{"id":"1dbcce44-3d39-4936-8ba0-5f2156db9ab2","arxiv_id":"2607.10835","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Acoustic-plasmon-mediated superconductivity in bilayers evolves into phonon-mediated pairing with increasing heavy-layer mass, yet Tc stays low (~1 K or less) for van der Waals parameters when frequency cut-offs enforce Migdal consistency.","lead":"The paper maps how acoustic-plasmon pairing in a light-heavy bilayer continuously becomes acoustic-phonon pairing as the heavy-layer mass grows, using Eliashberg theory with RPA screening. Realistic van der Waals densities and separations keep Tc below roughly 1 K once frequency cut-offs control non-adiabatic vertex corrections.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.5","headline":"The hand-chosen frequency cut-off that enforces Tc1L ≲ 50 mK is the single free parameter that can nullify the reported Tc maps.","rationale":"The reader correctly isolates the hand-chosen frequency cut-off as the weakest assumption. That cut-off is load-bearing: every quantitative statement about Tc (Figs. 2–3, Sec. V) is obtained by solving the same cut-off Eliashberg equation, and the paper supplies no independent microscopic estimate of ωc. The continuous evolution from phonon-like to plasmon-like pairing is theoretically sound in the large-mass-ratio limit where Migdal’s theorem holds, but the claim that Tc stays low once a realistic cut-off is imposed is only as reliable as the particular numerical value chosen for that cut-off. Because a more conservative yet still admissible cut-off can erase the reported Tc, the result remains conditional on an uncontrolled parameter. No stronger internal inconsistency is present, so the verdict stays CONDITIONAL.","tokens_in":11696,"tokens_out":604,"duration_ms":8623,"concrete_test":"Re-solve the eigenvalue problem (Eq. 11) on the same (n2, m2) grid of Fig. 2 while scanning ωc downward from 0.15 EF1 to 0.05 EF1 (keeping kc fixed). If the region with Tc > 100 mK shrinks to zero for any ωc still compatible with Tc1L < 50 mK, the headline upper bound of ∼1 K is not robust.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim that acoustic-plasmon-mediated Tc remains ≲ 1 K for realistic vdW densities and separations rests entirely on the numerical solution of the cut-off Eliashberg equation (Eq. 11) with ωc fixed by the auxiliary condition that the isolated light layer has Tc1L ≲ 50 mK (Sec. III and captions of Figs. 2–3). Because the same cut-off simultaneously encodes all unknown high-frequency vertex corrections and the Coulomb pseudopotential, any more conservative (but still formally allowed) choice ωc ≪ 0.15 EF1 drives the entire Tc surface below experimental relevance while remaining consistent with the absence of superconductivity in the isolated LL. The paper itself notes that the results are only lower bounds and that “ωc could be much smaller … leading to an insignificant Tc” (Sec. IV). Thus the quantitative claim is not robust against the single free parameter that the theory cannot determine.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The paper studies superconductivity in a light-layer/heavy-layer bilayer using the RPA dielectric function to obtain the dynamically screened interaction, then solves the linearized Eliashberg gap equation (with Fermi-surface averaging and a frequency cut-off ωc) for the light-layer pairing gap. By continuously increasing the heavy-layer mass m2 from order m1 up to ≳100 m1 they map the evolution of Tc from acoustic-plasmon-mediated pairing to acoustic-phonon-mediated pairing. Numerical results for densities ~10^12 cm^-2 and interlayer separations ~5–10 Å show that Tc remains ≲ 1 K once ωc is chosen so that the isolated light layer has Tc1L ≲ 50 mK; higher densities and smaller separations raise Tc only modestly. The authors conclude that acoustic-plasmon superconductivity is possible but does not yield high-Tc values under realistic van-der-Waals conditions.","tokens_in":11954,"tokens_out":1274,"duration_ms":27355,"significance":"If the numerical maps and the continuous plasmon-to-phonon crossover survive scrutiny, the work supplies a concrete, parameter-controlled demonstration that the acoustic-plasmon mechanism does not automatically produce high Tc simply by raising the effective boson frequency. The systematic use of a single frequency cut-off to encode both vertex corrections and the Coulomb pseudopotential, together with explicit Tc(m2,n2) surfaces, is a useful methodological contribution that can be reused for other bilayer or multi-band systems. The honest acknowledgment that the results are lower bounds set by ωc is also valuable for the community.","major_comments":[{"comment":"Sec. III and captions of Figs. 2–3: the quantitative claim Tc ≲ 1 K rests on the single free parameter ωc fixed by the auxiliary condition that the isolated light layer has Tc1L ≲ 50 mK. Because Tc is a monotonically increasing function of ωc (explicitly shown by the three panels of Fig. 2), any more conservative but still formally allowed choice ωc ≪ 0.15 EF1 drives the entire surface below experimental relevance while remaining consistent with the absence of superconductivity in the isolated layer. The paper itself notes that the maps are only lower bounds; a more systematic exploration of the ωc dependence (or an independent estimate of the vertex-corrected high-frequency kernel) is therefore required before the bound can be regarded as robust.","section":"Sec. III, Figs. 2–3"},{"comment":"Eq. (11) and the paragraph following it: the momentum cut-off kc is likewise free and is adjusted ad hoc to the largest Tc of interest. The infrared sensitivity of the long-range Coulomb interaction means that the reported Tc values also depend on this second cut-off. A short appendix or additional panel quantifying dTc/dkc (or fixing kc by a physical criterion such as the thermal de Broglie wavelength) would remove an unnecessary ambiguity.","section":"Eq. (11), Sec. IV"},{"comment":"Sec. V: the claim that the same bosonic mode continuously interpolates from acoustic plasmon to acoustic phonon is physically appealing, yet the RPA polarization used for both layers is strictly valid only for rs ≪ 1. At the densities shown in Figs. 2–3, rs is of order unity; the authors note the limitation but do not quantify how local-field or exchange-correlation corrections would alter the acoustic-plasmon pole or the resulting pairing kernel. Even a simple Hubbard-local-field estimate would strengthen the central conclusion.","section":"Sec. V"}],"minor_comments":[{"comment":"Throughout the manuscript (especially section headings) there are numerous spacing artifacts (“BILA YER”, “EQUA TION”, “RESUL TS FORT c”, “T c”). These appear to be residual typesetting or OCR issues and should be cleaned for readability.","section":"Section headings"},{"comment":"Fig. 1 caption and main text: the LL mass is given once as 0.023 me and later as 0.04 me (relative to the free-electron mass). The numerical value used for all calculations should be stated once and consistently.","section":"Fig. 1, Sec. IV"},{"comment":"Eq. (6)–(8): the dimensionless variables z = q/2kF,l and u = ω/qvF,l are introduced but the subsequent Fermi-surface average (Eq. 9) is written only in dimensional form. A brief remark on how the average is performed in the scaled variables would help reproducibility.","section":"Eqs. (6)–(9)"},{"comment":"Reference list: several arXiv preprints are cited without journal information even when the papers have since appeared; updating them would improve the archival value of the manuscript.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The cut-off dependence is the single most important technical vulnerability; if the authors cannot tighten it, the quantitative Tc bound will remain soft. The qualitative crossover story is nevertheless solid and of genuine interest to the 2D-materials community. I would not reject on novelty grounds—the continuous mass-ratio scan is new—but I would insist on a clearer statement of the limitations before acceptance."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The punchline is simple: they map how the bilayer acoustic mode continuously interpolates from a heavy-mass acoustic-phonon mediator (Migdal-safe) down to equal-mass acoustic plasmons, and for graphene-scale densities and separations the resulting Tc sits at or below ~1 K once the frequency cutoff is chosen so the isolated light layer has essentially no SC.\n\nWhat is actually new is the continuous mass-ratio scan itself, together with the explicit Tc surfaces versus n2, m2/m1 and ωc for the van-der-Waals numbers (d ~ 5–10 Å, n ~ 10^12 cm^-2). Earlier dielectric-function and acoustic-plasmon papers treated the two limits separately; this one stitches them together and shows the crossover is smooth with no phase transition. The RPA dielectric function, Fermi-surface average and linearized Eliashberg eigenvalue problem are standard and correctly implemented. The figures are transparent, the self-citations to their recent single-layer work are appropriate, and they repeatedly flag that the numbers are only lower bounds.\n\nThe soft spot is exactly the one the stress-test flags: ωc is hand-chosen so that Tc1L ≲ 50 mK, and Tc rises monotonically with that cutoff. A more conservative (still formally allowed) value can push the whole surface into irrelevance while remaining consistent with the absence of SC in the isolated layer. They say this themselves in Sec. IV. RPA at these densities is uncontrolled, transverse modes and possible Wigner-crystal effects are omitted, but those are secondary; the cutoff is the load-bearing free parameter. None of this makes the calculation incoherent—it just makes the quantitative claim conditional.\n\nThis is for people already working on electronic pairing mechanisms or moiré bilayers who want a controlled numerical benchmark. The math and citation pattern look solid. I would send it to referees; the community needs the map even if the absolute Tc numbers remain soft. Worth a careful read if the topic is on your desk; otherwise you can wait for the published version.","headline":"Clean mass-ratio scan from phonon-like to plasmon-like pairing in bilayers, with honest Tc maps that stay low for real vdW parameters once the cutoff is fixed by the isolated-layer constraint.","tokens_in":12565,"tokens_out":551,"would_cite":false,"duration_ms":21772,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["74.20.-z","74.78.-w","73.21.Ac"],"model":"grok-4.5","headline":"Bilayer acoustic plasmons can mediate superconductivity that continuously becomes phonon-like as one layer is made heavier, but realistic van der Waals densities and separations keep Tc below about 1 K once a frequency cut-off is imposed.","keywords":["acoustic plasmon","Eliashberg theory","bilayer 2DEG","van der Waals heterostructure","Migdal theorem","phonon-mediated superconductivity","frequency cut-off"],"falsifier":"Observation of superconductivity with Tc ≳ few K in a dual-gated bilayer graphene or TMD heterostructure whose measured densities, masses and interlayer distance lie inside the parameter window of Figs. 2–3, or a first-principles calculation of the high-frequency vertex that forces the cut-off well below 0.15 EF.","tokens_in":12592,"feed_emoji":"❄️","tokens_out":719,"duration_ms":10230,"temperature":0.7,"pith_summary":"The paper asks whether the acoustic plasmon of a light-layer/heavy-layer bilayer can act as a pairing glue and whether raising the heavy-layer mass continuously recovers ordinary acoustic-phonon superconductivity. Using Eliashberg theory with the RPA-screened Coulomb interaction, the authors show that superconductivity of the light-layer electrons persists across the entire mass-ratio range, from order-unity (plasmon-like) to very large (phonon-like). For densities and layer separations typical of van der Waals heterostructures, however, the transition temperature remains of order 1 K or lower once a frequency cut-off is chosen so that the isolated light layer itself is not superconducting. The result therefore both confirms that acoustic-plasmon pairing is possible and shows that the hope of high-Tc electronic superconductivity in these bilayers is limited by density, separation, and non-adiabatic vertex corrections.","feed_headline":"Bilayer plasmons give superconductivity, but only to ~1 K","feed_subtitle":"As one layer is made heavier the glue becomes phonon-like; realistic densities keep Tc low.","key_machinery":"The RPA dielectric function of the bilayer, whose inverse supplies the effective pairing interaction U(q,ω) for the light-layer electrons; this kernel is inserted into a cut-off Eliashberg equation whose single free parameter ωc encodes high-frequency vertex corrections.","core_discovery":"Superconductivity mediated by the bilayer acoustic mode survives continuously as the heavy-layer mass is tuned from large values (where the mode is an effective acoustic phonon obeying Migdal’s theorem) down to mass ratios of order unity (where the mode is an acoustic plasmon). For realistic van der Waals parameters the resulting Tc is at most of order 1 K once a frequency cut-off consistent with the absence of superconductivity in the isolated light layer is imposed.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Bilayer acoustic mode drives SC from plasmons to phonons at ~1 K","Heavy-layer mass tunes bilayer pairing from plasmon to phonon glue","Plasmon-to-phonon evolution keeps bilayer Tc near 1 K","Acoustic plasmons mediate SC continuously as mass ratio drops to 1","Eliashberg shows bilayer acoustic SC survives but caps at ~1 K"],"cache_read_input_tokens":128,"weakest_assumption_plain":"The frequency cut-off that keeps the isolated light layer non-superconducting is chosen by hand and therefore absorbs all unknown high-frequency vertex corrections; a more conservative choice can drive the predicted Tc arbitrarily low.","fun_headline_variants_meta":{"raw":{"variants":["Bilayer acoustic mode drives SC from plasmons to phonons at ~1 K","Heavy-layer mass tunes bilayer pairing from plasmon to phonon glue","Plasmon-to-phonon evolution keeps bilayer Tc near 1 K","Acoustic plasmons mediate SC continuously as mass ratio drops to 1","Eliashberg shows bilayer acoustic SC survives but caps at ~1 K"]},"model":"grok-4.5","effort":"low","cost_usd":0.005798,"raw_usage":{"total_tokens":1551,"prompt_tokens":781,"num_sources_used":0,"completion_tokens":79,"cost_in_usd_ticks":57980000,"prompt_tokens_details":{"text_tokens":781,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":691,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":781,"tokens_out":79,"duration_ms":9148,"temperature":1.0,"reasoning_tokens":691,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-14T08:53:48.469873+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Observation of superconductivity with Tc ≳ few K in a dual-gated bilayer graphene or TMD heterostructure whose measured densities, masses and interlayer distance lie inside the parameter window of Figs. 2–3, or a first-principles calculation of the high-frequency vertex that forces the cut-off well below 0.15 EF.","supporting_citations":[],"review_version":1}