{"id":"f92df378-2a8d-4062-803b-1d6de4e4a796","arxiv_id":"2411.14649","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"In MoS2, electrons and acoustic phonons drift together with a shared velocity at 100-300 K, a coupled electron-phonon hydrodynamic regime that boosts transport coefficients.","lead":"This paper models electron and phonon flow together in two-dimensional semiconductors and finds that strong electron-phonon coupling can lock electrons and phonons into a single moving fluid, sharply increasing predicted mobility and thermopower. This challenges the usual assumption that strong electron-phonon interactions always limit charge transport.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Unspecified impurity density in the Brooks-Herring model is the load-bearing unknown; at realistic levels the claimed joint electron-LA-phonon drift and transport enhancement may vanish.","rationale":"The reader's weakest assumption correctly identifies the missing charged-impurity density as the key control parameter. The paper's claim is a prediction of a new hydrodynamic regime, and the central observable—the common drift velocity of electrons and LA phonons—arises from the balance between momentum-conserving electron-phonon scattering and momentum-relaxing processes. The calculation includes impurity scattering, but without stating the impurity concentration or providing a sensitivity study, the reader cannot tell whether the predicted joint drift is robust to realistic disorder levels. The paper does include state-of-the-art coupled BTE solutions (Elphbolt), first-principles electron-phonon matrix elements, and a comparison material (black phosphorene) that strengthens the internal consistency. However, the missing parameter directly controls whether the central claim holds in any experimentally relevant sample. The conditional verdict is appropriate; if the requested sensitivity test shows robustness, the verdict could be upgraded, whereas if the joint drift collapses at moderate impurity densities, the claim would need to be downgraded to a clean-limit statement. The concern is not a disagreement with consensus but a request for a parameter that is essential to evaluate the claim.","tokens_in":11138,"tokens_out":7669,"duration_ms":81959,"concrete_test":"Obtain the N_i value (and screening length) used in the Brooks-Herring term, then rerun the coupled BTE in Elphbolt at T=100 K and n=1e13 cm^-2 with N_i = 0, 1e9, 1e10, 1e11, and 1e12 cm^-2. Track |1 - u_LA/u_e| and the mobility-enhancement ratio (coupled vs. uncoupled). If |1 - u_LA/u_e| exceeds 10% or the enhancement drops by more than a factor of two for N_i below realistic levels, the 'at and above 100 K' claim must be restricted to the ultra-clean limit.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that electrons and LA phonons in MoS2 exhibit a joint drift with the same velocity at and above 100 K, leading to low-dissipation transport. The only extrinsic momentum-relaxation channel included for electrons is charged-impurity scattering, described in SI Methods B with the Brooks-Herring model. The impurity concentration is never stated. This is load-bearing because the total-momentum lifetime of the coupled system is set by the competition between strong electron-phonon momentum exchange (which conserves total momentum and drives the two fluids toward a common drift) and momentum-relaxing processes: impurity scattering, phonon-isotope scattering, and umklapp phonon-phonon scattering. At 100 K, umklapp and isotope rates are weak; the impurity density is then the main parameter that can destroy the hydrodynamic regime. If the calculation used a very low N_i, the observed joint drift and the large mobility enhancement in Fig. 4 are close to a 'clean limit' prediction. If a realistic exfoliated-MoS2 impurity density (often 1e10–1e12 cm^-2 or higher) were used, the electron momentum relaxation from impurities could break the drag coupling and suppress both the drift-velocity equality and the predicted enhancement. No sensitivity analysis or stated value is provided, so the robustness of the claim cannot be assessed. The paper's own admission that measured mobilities are far below the calculated values (main text near Fig. 4) suggests the simulation describes an idealized sample, but the quantitative regime in which the prediction holds is not defined.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents first-principles calculations of coupled electron-phonon Boltzmann transport for monolayer MoS2 and black phosphorene, using the Elphbolt solver. It reports that in MoS2 the nonequilibrium electron and longitudinal-acoustic-phonon distributions under a unit electric field or a temperature gradient both follow a linear-in-wavevector form with the same slope, which the authors interpret as a joint drift velocity and coupled electron-phonon hydrodynamics at 100 K and above. Including momentum circulation between electrons and phonons strongly increases the predicted electron mobility and Seebeck coefficient in MoS2, whereas black phosphorene shows only a much smaller phonon-drag effect. A transient experiment is proposed in which an electrical pulse accompanies phonon second sound.","tokens_in":11432,"tokens_out":6760,"duration_ms":68285,"significance":"If correct, the central conclusion reframes strong electron-phonon coupling in 2D semiconductors as a potential enabler rather than a limiter of low-dissipation charge transport, because electron-phonon collisions conserve total momentum and couple the two components into a single drifting fluid. The manuscript's strengths are the use of a fully coupled ab initio BTE solver, the benchmark of the uncoupled limit against published mobility and Seebeck values, and the negative control provided by black phosphorene. The paper is potentially important, but the headline claim is currently supported mainly by visual slope matching in figures, by ratio plots without uncertainties, and by a Brooks-Herring impurity model whose parameters are not given. These points are fixable and do not invalidate the approach.","major_comments":[{"comment":"The charged-impurity density in the Brooks-Herring model is never specified, although electron-impurity scattering is the only extrinsic electron momentum-relaxation channel in the calculation and the main text states that it is included while the hydrodynamic feature is preserved. The total-momentum lifetime of the coupled system is controlled by the competition between electron-phonon momentum exchange and impurity, isotope, and umklapp scattering, so an unstated impurity density is load-bearing. Please state the impurity concentration and screening model used, and provide a sensitivity study (for example from 10^9 to 10^12 cm^-2) showing how the drift-velocity ratio and the mobility enhancement in Fig. 4 change with impurity density.","section":"SI Methods B; main text near Fig. 2"},{"comment":"The central signature, equal drift velocities of electrons and LA phonons, is inferred from the visual slopes of linear fits in Figs. 2 and 3, and the quantitative ratio plots in Fig. 2(d) and Fig. S11 contain no uncertainty estimates or a stated threshold for equality. The text also concedes that the normalized deviations are not strictly linear in wavevector at higher temperatures, which makes the slope extraction uncontrollable. Please report fitted drift velocities with uncertainties at each temperature and carrier concentration, define the fitting range, and state a quantitative criterion for 'the same drift velocity' (for example a maximum allowed value of |1 - u_LA/u_e|).","section":"Section II, Figs. 2, 3, S11"},{"comment":"No quantitative criterion is given to distinguish coupled electron-phonon hydrodynamics from ordinary phonon drag, even though both effects originate from momentum circulation and both enhance transport coefficients; the distinction is made solely by the presence or absence of joint drift. Please formulate the relevant rates or dimensionless ratios (for example the momentum-conserving electron-phonon rate versus the momentum-relaxing impurity, isotope, and umklapp rates) and show, as a function of temperature and carrier concentration, where the coupled hydrodynamic regime begins. This would also clarify whether the strong enhancement in Fig. 4 is an inevitable consequence of the same mechanism that produces the slope equality.","section":"Section II, Figs. 4; Boltzmann-transport analysis"}],"minor_comments":[{"comment":"Carrier concentrations such as '10 12 cm−2' and '1013 cm−2' are missing superscripts; please typeset them as 10^12 cm^-2 and 10^13 cm^-2.","section":"Section II"},{"comment":"In the sentence about earlier work, 'WP 2' should be written as 'WP2' to match the standard name of the compound discussed in Ref. [28].","section":"Introduction"},{"comment":"For the electric-field response, the caption should state explicitly that the phonon distributions are driven only through the electron-phonon collision term, since phonons have no direct coupling to the field.","section":"Figs. 2 and S1-S5"},{"comment":"The displaced Fermi function is written with a redundant factor ℏ((ε−µ)/ℏ − q·u); the equivalent expression exp(((ε−µ) − ℏ q·u)/(k_B T)) is clearer.","section":"Eq. (1)"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the journal's scope and the central idea is timely. My main concern is that the coupled hydrodynamic regime may be realized only in an ultra-clean limit; the requested impurity-density sensitivity analysis and quantitative drift-velocity fitting are necessary to make the claim robust. I have no concerns about novelty disclosure or citation patterns."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThis paper is the first first-principles calculation I've seen that actually shows coupled electron-phonon hydrodynamic drift in a 2D semiconductor. The methodology is standard but solid: fully coupled BTE solved with Elphbolt, no-coupling results benchmarked against published mobility and Seebeck values, and a black phosphorene control that cleanly shows the absence of joint drift when electron-phonon coupling is weak. The specific result, that electrons and LA phonons in MoS2 share a drift velocity at 100 K and above in response to both electric field and temperature gradient, is new and not present in the prior coupled-hydrodynamics papers. The conceptual point that strong electron-phonon coupling is not automatically a mobility killer is worth taking seriously.\n\nThe soft spots are real but concentrated. The load-bearing one is the undisclosed impurity density in the Brooks-Herring model. The paper states that electron-charged-impurity scattering was included, but never gives the impurity concentration. In this regime, impurity scattering is the main momentum-relaxing channel for electrons, and it competes directly with the electron-phonon momentum exchange that produces the joint drift. Without that number, the claim “at and above 100 K” is undefined. The paper's own admission that measured mobility is far below its calculated values suggests the calculation is effectively a clean-limit prediction. The absence of uncertainty estimates on the drift-velocity ratios in Fig. 2(d) and S11, and the reliance on visual linear-slope fitting, reinforce this concern. If the impurity density is very low, the result is interesting but not yet robust; if it is realistic and the joint drift still appears, that would be much stronger. As written, the reader cannot tell which regime is being computed.\n\nNone of this is fatal. Elphbolt is public, so the calculation is reproducible in principle. The phosphorene comparison is a good control. The physics is clearly explained. But the missing parameter is load-bearing, not a cosmetic omission.\n\nMy recommendation: send it to peer review. A serious referee should require the impurity density, a sensitivity sweep over it, and some error estimate or at least a stated fitting range for the slope ratios. If the joint drift survives at realistic impurity levels, this becomes a strong paper. Without that, it is a promising clean-limit prediction that overstates its own robustness.\n\nBring it to the reading group if you want a real debate about what counts as a hydrodynamic signature.","headline":"A serious first-principles calculation of coupled electron-phonon hydrodynamics in MoS2, but the undisclosed impurity density undermines the robustness of the central claim.","tokens_in":11958,"tokens_out":2925,"would_cite":false,"duration_ms":30342,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"In monolayer MoS2, electrons and longitudinal acoustic phonons drift together at the same speed in response to an electric field or a temperature gradient, a signature of coupled electron-phonon hydrodynamics.","keywords":["coupled electron-phonon hydrodynamics","electron-phonon drag","two-dimensional semiconductors","MoS2","Boltzmann transport equation","hydrodynamic transport","phonon drift","carrier mobility"],"falsifier":"In a clean monolayer MoS2 sample at 100 K, a heat pulse should produce an electrical pulse that arrives at the same time and speed; a time-resolved measurement that resolves separate arrival times for the two pulses would rule out the predicted joint drift.","tokens_in":10949,"feed_emoji":"⚡","tokens_out":6868,"duration_ms":64011,"temperature":0.7,"pith_summary":"This paper claims that in monolayer MoS2, electrons and longitudinal acoustic phonons do not simply lose momentum to each other; the strong electron-phonon interaction instead circulates momentum between the two systems, so the combined electron-phonon system has weakly dissipated total momentum and drifts as one fluid. Solving the fully coupled electron and phonon Boltzmann equations, the authors find that electrons and LA phonons share the same drift velocity at 100 K and above, which they read as a signature of coupled electron-phonon hydrodynamics. In this regime the calculated electron mobility, Seebeck coefficient, and thermal conductivity are all higher than when momentum circulation is ignored, and much higher than the enhancement from ordinary electron-phonon drag in a weakly coupled material like black phosphorene. If correct, the result challenges the usual assumption that strong electron-phonon coupling limits carrier mobility: the coupling strength itself is not the bottleneck when few other momentum-loss channels exist.","feed_headline":"Electrons and phonons drift together in MoS2 at 100 K","feed_subtitle":"Momentum circulation between electrons and phonons keeps charge transport low-dissipation in 2D semiconductors.","key_machinery":"The argument rests on solving the fully coupled Boltzmann transport equations for electrons and phonons, in which the electron-phonon collision terms include the nonequilibrium phonon distribution driven by electrons and vice versa. The hydrodynamic signature is read through the displaced equilibrium form of the distributions, $f_h = [\\exp(\\hbar((\\varepsilon-\\mu)/\\hbar-\\mathbf{q}\\cdot\\mathbf{u})/k_BT)+1]^{-1}$ and $n_h = [\\exp(\\hbar(\\omega-\\mathbf{q}\\cdot\\mathbf{u})/k_BT)-1]^{-1}$, which share one drift velocity $\\mathbf{u}$. After linearization, the slope of the normalized deviation $(f-f_0)/(f_0(1-f_0))$ or $(n-n_0)/(n_0(1+n_0))$ against the wavevector component along the drive direction gives the drift velocity; equal slopes for electrons and LA phonons are what define the coupled hydrodynamic regime. The same machinery also produces the transport coefficients with and without momentum circulation, by turning the circulation terms on or off.","core_discovery":"On the paper's own terms, the central discovery is that in monolayer MoS2, with carrier densities between $10^{12}$ and $10^{13}\\,\\mathrm{cm}^{-2}$ and temperatures from 100 K up toward room temperature, the nonequilibrium electron and LA phonon distributions both deviate from equilibrium linearly in the wavevector along the drive direction, with the same slope, that is, the same drift velocity, under a unit electric field and under a unit temperature gradient. The TA phonons drift more slowly and the ZA phonons barely respond, matching the computed strength of their coupling to electrons. In black phosphorene, where electron-phonon coupling is weaker, the same calculation shows no joint drift, only the smaller electron-phonon drag effect. Including momentum circulation raises the electron mobility and Seebeck coefficient in MoS2 far above the values obtained when the two systems are treated separately, while the increase in black phosphorene is much smaller.","pith_inferences":["If the mechanism is generic, other strongly coupled polar two-dimensional semiconductors with weak umklapp scattering and few impurities could show coupled electron-phonon hydrodynamics; computing the LA-phonon-to-electron drift velocity ratio for such materials would test this without new experiments.","The predicted mobility boost implies that in clean two-dimensional devices the practical mobility limit may be set by extrinsic scattering and contacts, not by intrinsic electron-phonon coupling, so defect engineering rather than material choice would be the main lever.","The proposed simultaneous electrical-thermal pulse experiment could be pushed further: measuring the arrival-time difference as a function of temperature would map the boundary where umklapp scattering destroys the joint drift, a prediction the paper leaves only qualitative.","Existing thermopower measurements in semiconductors attributed to phonon drag may need re-examination, since part of the enhancement could be the hydrodynamic joint-drift effect rather than drag in separate systems."],"forward_implications":["In MoS2 at 100 K and above, the calculated electron mobility and Seebeck coefficient are substantially higher when electron-phonon momentum circulation is included than when it is neglected, and the relative increase is tens of times larger than the drag-only increase in black phosphorene.","Phonon thermal conductivity in MoS2 is enhanced by the same electron-phonon momentum circulation, which the paper now identifies as a consequence of coupled electron-phonon hydrodynamics rather than a separate drag effect.","Strong electron-phonon coupling does not by itself imply low carrier mobility; the material property that matters is the total momentum dissipation through impurity, isotope, and umklapp phonon-phonon scattering.","A temperature pulse in the coupled regime should be accompanied by an electrical pulse arriving at the same time, providing a measurable signature analogous to second-sound experiments.","The joint drift is more robust at higher carrier concentrations, where more frequent electron-phonon interactions pull phonons into the common drift, and fades as umklapp phonon-phonon scattering grows at higher temperatures."],"supporting_citations":[{"why":"Supplies the displaced-equilibrium distribution form with a joint drift velocity that the paper uses to identify the hydrodynamic signature.","marker":"[27]"},{"why":"Provides the fully coupled electron-phonon Boltzmann transport solver used for the first-principles transport calculations.","marker":"[30]"},{"why":"Earlier result showing electron drag enhancement of thermal conductivity in MoS2, now reinterpreted as a consequence of coupled hydrodynamics.","marker":"[25]"},{"why":"Gives the theoretical framework for electron-phonon hydrodynamics and its transport coefficients, which the paper extends to two-dimensional semiconductors.","marker":"[26]"},{"why":"Baseline calculation showing phonon hydrodynamics in two-dimensional materials; its non-drift phonon result contrasts with the coupled case presented here.","marker":"[13]"},{"why":"Previous first-principles mobility and thermoelectric calculations that the non-hydrodynamic results in MoS2 reproduce.","marker":"[31, 32]"},{"why":"Experimental evidence of a coupled electron-phonon liquid in NbGe2, the prior system this work extends to a semiconductor.","marker":"[29]"},{"why":"Establishes the phonon drag contribution to thermopower, providing the basis for distinguishing drag from coupled hydrodynamics.","marker":"[21]"}],"fun_headline_variants":["Electrons and phonons drift together in 2D semiconductors","Momentum circulation between electrons and phonons enables low-dissipation transport","Joint electron-phonon drift cuts dissipation in 2D semiconductors","Low-dissipation 2D charge transport from electron-phonon momentum sharing","Momentum circulation lets electrons and phonons drift together in 2D"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The calculations assume a standard model of electron scattering by charged impurities with an impurity density that is never stated; if the true impurity density or its dependence on wavevector differs, the predicted joint drift and the size of the transport enhancement would change.","fun_headline_variants_meta":{"raw":{"variants":["Electrons and phonons drift together in 2D semiconductors","Momentum circulation between electrons and phonons enables low-dissipation transport","Joint electron-phonon drift cuts dissipation in 2D semiconductors","Low-dissipation 2D charge transport from electron-phonon momentum sharing","Momentum circulation lets electrons and phonons drift together in 2D"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000773,"raw_usage":{"total_tokens":3431,"prompt_tokens":963,"completion_tokens":2468,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":579,"completion_tokens_details":{"reasoning_tokens":2371}},"tokens_in":579,"tokens_out":2468,"duration_ms":16526,"temperature":1.0,"reasoning_tokens":2371,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T15:03:41.141457+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"In a clean monolayer MoS2 sample at 100 K, a heat pulse should produce an electrical pulse that arrives at the same time and speed; a time-resolved measurement that resolves separate arrival times for the two pulses would rule out the predicted joint drift.","supporting_citations":[{"cited_title":"Levchenko and J","cited_arxiv_id":null,"evidence_quote":"Supplies the displaced-equilibrium distribution form with a joint drift velocity that the paper uses to identify the hydrodynamic signature."},{"cited_title":"Quan and B","cited_arxiv_id":null,"evidence_quote":"Earlier result showing electron drag enhancement of thermal conductivity in MoS2, now reinterpreted as a consequence of coupled hydrodynamics."},{"cited_title":"Huang and A","cited_arxiv_id":null,"evidence_quote":"Gives the theoretical framework for electron-phonon hydrodynamics and its transport coefficients, which the paper extends to two-dimensional semiconductors."},{"cited_title":"Cepellotti, G","cited_arxiv_id":null,"evidence_quote":"Baseline calculation showing phonon hydrodynamics in two-dimensional materials; its non-drift phonon result contrasts with the coupled case presented here."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Experimental evidence of a coupled electron-phonon liquid in NbGe2, the prior system this work extends to a semiconductor."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes the phonon drag contribution to thermopower, providing the basis for distinguishing drag from coupled hydrodynamics."}],"review_version":1}