plasmon modes are excited when the slot width $L$ and the plasmon wavelength $\lambda$ satisfy the condition $L = \lambda/8 +n \times \lambda/2$, where $n=0, 1, 2 \ldots$. The lowest resonance occurs at a surprisingly small cavity size, specifically one eighth of the plasmon wavelength, which contrasts with the conventional half-wavelength Fabry-Perot cavities in optics. This unique quantization rule arises from a non-trivial phase shift of $-\pi/4$ acquired by the 2D plasmon upon reflection from the edge of the gate. The slot plasmon modes exhibit weak decay into the gated 2DES region, with the decay rate being proportional to the square root of the separation between the gate and the 2DES. Absorption cross-section by such slots reaches $\sim 50$ % of the fundamental dipole limit without any matching strategies, and is facilitated by field enhancement at the metal edges.

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 / 2 minor

Summary. The manuscript examines plasmonic cavities formed by a slot of width L between parallel metal gates above a 2DES. It claims that resonant modes obey the unconventional quantization condition L = λ/8 + n λ/2 (n = 0,1,2,…), originating from a fixed reflection phase shift of −π/4 acquired by the 2D plasmon at the gate edge. This yields a lowest resonance at L = λ/8 rather than the conventional λ/2. The work further states that slot modes decay weakly into the gated region with rate ∝ √d (d = gate-2DES separation) and that the absorption cross-section reaches ∼50 % of the fundamental dipole limit via edge-field enhancement.

Significance. If the phase-shift derivation and resulting quantization hold, the result would be significant for sub-wavelength plasmonic resonators and absorbers in gated 2DES. The parameter-free character of the L = λ/8 rule and the concrete prediction of a −π/4 phase shift constitute falsifiable claims that could guide THz device design. The reported absorption efficiency without external matching is a practical strength.

major comments (2)
  1. [Derivation of reflection phase and quantization condition] The quantization rule L = λ/8 + n λ/2 follows directly from the round-trip condition 2kL + 2φ = 2πn only when the reflection phase φ is exactly −π/4 and independent of d/λ. The electrostatic boundary-value problem at the gate edge (continuity of potential and normal current) must be solved explicitly to demonstrate that this value is obtained without corrections from the evanescent tail or finite d; any 10–15° deviation shifts the n=0 resonance away from L = λ/8 and collapses the claimed unconventional rule.
  2. [Validation of electrostatic model] No comparison is provided between the electrostatic phase calculation and either full-wave electromagnetic simulations or an exact integral-equation solution of the gate-edge discontinuity. Such a benchmark is required to confirm that the electrostatic approximation remains accurate across the relevant range of k d and to establish error estimates on the lowest resonance position.
minor comments (2)
  1. [Abstract] The abstract states the absorption reaches ∼50 % of the dipole limit; the main text should specify the frequency range, gate-2DES separation, and conductivity values for which this holds.
  2. [Introduction] Notation for the plasmon wavevector k and wavelength λ should be introduced consistently when the quantization condition is first written.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. We address each major comment below, providing clarifications on the derivation and model validation while indicating planned revisions to improve clarity.

read point-by-point responses

  1. Referee: [Derivation of reflection phase and quantization condition] The quantization rule L = λ/8 + n λ/2 follows directly from the round-trip condition 2kL + 2φ = 2πn only when the reflection phase φ is exactly −π/4 and independent of d/λ. The electrostatic boundary-value problem at the gate edge (continuity of potential and normal current) must be solved explicitly to demonstrate that this value is obtained without corrections from the evanescent tail or finite d; any 10–15° deviation shifts the n=0 resonance away from L = λ/8 and collapses the claimed unconventional rule.

    Authors: The manuscript derives the reflection phase by explicitly solving the electrostatic boundary-value problem at the gate edge, enforcing continuity of the electrostatic potential and the normal component of the current. This yields a reflection coefficient with phase shift exactly −π/4 in the leading electrostatic limit. We show that evanescent-mode corrections are exponentially localized and enter only at higher order in kd, leaving the phase shift unchanged to the accuracy required for the quantization condition. In the revised manuscript we will expand this section to include the full algebraic steps of the boundary matching and an explicit demonstration that the phase remains independent of d/λ within the stated approximation. revision: partial

  2. Referee: [Validation of electrostatic model] No comparison is provided between the electrostatic phase calculation and either full-wave electromagnetic simulations or an exact integral-equation solution of the gate-edge discontinuity. Such a benchmark is required to confirm that the electrostatic approximation remains accurate across the relevant range of k d and to establish error estimates on the lowest resonance position.

    Authors: We agree that an explicit numerical benchmark would strengthen the presentation. The electrostatic treatment is the standard and well-controlled approximation for 2D plasmons in the regime kd ≪ 1 that applies to the structures considered. We already provide an order-of-magnitude error estimate based on the neglected retardation and evanescent contributions. Performing full-wave simulations lies outside the present scope, but we will add a dedicated paragraph discussing the validity range of the electrostatic model together with references to prior literature that has performed similar benchmarks for gate-edge discontinuities in 2DES. revision: partial

Circularity Check

0 steps flagged

No circularity: quantization follows from independent boundary-condition phase calculation

full rationale

The paper obtains the reflection phase shift of −π/4 by solving the electrostatic boundary-value problem (continuity of potential and current) at the abrupt gate termination. This phase is inserted into the standard round-trip condition 2kL + 2φ = 2πn to produce the reported quantization L = λ/8 + nλ/2. Because the phase value is computed from the model equations rather than fitted to resonance data or defined in terms of the final result, the derivation does not reduce to its inputs by construction. No self-citation chain, ansatz smuggling, or renaming of a known empirical pattern is required for the central claim. The result is therefore self-contained against external benchmarks such as full-wave checks or independent electrostatic solvers.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim depends on standard electromagnetic boundary conditions for gated 2DES and on the calculated reflection phase; no new particles or forces are introduced.

axioms (1)
  • domain assumption 2D plasmon dispersion and boundary conditions at metal-gate edges follow standard electromagnetic theory for gated electron systems
    Invoked to obtain the reflection phase shift of −π/4

pith-pipeline@v0.9.0 · 5746 in / 1363 out tokens · 41307 ms · 2026-05-18T00:41:24.643608+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

46 extracted references · 46 canonical work pages

  1. [1]

    The slot plasmon spectrum obtained from Eqs

    or its simplified version ( 14). The slot plasmon spectrum obtained from Eqs. ( 15) and (14) reads as ω n = ω ′ n − iω ′′ n, (16) ω ′ n = π ( n + 1 4 ) cη′′ L , (17) ω ′′ n = ln [ 1 + qu(w′ n)/q g(w′ n) 1 − qu(w′n)/q g(w′n) ] cη′′ L + ω ′ nη′ η′′ . (18) The first remarkable property of the slot plasmon modes is the unconventional quantization rule ( 17), wh...

    work page

  2. [2]

    Although it fully accounts for evanescent field effects at a single boundary (encoded in arg r), it neglects the interactions of evanescent fields be- tween the two boundaries

    for calcula- tion of the eigenmodes. Although it fully accounts for evanescent field effects at a single boundary (encoded in arg r), it neglects the interactions of evanescent fields be- tween the two boundaries. This neglect is well justified for high-order modes n ≫ 1, whereas its applicability for n ∼ 1 may be questionable. The situation is analogous to B...

    work page

  3. [3]

    (b) The linewidth of the plasmon modes n = 0, 2, 4 calculated analytically using Eq

    as function of the slot width W obtained analytically. (b) The linewidth of the plasmon modes n = 0, 2, 4 calculated analytically using Eq. 18 (dashed curves) and fitted from the simulations data (solid curves). order of Z − 1 0 λ 0/λ pl. In a slot cavity, no special matching conditions are required. Another applied consequence of our study is the for- mat...

    work page

  4. [4]

    In summary, we have theoretically studied a new class of resonant cavities for 2D plasmons formed by slot in the metal gates

    is found. In summary, we have theoretically studied a new class of resonant cavities for 2D plasmons formed by slot in the metal gates. The unusual ’quantization rule’ for the mode frequencies L = λ/ 8 +n × λ/ 2, where n = 0, 1, 2 . . . is a consequence of anomalous − π/ 4 phase shift of 2D plasmon reflecting from the gate edge. Large excita- tion cross se...

    work page

  5. [5]

    S. A. Maier et al., Plasmonics: fundamentals and applications , Vol. 1 (Springer, 2007)

    work page 2007

  6. [6]

    W. L. Barnes, A. Dereux, and T. W. Ebbesen, Surface plasmon subwavelength optics, Nature 424, 824 (2003)

    work page 2003

  7. [7]

    Stern, Polarizability of a Two-Dimensional Electron Gas, Physical Review Letters 18, 546 (1967)

    F. Stern, Polarizability of a Two-Dimensional Electron Gas, Physical Review Letters 18, 546 (1967)

    work page 1967

  8. [8]

    Woessner, M

    A. Woessner, M. B. Lundeberg, Y. Gao, A. Prin- cipi, P. Alonso-Gonz´ alez, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hil- lenbrand, and F. H. L. Koppens, Highly confined low- loss plasmons in graphene–boron nitride heterostruc- tures, Nature Materials 14, 421 (2015)

    work page 2015

  9. [9]

    G. X. Ni, A. S. McLeod, Z. Sun, L. Wang, L. Xiong, K. W. Post, S. S. Sunku, B.-Y. Jiang, J. Hone, C. R. Dean, M. M. Fogler, and D. N. Basov, Fundamental lim- its to graphene plasmonics, Nature 557, 530 (2018)

    work page 2018

  10. [10]

    W. F. Andress, H. Yoon, K. Y. Yeung, L. Qin, K. West, L. Pfeiffer, and D. Ham, Ultra- subwavelength two-dimensional plasmonic circuits, Nano letters 12, 2272 (2012)

    work page 2012

  11. [11]

    R. F. Oulton, V. J. Sorger, D. Genov, D. Pile, and X. Zhang, A hybrid plasmonic waveguide for sub- wavelength confinement and long-range propagation, nature photonics 2, 496 (2008) . 6

    work page 2008

  12. [12]

    Basov, M

    D. Basov, M. Fogler, and F. Garc ´ ıa de Abajo, Polaritons in van der waals materials, Science 354, aag1992 (2016)

    work page 2016

  13. [13]

    R. B. Nielsen, I. Fernandez-Cuesta, A. Boltasseva, V. S. Volkov, S. I. Bozhevolnyi, A. Klukowska, and A. Kristensen, Channel plasmon polariton propagation in nanoimprinted v-groove waveguides, Opt. Lett. 33, 2800 (2008)

    work page 2008

  14. [14]

    Woessner, Y

    A. Woessner, Y. Gao, I. Torre, M. B. Lundeberg, C. Tan, K. Watanabe, T. Taniguchi, R. Hillenbrand, J. Hone, M. Polini, and F. H. Koppens, Electrical 2 π phase control of infrared light in a 350-nm footprint using graphene plasmons, Nature Photonics 11, 421 (2017)

    work page 2017

  15. [15]

    Alonso-Gonzalez, A

    P. Alonso-Gonzalez, A. Y. Nikitin, F. Golmar, A. Cen- teno, A. Pesquera, S. Velez, J. Chen, G. Navickaite, F. Koppens, A. Zurutuza, F. Casanova, L. E. Hueso, and R. Hillenbrand, Controlling graphene plasmons with res- onant metal antennas and spatial conductivity patterns, Science 344, 1369 (2014)

    work page 2014

  16. [16]

    Malyuzhinets, The excitation, reflection and radiat ion of surface waves in a wedge-like region with given face impedances, in Doklady Akademii Nauk , Vol

    G. Malyuzhinets, The excitation, reflection and radiat ion of surface waves in a wedge-like region with given face impedances, in Doklady Akademii Nauk , Vol. 121 (Rus- sian Academy of Sciences, 1958) pp. 436–439

    work page 1958

  17. [17]

    Sommerfeld, Mathematische theorie der diffraction, Mathematische Annalen 16, 317 (1896)

    A. Sommerfeld, Mathematische theorie der diffraction, Mathematische Annalen 16, 317 (1896)

    work page

  18. [18]

    Jiang, E

    B.-Y. Jiang, E. J. Mele, and M. M. Fogler, Theory of plasmon reflection by a 1D junction, Optics Express 26, 17209 (2018)

    work page 2018

  19. [19]

    Sydoruk, R

    O. Sydoruk, R. R. A. Syms, and L. Solymar, Amplify- ing mirrors for terahertz plasmons, Journal of Applied Physics 112, 10.1063/1.4766924 (2012)

    work page doi:10.1063/1.4766924 2012

  20. [20]

    A. Y. Nikitin, T. Low, and L. Martin-Moreno, Anoma- lous reflection phase of graphene plasmons and its influ- ence on resonators, Phys. Rev. B 90, 041407 (2014)

    work page 2014

  21. [21]

    Semenenko, M

    V. Semenenko, M. Liu, and V. Perebeinos, Scattering of quasistatic plasmons from one-dimensional junctions of graphene: Transfer matrices, fresnel relations, and non- locality, Phys. Rev. Appl. 14, 024049 (2020)

    work page 2020

  22. [22]

    Rejaei and A

    B. Rejaei and A. Khavasi, Scattering of surface plasmon s on graphene by a discontinuity in surface conductivity, Journal of Optics (United Kingdom) 17, 75002 (2015)

    work page 2015

  23. [23]

    D. A. Svintsov and G. V. Alymov, Re- fraction laws for two-dimensional plasmons, Physical Review B 108, L121410 (2023)

    work page 2023

  24. [24]

    Farajollahi, B

    S. Farajollahi, B. Rejaei, and A. Khavasi, Re- flection and transmission of obliquely incident graphene plasmons by discontinuities in surface conductivity: observation of the Brewster-like effect, Journal of Optics 18, 075005 (2016)

    work page 2016

  25. [25]

    Sydoruk, K

    O. Sydoruk, K. Choonee, and G. C. Dyer, Transmission and Reflection of Terahertz Plas- mons in Two-Dimensional Plasmonic Devices, IEEE Transactions on Terahertz Science and Technology 5, 486 (2015)

    work page 2015

  26. [26]

    G. R. Aizin and G. C. Dyer, Transmission line theory of collective plasma excitations in periodic two-dimensiona l electron systems: Finite plasmonic crystals and Tamm states, Physical Review B 86, 235316 (2012)

    work page 2012

  27. [27]

    Moiseenko, D

    I. Moiseenko, D. Svintsov, and E. Nikulin, Elec- tromagnetic diffraction and bidirectional plasmon launching in partially gated two-dimensional systems, Phys. Rev. Appl. 24, 014059 (2025)

    work page 2025

  28. [28]

    A. A. Zabolotnykh and V. A. Volkov, Interaction of gated and ungated plasmons in two-dimensional electron sys- tems, Physical Review B 99, 165304 (2019)

    work page 2019

  29. [29]

    S. A. Mikhailov, Plasma instability and amplification o f electromagnetic waves in low-dimensional electron sys- tems, Physical Review B 58, 1517 (1998)

    work page 1998

  30. [30]

    Kay, Scattering of a surface wave by a discontinuity in reactance, IRE Transactions on Antennas and Propagation 7, 22 (1959)

    A. Kay, Scattering of a surface wave by a discontinuity in reactance, IRE Transactions on Antennas and Propagation 7, 22 (1959)

    work page 1959

  31. [31]

    Noble, Methods Based on the Wiener-Hopf Technique for the Solution of Partial Differential Equations (Perg- amon Press, 1958)

    B. Noble, Methods Based on the Wiener-Hopf Technique for the Solution of Partial Differential Equations (Perg- amon Press, 1958)

    work page 1958

  32. [32]

    For Drude model ω ′′ = 1/ (2τp) and is frequency-independent

    The contribution of intrinsic dissipation to linewidt h ω ′′ ∼ (η′/η ′′)ω ′ grows with frequency only for non- dispersive 2DES conductivity. For Drude model ω ′′ = 1/ (2τp) and is frequency-independent

    work page

  33. [33]

    Ruan and S

    Z. Ruan and S. Fan, Superscattering of Light from Subwavelength Nanostructures, Physical Review Letters 105, 013901 (2010)

    work page 2010

  34. [34]

    Mylnikov and D

    D. Mylnikov and D. Svintsov, Limiting capabilities of two-dimensional plasmonics in electromagnetic wave de- tection, Physical Review Applied 17, 064055 (2022)

    work page 2022

  35. [35]

    E. J. Dias and F. J. Garc ´ ıa De Abajo, Fundamental Lim- its to the Coupling between Light and 2D Polaritons by Small Scatterers, ACS Nano 13, 5184 (2019)

    work page 2019

  36. [36]

    D. A. Iranzo, S. Nanot, E. J. Dias, I. Epstein, C. Peng, D. K. Efetov, M. B. Lundeberg, R. Parret, J. Osmond, J. Y. Hong, J. Kong, D. R. Englund, N. M. Peres, and F. H. Koppens, Probing the ultimate plasmon con- finement limits with a van der Waals heterostructure, Science 360, 291 (2018)

    work page 2018

  37. [37]

    Alonso Calafell, L

    I. Alonso Calafell, L. A. Rozema, D. Alcaraz Iranzo, A. Trenti, P. K. Jenke, J. D. Cox, A. Kumar, H. Bieli- aiev, S. Nanot, C. Peng, D. K. Efetov, J.-Y. Hong, J. Kong, D. R. Englund, F. J. Garc ´ ıa de Abajo, F. H. L. Koppens, and P. Walther, Giant enhancement of third- harmonic generation in graphene–metal heterostructures, Nature Nanotechnology 16, 318 (2021)

    work page 2021

  38. [38]

    V. Y. Kachorovskii and M. S. Shur, Current- induced terahertz oscillations in plasmonic crystal, Applied Physics Letters 100, 232108 (2012)

    work page 2012

  39. [39]

    Gorbenko and V

    I. Gorbenko and V. Kachorovskii, Lateral plasmonic cry s- tals: Tunability, dark modes, and weak-to-strong cou- pling transition, Phys. Rev. B 110, 155406 (2024)

    work page 2024

  40. [40]

    D. A. Miranda, Y. V. Bludov, N. Asger Mortensen, and N. M. R. Peres, Topology in a one- dimensional plasmonic crystal: the optical approach, Journal of Optics 26, 125001 (2024)

    work page 2024

  41. [41]

    S. J. Allen, D. C. Tsui, and R. A. Logan, Observation of the two-dimensional plasmon in silicon inversion layers, Physical Review Letters 38, 980 (1977)

    work page 1977

  42. [42]

    T. N. Theis, Plasmons in inversion layers, Surface Science 98, 515 (1980)

    work page 1980

  43. [43]

    A. R. Khisameeva, A. Shuvaev, A. A. Zabolotnykh, A. S. Astrakhantseva, D. A. Khudaiberdiev, A. Pi- menov, I. V. Kukushkin, and V. M. Muravev, Spec- trum of plasma excitations in a plasmonic crys- tal fabricated in an AlGaAs/GaAs heterostructure, Phys. Rev. Res. 7, 033224 (2025)

    work page 2025

  44. [44]

    Bylinkin, E

    A. Bylinkin, E. Titova, V. Mikheev, E. Zhukova, S. Zhukov, M. Belyanchikov, M. Kashchenko, A. Mi- akonkikh, and D. Svintsov, Tight-Binding Terahertz Plasmons in Chemical-Vapor-Deposited Graphene, Physical Review Applied 11, 054017 (2019)

    work page 2019

  45. [45]

    P. Sai, V. V. Korotyeyev, M. Dub, M. S/suppress lowikowski, M. Filipiak, D. B. But, Y. Ivonyak, M. Sakowicz, Y. M. Lyaschuk, S. M. Kukhtaruk, G. Cywi´ nski, and W. Knap, Electrical Tuning of Terahertz Plasmonic Crystal Phases, 7 Physical Review X 13, 041003 (2023)

    work page 2023

  46. [46]

    A. R. Khisameeva, A. Shuvaev, I. Moiseenko, P. A. Gusikhin, A. S. Astrakhantseva, A. Pimenov, D. Sv- intsov, I. V. Kukushkin, and V. M. Muravev, Discovery of slot plasma excitations in a AlGaN/GaN plasmonic crystal, arxiv preprint, jointly submitted with the presen t paper (2025). Appendix A: Derivation of electromagnetic scattering equa tion Derivation o...

    work page 2025