Pith. sign in

REVIEW 4 major objections 5 minor 44 references

Emission of plasmons by drifting Dirac electrons: where hydrodynamics matters

T0 review · 4 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Drifting Dirac electrons emit plasmons only when electron-electron collisions make their flow hydrodynamic; in the ballistic regime the singular conductivity at $\omega = q v_0$ forbids the emission.

desk verdict A solid analytic theory of drift-induced Cerenkov instabilities in Dirac plasmons, but the 'fully prohibited in ballistic' claim is stronger than the model supports. read the letter →

arxiv 1908.02345 v1 pith:JRPBJHGN submitted 2019-08-06 cond-mat.mes-hall

Dmitry Svintsov This is my paper · ORCID
classification cond-mat.mes-hall PACS 73.20.Mf72.10.-d
keywords grapheneplasmonshydrodynamictransportCerenkovemissionnonlocalconductivityelectron-electroncollisionsdriftingDiracelectronsterahertzplasmoninstability
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

The paper claims that Cerenkov emission of plasmons—wave emission by a charge flow moving faster than the wave—is a hallmark of hydrodynamic electron transport in graphene: it occurs only when electron-electron collisions slow the plasmon phase velocity below the drift velocity, and it is completely absent in the collisionless ballistic regime. In ballistic graphene the nonlocal conductivity is singular at phase velocity equal to the Fermi velocity $v_0$, which pins the plasmon above the drift velocity and leaves no eigenmode in the gain region $\omega < q u_0$. The author derives an analytic nonlocal conductivity for drifting Dirac electrons that interpolates across the hydrodynamic-to-ballistic crossover and uses it to show that counter-streaming graphene layers and grating-coupled graphene become unstable above a threshold drift whose lower bound is $v_0/\sqrt{2}$. If correct, this gives a frequency-domain, current-tunable test of hydrodynamic transport and a mechanism for terahertz plasmonic emission.

What carries the argument

The load-bearing object is the high-frequency nonlocal conductivity $\sigma(q,\omega)$ of drifting Dirac electrons, built from the kinetic equation with a BGK electron-electron collision integral: collisions pull the perturbed distribution toward a local equilibrium at a single rate $\gamma_{ee}$ while conserving particle number, momentum, and energy (Eqs. 2-3). Solving the resulting generalized hydrodynamic system (Eqs. 4-5) gives the conductivity across the whole crossover; as $\gamma_{ee}$ tends to zero the angular integrals $I_{nm}$ diverge at $\omega = q v_0$, reproducing the ballistic singularity, while at large $\gamma_{ee}$ the system reduces to viscous hydrodynamic equations. The argument turns on two special features: the undamping condition $\omega u_0 = q v_0^2$, where the collision integral has no effect because the excited distribution coincides with its momentum mode, and the threshold $\beta_{\rm th}^{-} \ge v_0/\sqrt{2}$ at which the acoustic plasmon frequency crosses zero.

What would settle it

Measure the reflectance spectrum of a grating-coupled graphene device while sweeping the DC drift current and track the plasmon dip frequency and reflectance magnitude: the hydrodynamic theory predicts the dip moves to zero frequency and reflectance rises above unity above a threshold drift velocity with lower bound $v_0/\sqrt{2}$, whereas the ballistic theory predicts an almost current-independent dip with reflectance below unity. Observing no reflectance above unity across the full current range in an otherwise clean sample would rule against the central claim.

Watch

Extended reading notes

Core claim

In the collisionless ballistic regime, the nonlocal conductivity of graphene is singular at the boundary of single-particle excitations $\omega = q v_0$, and this singularity prevents any plasmon eigenmode from entering the Cerenkov gain region $\omega < q u_0$, so current-driven plasmon instability cannot occur. In the hydrodynamic regime, electron-electron collisions soften the singularity and lower the minimum plasmon phase velocity from $v_0$ to $v_0/\sqrt{2}$; the acoustic mode of a counter-streaming double layer then crosses the $\omega = q v_0$ boundary as drift increases, and above a threshold drift velocity $\beta_{\rm th}^{-}$ (with lower bound $v_0/\sqrt{2}$) the mode becomes aperiodically growing with ${\rm Re}\,\omega = 0$ and ${\rm Im}\,\omega > 0$. The same mechanism appears in grating-coupled graphene: the plasmon dip moves to zero frequency with increasing current and then reflectance exceeds unity, signaling amplification; at the Fabry-Perot condition the reflectance diverges, indicating feedback-laser-like growth. The paper argues this is tied only to the singular structure of Dirac conductivity, not to the specific dielectric environment, so the same instability should be looked for in two- and three-dimensional Dirac materials.

Load-bearing premise

The predictions rest on modeling electron-electron collisions as a single-rate pull to a local equilibrium that conserves only particle number, momentum, and energy, with instability onset judged by the mode frequency reaching zero; if real collisions have additional slowly relaxing modes or equilibrate differently, the undamping points $\omega u_0 = q v_0^2$, thresholds, and growth rates will shift or disappear.

Editorial extensions

If this is right

  • In a double layer with counter-streaming currents, raising the drift velocity above the threshold makes the acoustic plasmon mode grow aperiodically without any external ac drive, so the structure should emit or oscillate on its own.
  • The threshold lower bound is the hydrodynamic sound speed $v_0/\sqrt{2}$, and in tightly coupled layers it is nearly independent of carrier density, giving a robust target for experiments.
  • In grating-coupled graphene, increasing current first shifts the plasmon resonance to zero frequency and then makes the reflectance exceed unity; tuning the substrate distance to the Fabry-Perot condition raises the reflectance to divergence, the signature of feedback-laser operation.
  • Because the hydrodynamic-to-ballistic transition is governed by the Knudsen number $q v_0/\gamma_{ee}$, the instability can be reached in clean samples by choosing a sufficiently long plasmon wavelength.
  • In the ballistic limit the same setups show almost no current-induced shift of the plasmon frequency, which would distinguish the two regimes in a single experiment.

Reading between the lines

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

  • A direct probe suggests itself: measure the absorption of a current-carrying graphene sheet at the dissipationless condition $\omega u_0 = q v_0^2$, where the paper's conductivity has vanishing real part; observation of collision-induced transparency at this tunable line would confirm the predicted collision zero mode.
  • The singularity-softening argument is not limited to two dimensions; three-dimensional Dirac and Weyl semimetals have a logarithmic conductivity singularity at $\omega = q v_0$, so current-driven Cerenkov emission might be sought in bulk Weyl samples with a similar threshold criterion.
  • If measured instability thresholds and growth rates deviate from these predictions in the direction of weaker instability, that would indicate additional slowly relaxing modes beyond density, momentum, and energy, guiding improvements to the collision model.
  • The sharp threshold current that distinguishes this emission from hot-plasmonic background could serve as a clean experimental discriminator; a null result at the predicted drift velocity in a nominally hydrodynamic sample would cast doubt on the single-rate collision ansatz.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

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 manuscript develops an analytical kinetic-theory description of the linear response of a drifting Dirac electron fluid, with electron-electron collisions modeled by the BGK-type operator in Eq. (2) that relaxes the distribution to a local equilibrium while conserving particle number, momentum, and energy. It derives a generalized hydrodynamic matrix, Eqs. (4)-(5), and the corresponding nonlocal conductivity, and uses it to compute plasmon dispersions and damping in single-layer graphene, in a counter-streaming graphene double layer, and in a grating-coupled graphene structure. The central claims are that (i) the plasmon velocity in the hydrodynamic regime is reduced by e-e collisions so that the Cherenkov condition ω < q u0 can be met, (ii) this leads to plasmon instabilities with thresholds bounded below by u0 = v0/√2, and (iii) such instabilities are absent in the collisionless ballistic regime because the singular conductivity at ω = q v0 blocks modes from entering the Cherenkov domain.

Significance. If established, the paper would provide a sharp, experimentally testable distinction between hydrodynamic and ballistic high-frequency transport in Dirac materials, and would correct earlier claims of ballistic Cherenkov instabilities. The analytic crossover conductivity itself, including its limiting cases, is a useful technical contribution. The paper is careful to note the limits of the model in several places, and the computations are presented in sufficient detail to be checked. The strength of the main claim, however, is currently tied to idealized conditions, namely strict zero temperature and zero non-e-e relaxation, and to the single-rate BGK collision model. These idealizations affect the uniqueness of the hydrodynamic mechanism that is the paper's headline conclusion.

major comments (4)
  1. [Discussion and SI Eqs. (44)-(46)] The ballistic no-go claim is established only in the strictly degenerate, collisionless limit. In the Discussion, the prohibition of Cherenkov modes in the ballistic regime is argued from the singularity of σ(q,ω) at ω = q v0, and the same singular structure enters the SI integrals J02, J12, J03 in Eqs. (44)-(46). This singularity is a property of T → 0 and γ_imp, γ_ph → 0; Eq. (8) explicitly uses the T/ε_F ≪ 1 limit, and Eq. (1) contains no impurity or phonon collision terms. Any finite broadening, whether from finite temperature, impurity scattering, or phonon scattering, softens the singularity, and the manuscript does not show that such broadening cannot let a mode cross into ω < q u0. As written, the statement that Cherenkov emission is 'fully prohibited' in the ballistic regime, and hence a 'hallmark' of hydrodynamics, overstates what the model proves. Please either extend the analysis to include a minimal broadening mechanism in the ballistic conductivity, or explicitly qualify the no-go claim as valid for the idealized collisionless degenerate limit.
  2. [SI, Analysis of instabilities in the double-layer system] The instability-onset criterion is assumed, not derived. The SI states that the instability sets in when the acoustic mode frequency crosses zero, i.e. at Re ω_- = 0, and continues by saying that a direct verification of this fact is challenging but that numerical experience indicates it is the case. This criterion is used to produce the thresholds in Eq. (10) and the stability diagram in Fig. 3C. Because the stability boundary is load-bearing for the quantitative predictions, please provide a proof of the onset criterion, for example by analyzing the quartic dispersion near the crossing or by applying Routh-Hurwitz conditions, or present an independent numerical check that the growth rate changes sign exactly at Re ω_- = 0.
  3. [Main text Eq. (10); SI Eqs. (49) and (52)] There is an inconsistency between the threshold formula in the main text and the corresponding formula in the Supporting Information. Equation (10) of the main text contains exp(-qd) in the factors (1 ± e^{-qd}), whereas the SI dispersion in Eq. (49) and the threshold in Eq. (52) contain exp(-2qd), consistent with the interlayer coupling term e^{-2|q|d} in Eq. (48). Since the threshold velocity is central to the experimental comparison and to Fig. 3C, please reconcile this discrepancy and correct whichever expression is wrong.
  4. [Eqs. (2), (8)-(9), and Fig. 2] The exact undamping points and the dissipationless conductivity at ω u0 = q v0^2 are a direct consequence of the three-mode BGK collision operator in Eq. (2). The demonstration in Eqs. (8)-(9) relies on the excited perturbation coinciding with the momentum zero mode of Cee, which is an exact zero mode only because the collision operator conserves exactly three moments. A more realistic e-e collision integral will also relax higher angular harmonics, so the exact zeros at the undamping points, and hence the claim that the conductivity becomes strictly dissipationless, would become approximate. Since the growth rates in Fig. 3B and the reflectance spectra in Fig. 4 are computed with this operator, please discuss the sensitivity of these results to the choice of collision model, or test a variant with an additional relaxation channel.
minor comments (5)
  1. [Fig. 2] The vertical-axis label in Fig. 2, 'Frequency, ω ( ) /2π p THz', appears to be corrupted by a typesetting error; please replace it with a clean expression such as 'ω/2π (THz)'.
  2. [Title page] The first line of the main text contains the typo 'hyd rodynamics' in the title; please correct it to 'hydrodynamics'.
  3. [Main text after Eq. (5)] The 'relativistic mass' m is introduced after Eq. (5) but is used in Eq. (5) itself; please move the definition before Eq. (5) or add a forward reference at the point of use.
  4. [SI, Eqs. (38)-(39)] The neglect of the difference between the kinetic mass m_k,β=0 and the hydrodynamic mass m_hd,β=0 is justified only briefly by the degenerate limit; please state the expected magnitude of the resulting error in the polarizability at the parameters used in Figs. 2-4.
  5. [References and notation] Please standardize the spelling of author names in the references, for example 'Feigelman' versus 'Feigel'man', and ensure all arXiv identifiers and journal references are complete and consistent with the journal's style.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the hydrodynamic Cerenkov-instability prediction follows from an explicit kinetic-equation derivation, not from fitting or self-referential definitions.

full rationale

The paper's central claim — that drifting Dirac electrons emit plasmons only in the hydrodynamic regime — is derived from an explicit kinetic-equation calculation. The conductivity entering the plasmon dispersion is obtained in Eqs. (4)-(5) by solving Eq. (1) with the BGK collision integral Eq. (2); the hydrodynamic and ballistic limits are then taken from the same formula rather than imposed separately. The threshold condition β−th ≥ v0/√2, Eq. (10), follows algebraically from the hydrodynamic polarizability Eq. (23) and the double-layer dispersion Eq. (48), and the 'undamping points' ωu0=qv0^2 follow from the explicit pole structure of the integrals I_nm, Eqs. (44)-(46), not from the ansatz. The ballistic no-go argument rests on the singular conductivity at ω=qv0 derived in the same calculation (the divergence of I_nm at a→1, stated in the Supporting Information), with external support from refs. [18,19] for the absence of ballistic plasmons below the single-particle boundary. Self-citations [20,21] and [25] are used for velocity bounds and Galilean-invariance breakdown, but those claims are also sourced to independent refs. [18,19,24,26-28] and are not the unique load-bearing support. The admitted reliance on the Re ω−=0 onset criterion is an acknowledged numerical/approximation judgment, not an input-to-output equivalence. No fitted parameter is renamed as a prediction; no quantity is defined in terms of the result it is used to derive.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central claim rests mainly on the hydrodynamic description of the drifting Dirac fluid (local-equilibrium distribution, conservation laws, single-rate relaxation model) and on standard analytic evaluations. The free parameters are inputs chosen per figure: the e-e collision rate gamma_ee, the drift velocity u0, the Fermi energy, and the geometry/environment constants. No invented physical entities are introduced; the dissipationless modes and undamping points are properties of the model collision operator, not new objects.

free parameters (4)
  • electron-electron collision rate gamma_ee (inverse of tau_ee) = input parameter, chosen per figure (tau_ee = 18.1 fs in Fig. 3; tau_ee = 24 THz^-1 in Fig.
    Controls the hydrodynamic-to-ballistic crossover, growth rates, and reflectance spectra; it is introduced by hand as the single relaxation rate of the BGK model rather than derived or fitted to data.
  • drift velocity u0 (dimensionless beta = u0/v0) = varied from 0 to about 0.9 in the figures
    The carrier drift drives the Cerenkov effect; its value is an input, and the dc transport solution for u0, mu, T is explicitly left for future work.
  • Fermi energy epsilon_F = 25 meV (Figs. 2, 3), 50 meV (Fig. 4)
    Sets carrier density and hydrodynamic mass m ~ epsilon_F/v0^2; a material parameter chosen for the figures.
  • geometry and environment constants (interlayer distance d, dielectric constant kappa, grating period, filling factor… = d = 1 nm, kappa = 5 (Figs. 2, 3); d = 3 nm, kappa = 12, D = 100 micrometers, period 2 micrometers, filling 1/2 (Fig. 4)
    Standard inputs for the two proposed setups; they set the plasma frequency and the Fabry-Perot condition but are not fitted to any target result.
assumptions (6)
  • domain assumption The drifting electron system is described at all times by a local-equilibrium Fermi-Dirac distribution f0 = [1 + exp((epsilon_p - p u0 - epsilon_F)/T)]^-1, with drift velocity u0, Fermi energy epsilon_F, and temperature T as inputs.
    Invoked in Eq. (11) of the Supporting Information. The paper explicitly leaves the derivation of u0, epsilon_F, T from dc transport to further work.
  • domain assumption Electron-electron collisions conserve particle number, momentum, and energy and act on perturbations only as a relaxation to local equilibrium at a single rate gamma_ee (Eq. (2) of the main text).
    This BGK-type model (refs 13, 16) replaces the full collision integral; the undamping points and all growth rates follow from its zero-mode structure, and its fidelity to real e-e scattering is not quantified.
  • domain assumption The degenerate limit T/epsilon_F << 1 allows neglecting the difference between the kinetic mass m_k and hydrodynamic mass m_hd.
    Stated in the Supporting Information near Eq. (39); the author notes that a mass difference would add extra plasmon damping in non-parabolic bands.
  • domain assumption Waves and carrier drift are taken collinear, q parallel to u0.
    Stated in the main text before Eq. (1); the angular integrals and the stability analyses are performed for this geometry only.
  • standard math The angular integrals J_nm in Eq. (33) are evaluated by residues with consistent branch choices for sqrt(a^2 - 1), and the beta -> 1 divergences are reabsorbed into the density and mass definitions.
    Supporting Information, Eqs. (42)-(46). The spurious singularity at a beta = 1 is shown to be canceled by a zero numerator.
  • ad hoc to paper Instability in the counter-streaming double layer sets on when the acoustic mode frequency crosses zero, Re omega_- = 0.
    Supporting Information, stability section: the authors say direct verification is challenging and the criterion is suggested by numerical experience.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Emission of plasmons by drifting Dirac electrons: where hydrodynamics matters." pith.science (2026). https://pith.science/paper/JRPBJHGN

@misc{pith2026190802345,
  author       = {Pith},
  title        = {Pith review of: Emission of plasmons by drifting Dirac electrons: where hydrodynamics matters},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JRPBJHGN}},
  note         = {Machine review of arXiv:1908.02345}
}
read the original abstract

Direct current in clean semiconductors and metals was recently shown to obey the laws of hydrodynamics in a broad range of temperatures and sample dimensions. However, the determination of frequency window for hydrodynamic phenomena remains challenging. Here, we reveal a phenomenon being a hallmark of high-frequency hydrodynamic transport, the Cerenkov emission of plasmons by drifting Dirac electrons. The effect appears in hydrodynamic regime only due to reduction of plasmon velocity by electron-electron collisions below the velocity of carrier drift. To characterize the Cerenkov effect quantitatively, we analytically find the high-frequency non-local conductivity of drifting Dirac electrons across the hydrodynamic-to-ballistic crossover. We find the growth rates of hydrodynamic plasmon instabilities in two experimentally relevant setups: parallel graphene layers and graphene covered by subwavelength grating, further showing their absence in ballistic regime. We argue that the possibility of Cerenkov emission is linked to singular structure of non-local conductivity of Dirac materials and is independent on specific dielectric environment.

Figures

Figures reproduced from arXiv: 1908.02345 by the authors.

Figure 1
Figure 1. FIG. 1. Two possible graphene-based setups where hydro [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Plasmon dispersion and damping in single graphene [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Plasmons in graphene double layers with counter [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Evolution of reflectance spectra of graphene cov [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

44 extracted references · 38 canonical work pages

  1. [1]

    It is subsequently used as a build- ing block for analysis of current-driven plasmon instabil- ities in experimentally relevant setups, including parallel graphene layers and graphene covered by sub-wavelength gratings, shown in Fig. 1. The conductivity σ(q, ω) of drifting Dirac electron fluid is obtained by solving the kinetic equation for distribu- 2 Ele...

    work page

  2. [2]

    P. J. W. Moll, P. Kushwaha, N. Nandi, B. Schmidt, and A. P. Mackenzie, Science 351, 1061 (2016)

    2016

  3. [3]

    Physical kinetics (cour se of theoretical physics),

    E. Lifshits and L. Pitaevskii, “Physical kinetics (cour se of theoretical physics),” (1981)

    work page 1981

  4. [4]

    A. D. Levin, G. M. Gusev, E. V. Levinson, Z. D. Kvon, and A. K. Bakarov, Phys. Rev. B 97, 245308 (2018)

    2018

  5. [5]

    Gooth, F

    J. Gooth, F. Menges, N. Kumar, V. S¨ u β , C. Shekhar, Y. Sun, U. Drechsler, R. Zierold, C. Felser, and B. Gots- mann, Nat. Commun. 9 (2018)

    work page 2018

  6. [6]

    R. K. Kumar, D. Bandurin, F. Pellegrino, Y. Cao, A. Principi, H. Guo, G. Auton, M. B. Shalom, L. A. Ponomarenko, G. Falkovich, et al. , Nat. Phys. 13, 1182 (2017)

    work page 2017

  7. [7]

    The acoustic mode, however, readily reaches the re- gion of Cerenkov gain in the hydrodynamic regime, as shown in Fig

    As a result, the gain region encloses no plasmon eigenmode. The acoustic mode, however, readily reaches the re- gion of Cerenkov gain in the hydrodynamic regime, as shown in Fig. 3 A. The non-local dielectric response of graphene in this regime is no more singular, and the wave frequency unimpededly passes through ω = qv0 border. Above the critical veloci...

    work page

  8. [8]

    D. A. Bandurin, I. Torre, R. K. Kumar, M. Ben Shalom, A. Tomadin, A. Principi, G. H. Auton, E. Khestanova, K. S. Novoselov, I. V. Grigorieva, L. A. Ponomarenko, A. K. Geim, and M. Polini, Science 351, 1055 (2016)

    work page 2016

Show all 44 references
  1. [9]

    J. A. Sulpizio, L. Ella, A. Rozen, J. Birkbeck, D. J. Perello, D. Dutta, M. Ben-Shalom, T. Taniguchi, K. Watanabe, T. Holder, et al. , arXiv preprint arXiv:1905.11662 (2019)

    2019 arXiv

  2. [10]

    D. Y. H. Ho, I. Yudhistira, N. Chakraborty, and S. Adam, Phys. Rev. B 97, 121404 (2018)

    2018

  3. [11]

    A. S. Mayorov, R. V. Gorbachev, S. V. Morozov, L. Britnell, R. Jalil, L. A. Ponomarenko, P. Blake, K. S. Novoselov, K. Watanabe, T. Taniguchi, et al. , Nano Lett. 11, 2396 (2011)

    2011

  4. [12]

    D. A. Bandurin, A. V. Shytov, L. S. Levitov, R. K. Kumar, A. I. Berdyugin, M. B. Shalom, I. V. Grigorieva, A. K. Geim, and G. Falkovich, Nat. Commun. 9, 4533 (2018)

    2018

  5. [13]

    Shytov, J

    A. Shytov, J. F. Kong, G. Falkovich, and L. Levitov, Phys. Rev. Lett. 121, 176805 (2018)

    2018

  6. [14]

    Gallagher, C.-S

    P. Gallagher, C.-S. Yang, T. Lyu, F. Tian, R. Kou, H. Zhang, K. Watanabe, T. Taniguchi, and F. Wang, Science 364, 158 (2019)

    2019

  7. [15]

    P. L. Bhatnagar, E. P. Gross, and M. Krook, Phys. Rev. 94, 511 (1954)

    1954

  8. [16]

    A. A. Abrikosov and I. M. Khalatnikov, Reports on Progress in Physics 22, 329 (1959)

    1959

  9. [17]

    Conti and G

    S. Conti and G. Vignale, Phys. Rev. B 60, 7966 (1999)

    1999

  10. [18]

    G. S. Atwal and N. W. Ashcroft, Phys. Rev. B 65, 115109 (2002)

    2002

  11. [19]

    Crossno, J

    J. Crossno, J. K. Shi, K. Wang, X. Liu, A. Harzheim, A. Lucas, S. Sachdev, P. Kim, T. Taniguchi, K. Watanabe, T. A. Ohki, and K. C. Fong, Science 351, 1058 (2016)

    2016

  12. [20]

    Ryzhii, Jpn

    V. Ryzhii, Jpn. J. Appl. Phys. 45, L923 (2006)

    2006

  13. [21]

    M. B. Lundeberg, Y. Gao, R. Asgari, C. Tan, B. Van Duppen, M. Autore, P. Alonso-Gonz´ alez, A. Woessner, K. Watanabe, T. Taniguchi, R. Hillen- brand, J. Hone, M. Polini, and F. H. L. Koppens, Science 357, 187 (2017)

    2017

  14. [22]

    Svintsov, V

    D. Svintsov, V. Vyurkov, S. Yurchenko, T. Otsuji, and V. Ryzhii, J. Appl. Phys. 111, 083715 (2012)

    2012

  15. [23]

    Svintsov, Phys

    D. Svintsov, Phys. Rev. B 97, 121405 (2018)

    2018

  16. [24]

    Gumbs, A

    G. Gumbs, A. Iurov, D. Huang, and W. Pan, Journal of Applied Physics 118, 054303 (2015)

    2015

  17. [25]

    T. A. Morgado and M. G. Silveirinha, Phys. Rev. Lett. 119, 133901 (2017) . 6

    2017

  18. [26]

    L. S. Levitov, A. V. Shtyk, and M. V. Feigelman, Phys. Rev. B 88, 235403 (2013)

    2013

  19. [27]

    D. A. Svintsov and V. Ryzhii, arXiv preprint (2019)

    2019

  20. [28]

    B. V. Duppen, A. Tomadin, A. N. Grigorenko, and M. Polini, 2D Materials 3, 015011 (2016)

    2016

  21. [29]

    Wenger, G

    T. Wenger, G. Viola, J. Kinaret, M. Fogelstr¨ om, and P. Tassin, Phys. Rev. B 97, 085419 (2018)

    2018

  22. [30]

    Sabbaghi, H.-W

    M. Sabbaghi, H.-W. Lee, T. Stauber, and K. S. Kim, Phys. Rev. B 92, 195429 (2015)

    2015

  23. [31]

    Here, we consider only the intra-band plasmon emission

    The instability obtained in [ 28] is related to current- induced interband population inversion which can be ob- tained near the charge neutrality point. Here, we consider only the intra-band plasmon emission

  24. [32]

    Kukhtaruk, V

    S. Kukhtaruk, V. Kochelap, V. Sokolov, and K. Kim, Physica E: Low-dimensional Systems and Nanostructures 79, 26 (2016)

    2016

  25. [33]

    Briskot, M

    U. Briskot, M. Sch¨ utt, I. V. Gornyi, M. Titov, B. N. Narozhny, and A. D. Mirlin, Phys. Rev. B 92, 115426 (2015)

    2015

  26. [34]

    Moors, T

    K. Moors, T. L. Schmidt, and O. Kashuba, arXiv preprint arXiv:1905.01247 (2019)

    2019 arXiv

  27. [35]

    Krasheninnikov and A

    M. Krasheninnikov and A. Chaplik, Sov. Phys. JETP 52 (1980)

    1980

  28. [36]

    S. J. Allen, D. C. Tsui, and R. A. Logan, Phys. Rev. Lett. 38, 980 (1977)

    1977

  29. [37]

    S. A. Mikhailov, Phys. Rev. B 58, 1517 (1998)

    1998

  30. [38]

    O. R. Matov, O. V. Polischuk, and V. V. Popov, International Journal of Infrared and Millimeter Waves 14, 1455 (1993)

    1993

  31. [39]

    Lv and S.-C

    M. Lv and S.-C. Zhang, Int. J. Mod. Phys. B 27, 1350177 (2013)

    2013

  32. [40]

    L. C. Silleabhin, H. P. Hughes, A. C. Churchill, D. A. Ritchie, M. P. Grimshaw, and G. A. C. Jones, Journal of Applied Physics 76, 1701 (1994)

    1994

  33. [41]

    Z. S. Gribnikov, N. Z. Vagidov, and V. V. Mitin, Journal of Applied Physics 88, 6736 (2000)

    2000

  34. [42]

    D. Tsui, E. Gornik, and R. Logan, Solid State Communications 35, 875 (1980)

    1980

  35. [43]

    El Fatimy, N

    A. El Fatimy, N. Dyakonova, Y. Meziani, T. Ot- suji, W. Knap, S. Vandenbrouk, K. Madjour, D. Thron, C. Gaquiere, M. A. Poisson, S. De- lage, P. Prystawko, and C. Skierbiszewski, Journal of Applied Physics 107, 024504 (2010)

    2010

  36. [44]

    Boubanga-Tombet, D

    S. Boubanga-Tombet, D. Yadav, W. Knap, V. V. Popov, and T. Otsuji, arXiv preprint arXiv:1801.04518 (2018). SUPPOR TING INFORMATION Hydrodynamic transport regime The hydrodynamic equations for electron drift velocity u, chemical potential µ and temperature T can be obtained by ...

    2018 arXiv

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.