{"id":"6619ad60-935e-43b8-9d29-f7f20bbae725","arxiv_id":"1908.02345","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":8.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Cerenkov emission of plasmons by drifting Dirac electrons occurs in the hydrodynamic regime, where electron-electron collisions soften the plasmon velocity below the drift velocity, and is absent in the ballistic regime.","lead":"This theory paper predicts that drifting electrons in graphene can emit plasmons like a sonic boom, but only when electron-electron collisions are frequent enough that the electrons behave as a fluid. The effect would give a sharp experimental test for hydrodynamic electron transport and a route to current-tunable terahertz sources.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Ballistic no-go proof assumes strict T=0 plus zero disorder; finite temperature or any non-e-e relaxation broadens the ω=qv0 singularity that does the blocking, so 'fully prohibited' and 'hallmark of hydrodynamics' are not yet proven beyond that idealization.","rationale":"In good faith, the paper is a model-based theory letter with a clear falsifiable claim. The hydrodynamic instability threshold in the ideal limit is robust: Eq. (10) follows from the acoustic mode of the Euler equations, which are conservation-law statements independent of the single-rate BGK details. The reader's BGK concern is real but mostly quantitative: the qualitative HD mechanism survives replacing single-rate BGK with any collision operator that restores local equilibrium, because the ideal hydrodynamic equations and threshold Eq. (10) do not depend on the collision rate. The genuinely load-bearing part of the central claim is the converse: no instability in the ballistic regime. That is argued by the singularity-blocking picture, which is the entire basis for 'fully prohibited' and hence for 'hallmark'. But the singularity is an idealization of a zero-temperature, perfectly collisionless system. The manuscript itself notes in the Discussion that the singularity arguments do not apply to hybrid Dirac/parabolic systems; an analogous caveat for finite lifetime and finite temperature is not supplied or tested. A controlled check with the same RPA machinery, adding either disorder relaxation or finite temperature while removing e-e collisions, would settle whether a non-hydrodynamic broadening mechanism also permits Cerenkov gain. If the concern lands, the paper should be reworded from 'fully prohibited' to 'prohibited in the strictly collisionless, degenerate limit', and the uniqueness of hydrodynamics as the enabling mechanism would need additional evidence. If the test returns no growing mode, the concern is refuted. Either way, the reader's CONDITIONAL verdict remains appropriate; no verdict change is needed, but the condition should include this test.","tokens_in":13601,"tokens_out":20641,"duration_ms":266388,"concrete_test":"Use the same drifted Fermi-Dirac distribution as in the paper, but set the e-e collision term to zero and replace it with (a) a momentum-relaxation (disorder/phonon) rate γ_imp in a simple relaxation-time term in Eq. (1), and/or (b) finite temperature T/εF ≈ 0.2–0.5. Then numerically solve the double-layer dispersion relation, Eq. (48), scanning β up to ~0.99 and q over the range of Fig. 3, looking for eigenmodes with Reω < qu0 and Imω > 0. If such a growing Cerenkov mode appears for γ_imp > 0 or T > 0, the ballistic no-go is not robust and the 'hallmark' claim is overstated. If all such modes remain damped or evanescent for every non-e-e broadening channel tried, the claim that hydrodynamic collisions are uniquely enabling is supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is not just that hydrodynamic plasmons can become unstable; it is that Cerenkov emission is a hallmark of hydrodynamics and is fully prohibited in the collisionless ballistic regime. The prohibition rests on the singular conductivity at ω=qv0 (main text, Discussion, and SI around Eqs. 44-47): the singularity blocks the plasmon mode from crossing into the Cerenkov domain ω<qu0. This singularity is a strictly degenerate (T/εF→0), strictly collisionless property. The manuscript uses the degenerate limit explicitly in Eq. (8) and omits impurity/phonon scattering from Eq. (1) entirely. Any finite relaxation rate, e-e or otherwise, softens the singularity—the paper's own BGK term does this through Im a = γee/(qv0)—and finite temperature also rounds it. The paper demonstrates that e-e collisions can remove the block while preserving a drifted local equilibrium, but it does not show that other broadening mechanisms cannot do the same. If residual disorder or finite T in a nominally ballistic sample also lets a mode enter ω<qu0 and grow, then the effect is not exclusively hydrodynamic and the 'fully prohibited' claim is an artifact of the idealized model rather than a property of Dirac plasmons. This is more central than the BGK fidelity issue: it questions the uniqueness of the hydrodynamic mechanism, not just the numerical values of thresholds. Secondary admitted gaps (onset criterion from numerical experience; dc parameters left to future work) reinforce the need for a check but are not the hinge.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":13882,"tokens_out":5941,"duration_ms":61181,"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":[{"comment":"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.","section":"Discussion and SI Eqs. (44)-(46)"},{"comment":"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.","section":"SI, Analysis of instabilities in the double-layer system"},{"comment":"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.","section":"Main text Eq. (10); SI Eqs. (49) and (52)"},{"comment":"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.","section":"Eqs. (2), (8)-(9), and Fig. 2"}],"minor_comments":[{"comment":"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)'.","section":"Fig. 2"},{"comment":"The first line of the main text contains the typo 'hyd rodynamics' in the title; please correct it to 'hydrodynamics'.","section":"Title page"},{"comment":"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.","section":"Main text after Eq. (5)"},{"comment":"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.","section":"SI, Eqs. (38)-(39)"},{"comment":"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.","section":"References and notation"}],"recommendation":"major_revision","confidential_remarks":"This is a technically substantial single-author Letter with a self-contained analytic derivation and clear experimental proposals. The main concern is that the headline claim, that Cherenkov plasmon emission is a hallmark of hydrodynamics and fully prohibited in the ballistic regime, is formulated more strongly than the idealized model supports; the manuscript's own SI admits an unproven onset criterion, and there is a concrete inconsistency between Eq. (10) and SI Eq. (52). These issues are fixable within the manuscript's scope, so I recommend major revision rather than rejection. I do not see grounds for questioning novelty, but the authors should be asked to either prove or visibly soften the ballistic no-go statement."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nThis paper is a serious theory contribution, not a stunt. The author derives the nonlocal conductivity of drifting Dirac electrons across the hydrodynamic-to-ballistic crossover, starting from a kinetic equation with a BGK collision integral that conserves particle number, momentum, and energy. From this he predicts that in the hydrodynamic regime the acoustic plasmon mode in a graphene double layer can cross the omega = qv0 line and become unstable, while in the ballistic regime the singular conductivity at omega = qv0 blocks it. Two concrete experimental setups are worked out: counter-streaming double layers and grating-coupled graphene. The analysis is self-consistent and detailed; the Supporting Information contains explicit integral evaluations. The qualitative mechanism, that electron-electron collisions soften the plasmon velocity below the drift velocity, is physically plausible and new, since previous collisionless studies found no Cerenkov instabilities.\n\nThe main soft spot is the strength of the headline claim. The paper says Cerenkov emission is a hallmark of hydrodynamics and 'fully prohibited' in the collisionless ballistic regime. That prohibition rests on the singular conductivity at omega = qv0, which is a strictly degenerate property: zero temperature, zero disorder, no phonon scattering. The author works in that limit. Any finite relaxation rate or finite temperature will round the singularity. The paper shows e-e collisions can remove the block while preserving a drifted local equilibrium, but it does not show that other broadening mechanisms cannot do the same. If weak disorder in a nominally ballistic device softens the singularity enough to let a mode into the Cerenkov domain, the effect is not uniquely hydrodynamic. This is central, not peripheral.\n\nThe instability-onset criterion, set by Re omega- = 0, is admitted to be based on numerical experience rather than proof. That is an honest limitation, and the threshold formula in Eq. (10) may well be right, but a referee should ask for a stronger argument. The quantitative results also inherit the single-rate BGK assumption, and the author leaves dc parameters to future work, which caps the precision.\n\nOdds are this paper is correct in its main qualitative claim within its model. The question is whether the 'fully prohibited' language survives contact with realistic ballistic samples. That is worth a careful referee.\n\nRecommendation: send it to peer review, and push on the uniqueness question. The analytic framework is useful and citable regardless.\n\nBest,\n[Your name]","headline":"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.","tokens_in":14461,"tokens_out":3091,"would_cite":true,"duration_ms":31249,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["73.20.Mf","72.10.-d"],"model":"deepseek-v4-flash","headline":"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.","keywords":["graphene plasmons","hydrodynamic transport","Cerenkov emission","nonlocal conductivity","electron-electron collisions","drifting Dirac electrons","terahertz emission","plasmon instability"],"falsifier":"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.","tokens_in":13300,"feed_emoji":"⚡","tokens_out":14496,"duration_ms":137970,"temperature":0.7,"pith_summary":"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.","feed_headline":"Electron collisions switch on Cerenkov plasmon emission in graphene","feed_subtitle":"The instability appears only when electrons flow as a viscous fluid, not ballistically, and has a sharp threshold.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"It justifies modeling e-e collisions as relaxation to local equilibrium rather than to zero, the starting point of the collision integral.","marker":"[13, 16]"},{"why":"It establishes that the ballistic plasmon phase velocity in Dirac materials cannot fall below $v_0$, defining the Cerenkov gain region.","marker":"[18, 19]"},{"why":"It gives the hydrodynamic lower bound $v_0/\\sqrt{2}$ for the plasmon velocity and the graphene hydrodynamic polarizability used here.","marker":"[20, 21]"},{"why":"These earlier predictions placed Cerenkov instabilities in the ballistic regime; the paper argues they are spurious, so they set the baseline to be corrected.","marker":"[22, 23]"},{"why":"It shows the negative real conductivity in the Cerenkov domain and the breakdown of the Galilean Doppler transform in Dirac systems.","marker":"[25]"},{"why":"These collisionless studies found no Cerenkov instability; their regime is the ballistic limit of the present crossover solution.","marker":"[26–28]"},{"why":"It supplies the counter-streaming instability theory for massive electrons that the paper extends to Dirac fluids in the hydrodynamic regime.","marker":"[33]"},{"why":"It demonstrates the grating-gated two-dimensional electron system geometry used for plasmon spectroscopy and for the calculated reflectance spectra.","marker":"[34]"},{"why":"It provides the electromagnetic formalism for reflectance of grating-coupled two-dimensional electron systems that the paper uses with its conductivity as input.","marker":"[35, 36]"},{"why":"It documents square-root and logarithmic conductivity singularities at $\\omega = q v_0$ in 2D and 3D Dirac materials, supporting the environment-independence argument.","marker":"[37]"}],"fun_headline_variants":["Hydrodynamic flow enables Cerenkov plasmons in graphene","Viscous electrons emit plasmons via Cerenkov effect","Hydrodynamic drift triggers Cerenkov plasmon instability"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Hydrodynamic flow enables Cerenkov plasmons in graphene","Viscous electrons emit plasmons via Cerenkov effect","Hydrodynamic drift triggers Cerenkov plasmon instability"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000484,"raw_usage":{"total_tokens":2398,"prompt_tokens":966,"completion_tokens":1432,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":582,"completion_tokens_details":{"reasoning_tokens":1380}},"tokens_in":582,"tokens_out":1432,"duration_ms":9880,"temperature":1.0,"reasoning_tokens":1380,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T14:48:48.035704+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It shows the negative real conductivity in the Cerenkov domain and the breakdown of the Galilean Doppler transform in Dirac systems."},{"cited_title":"Briskot, M","cited_arxiv_id":null,"evidence_quote":"It supplies the counter-streaming instability theory for massive electrons that the paper extends to Dirac fluids in the hydrodynamic regime."},{"cited_title":"Voltage characteristics of hydrodynamic Dirac electron nozzles with supersonic flow","cited_arxiv_id":"1905.01247","evidence_quote":"It demonstrates the grating-gated two-dimensional electron system geometry used for plasmon spectroscopy and for the calculated reflectance spectra."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It documents square-root and logarithmic conductivity singularities at $\\omega = q v_0$ in 2D and 3D Dirac materials, supporting the environment-independence argument."}],"review_version":1}