{"id":"be1565ce-1397-4d4c-8870-0315d9f503e6","arxiv_id":"2411.18041","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Computer models show that amorphous carbon films with similar disorder metrics can differ enormously in conductance, and that gating moves conduction from crystallites to defects.","lead":"This paper simulates how the atomic disorder of amorphous carbon films changes their electrical conductance. It finds that similar-looking disorder measures can hide very different conductances, and that voltage gating shifts current-carrying regions from crystalline patches to defects.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The ensemble-dependent a_max cutoff in the VRH site construction is the load-bearing weak point: it admits sites up to 136-199 Angstrom in the ordered ensembles but only 18 Angstrom in sAMC-500, so the claimed q400 conductance and non-unique morphology-conductance map may be artifacts of this…","rationale":"The paper has real independent support: code and data are provided (S10), the Lanczos diagonalization is benchmarked against exact diagonalization on a 5862-atom fragment to about 1e-13 (S6), and the experimentally reported five-order conductance gap between sAMC-500 and sAMC-300 is reproduced (Fig. 3a). These features make the overall methodology credible. The concern I identify is not about the diagonalization or the percolation framework itself, but about the unbenchmarked, post hoc construction of the VRH site set that feeds the percolation calculation. The site set is load-bearing specifically for the headline claim: the claim is operationalized as the relative conductance of sAMC-q400 versus sAMC-300 and versus the experimental AMC-400 point, and the a_max filter is the one step whose parameters change by an order of magnitude across ensembles (18 vs 136 vs 199 Angstrom) and are chosen from the very structures whose conductance is being computed. A fixed or disabled a_max could remove the conductance overlap that motivates the non-uniqueness claim, or it could leave it intact; until that sweep is done, the claim is conditional. This is the same weakest assumption the reader identified, so my agreement is 'agree.' The correct verdict remains CONDITIONAL: the paper should not be rejected on this basis, but the a_max sensitivity check should be a condition of acceptance.","tokens_in":19748,"tokens_out":12296,"duration_ms":106772,"concrete_test":"Re-run the numerical percolation calculation for all three ensembles with a common a_max value, sweeping a_max in {18, 50, 136, 200} Angstrom and also with the a_max filter disabled, and recompute G(mu=epsilon_F) for each ensemble. If, at a_max = 18 Angstrom, G(sAMC-q400) drops by more than an order of magnitude or no longer overlaps G(sAMC-300), then the non-uniqueness claim is an artifact of the ensemble-dependent cutoff. Report the number of sites removed per ensemble at each cutoff to gauge the protocol's leverage.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central non-uniqueness claim rests on the prediction that sAMC-q400 conducts like sAMC-300 in the ungated regime (Table 1: G(mu=epsilon_F) = (2.51 +/- 0.40)e-5 S vs (1.30 +/- 0.15)e-5 S) while occupying the same (log eta_MRO, rho_sites) region as the insulating experimental AMC-400. This prediction depends on the VRH site-construction protocol of Section S7, and its most fragile step is the site-radius cutoff a_max. a_max is not a physical localization length; it is set per ensemble equal to the radius of the largest crystalline inclusion (Table 1: 18.03 Angstrom for sAMC-500, 136.47 Angstrom for sAMC-q400, 199.33 Angstrom for sAMC-300), and any site with pi a^2 exceeding this is deleted as 'numerically artificial.' Because the Miller-Abrahams overlap f (Eq. S6) increases with site radii, the filter differentially suppresses hopping in sAMC-500 while preserving very large sites in sAMC-300 and sAMC-q400. The stated justification, that a physical site cannot be larger than the largest crystallite, is not established; VRH localization lengths are not bounded by crystallite size. Thus the predicted q400/sAMC-300 conductance overlap could be created by the site-construction choices rather than by physics. A controlled a_max sweep would settle this.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper combines MAP-generated mesoscale amorphous graphene structures (sAMC-500, sAMC-q400, sAMC-300) with a tight-binding Lanczos partial diagonalization and a Miller-Abrahams variable-range hopping percolation model to compute ensemble conductances. The authors reproduce the experimentally reported five-order-of-magnitude conductance gap between the most and least ordered ensembles, predict that the sAMC-q400 ensemble conducts similarly to sAMC-300 despite lying near the insulating experimental AMC-400 in the (log η_MRO, ρ_sites) descriptor space, and conclude that a unique morphology-to-conductance map does not exist in this descriptor space. They also analyze the crystallinity of the hopping sites and report a metamorphosis from crystallite-localized conduction at band edges to defect-localized conduction near the Fermi energy.","tokens_in":20071,"tokens_out":5338,"duration_ms":48505,"significance":"The paper is methodologically transparent and has several genuine strengths: it provides a machine-precision benchmark of the Lanczos diagonalization against exact diagonalization (SI Section S6), makes code and data publicly available (SI Section S10), uses mesoscale aperiodic samples without periodic boundary conditions, and reproduces a nontrivial experimental conductance gap. If the central predictions are robust, the conclusion that partial morphology descriptors such as (log η_MRO, ρ_sites) cannot uniquely determine conductance would be a useful cautionary result for the amorphous-materials community, and the crystallinity analysis of conduction networks would open a genuinely new way to think about gate-controlled transport in AMCs. The strength of these claims, however, rests on the site-construction protocol in the VRH model, which is the main fragility discussed below.","major_comments":[{"comment":"The site-radius cutoff amax is an ensemble-dependent numerical filter that is load-bearing for the central conductance predictions. In the hopping-rate expression (Eq. S5) and overlap function f (Eq. S6), larger site radii increase inter-site overlap and therefore increase hopping rates; removing all sites with radius above the largest crystalline inclusion in each ensemble (Table 1: 18.03 Å for sAMC-500 versus 136.47 Å for sAMC-q400 and 199.33 Å for sAMC-300) disproportionately suppresses hopping in the most disordered ensemble while preserving very large sites in the ordered ones. The stated justification, that a physical site cannot be larger than the largest crystallite, is not established: VRH localization lengths are not bounded by crystallite size. Because the predicted sAMC-q400 conductance (G(μ=ε_F) = (2.51 ± 0.40)×10^-5 S, Table 1) and the resulting claim that no unique (log η_MRO, ρ_sites)-to-conductance map exists depend on this filter, I request a controlled sweep over amax or a physically derived localization-size criterion to show that the q400/sAMC-300 conductance overlap and the sAMC-500/sAMC-300 gap are not artifacts of the cutoff.","section":"Supporting Information §S7; Table 1"},{"comment":"The k-means site-construction protocol is another load-bearing choice that is not validated. The manuscript classifies multi-pocket delocalized MOs as 'pathological' and partitions them into sites using a 100×100 grid, a density threshold of 0.3 of the maximum, and a minimum separation of 20 Å; these parameters are hand-selected, and the protocol is assumed not to bias the relative site density between crystalline and defective regions or between ensembles. Since the near-ε_F states are reported to be the most affected (main text), and since Figure 3d's 'conducting sites preferentially on defects' conclusion is based on these sites, the absence of any sensitivity analysis with respect to the clustering parameters or an alternative site-definition leaves open the possibility that the defect-localization and q400 conductance results are artifacts of the localization procedure.","section":"Supporting Information §S7; main text, 'Constructing the VRH network'"},{"comment":"The non-uniqueness claim is stronger than the evidence presented. The sAMC-q400 ensemble is compared with the experimental AMC-400, but the two differ not only in the (log η_MRO, ρ_sites) position (which is close, not identical) but also in ring statistics: the manuscript states that the 6-c/6-i ratio is reversed relative to experiment (Figure 2c and main text). Because the experimental AMC-400 was not generated with the same MAP protocol and its conductance was measured in a different setup, the comparison conflates structural differences not captured by the two chosen descriptors with a genuine breakdown of the morphology-conductance map. The conclusion should be rephrased as showing that the two descriptors are insufficient, or supported by a simulated ensemble with experimentally matched ring statistics and a controlled comparison within the same simulation pipeline.","section":"Results, 'sAMC-q400' paragraph; Figure 2c"}],"minor_comments":[{"comment":"The manuscript contains several typographical errors, including 'postitve' (p. 9), 'experimetnal' (SI Section S3), 'aloogrithm' (SI Section S5), 'devation' (SI Section S6), and 'pecularities' (p. 17).","section":"Throughout"},{"comment":"The choice of the attempt frequency ω0 = 1 fs^-1 and the 4kBT energy window should be justified or tested; the absolute conductances in Table 1 scale with ω0, even if the relative gap does not.","section":"Equation (S5); Table 1"},{"comment":"Figure 3a states that error bars are omitted because they are too small to be visible, but Table 1 reports relative uncertainties of roughly 40–100% for several band-edge conductances (e.g., G(μ=ε0) for sAMC-500 = (2.99 ± 2.43)×10^-13 S); please clarify how these are represented in the figure.","section":"Figure 3a and Table 1"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is transparent and methodologically interesting, and the open code/data and machine-precision benchmark are commendable. The main risk is that the central non-uniqueness claim and the defect-localization conclusion rest on the ad hoc amax filter and the k-means site-construction choices; a sensitivity analysis or a physically derived cutoff would substantially strengthen the paper. The self-citations are mostly methodological building blocks and are appropriate. I recommend major revision rather than rejection because the issues are addressable within the manuscript's scope."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nThe paper is worth your time, but read the SI carefully before trusting the q400 prediction. The genuinely new result—sAMC-q400 sits in the same (logη_MRO, ρ_sites) region as the insulating experimental AMC-400 yet is predicted to conduct like the much more ordered sAMC-300—is interesting and would matter if it holds. The other claim, that VRH conduction networks move from crystallites at band edges to defects near the Fermi energy, is a nice qualitative finding that seems grounded in the crystallinity analysis.\n\nWhat the paper does well: it ships code and data, benchmarks the Lanczos diagonalization against exact diagonalization to machine precision, and reproduces the experimental five-order conductance gap between sAMC-500 and sAMC-300 without fitting. The percolation framework is a forward model with parameters from prior literature; the q400 conductance is a prediction, not a fit.\n\nWhere I worry: the VRH site construction is load-bearing for the q400 claim, and its most fragile step is the a_max cutoff. The paper deletes any hopping site whose effective radius exceeds the largest crystalline inclusion in that ensemble, with a_max equal to 18 Å (sAMC-500) but 136 Å and 199 Å (sAMC-q400 and sAMC-300). The justification—a physical site cannot be larger than the largest crystallite—is not established; VRH localization lengths are not bounded by crystallite size. Because the Miller-Abrahams overlap grows with site radius, this filter differentially suppresses hopping in the most disordered ensemble while preserving very large sites in the ordered ones. The exact conductance overlap between q400 and sAMC-300 could be an artifact of this choice. The k-means localization parameters and the HOMO exclusion are also hand-picked. A sensitivity sweep over a_max, and ideally the other parameters, is needed before I'd bet on the non-uniqueness claim.\n\nThat said, the concern is not a proven flaw. The paper is transparent about every choice, the reproduction of the known conductance gap is a good sanity check, and the q400 ensemble differs from experimental AMC-400 in ring statistics, which is an independent morphological distinction.\n\nThe paper is for anyone working on amorphous carbon transport, and for groups using ML-generated structures in transport modeling. Bottom line: it deserves a serious referee. I'd send it to review with a request for sensitivity analysis on the site-construction protocol. The paper is honest, reproducible, and the central claim is falsifiable—that is exactly what a referee can work with.\n\nBest,\n[You]","headline":"A transparent, reproducible computational study whose central non-uniqueness claim hinges on an ad hoc site-radius cutoff that needs a sensitivity sweep.","tokens_in":20604,"tokens_out":2748,"would_cite":true,"duration_ms":24265,"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":"The paper claims that the standard two-descriptor morphology space does not uniquely determine conductance in amorphous graphene, and that gate voltage can switch conduction between crystallite-based and defect-based hopping networks.","keywords":["amorphous graphene","amorphous monolayer carbon","variable-range hopping","percolation theory","morphology-conductance relationship","tight-binding electronic structure","gate-voltage tunability","mesoscale simulation"],"falsifier":"Measure the conductance of a real AMC film whose ring statistics match sAMC-q400 (crystalline hexagons more abundant than isolated hexagons) rather than AMC-400: if it is insulating, the claimed non-uniqueness of the descriptor map would fail. Alternatively, recompute sAMC-q400 Fermi-energy conductance after varying the k-means localization thresholds (grid resolution, density cutoff, 20 \\AA{} pocket separation, and the $a_{\\max}$ cutoff) and check whether the $\\approx 2.5\\times 10^{-5}$ S prediction survives.","tokens_in":19517,"feed_emoji":"⚡","tokens_out":9276,"duration_ms":76031,"temperature":0.7,"pith_summary":"Amorphous monolayer carbon films can differ enormously in electrical conductance even when the usual structural descriptors make them look nearly identical. The paper generates three ensembles of roughly 40 nm amorphous graphene samples with a deep-learning structure generator, computes their variable-range hopping conductance from tight-binding electronic states, and compares the results with experimental AMC-300, AMC-400, and AMC-500 films. It reproduces the observed five-order-of-magnitude conductance gap between the most ordered and most disordered ensembles. The central claim is that the descriptor space $(\\log \\eta_{\\mathrm{MRO}}, \\rho_{\\mathrm{sites}})$ does not determine conductance: a simulated ensemble sitting on top of the insulating AMC-400 in that space is predicted to conduct almost as well as the most ordered material. The paper further claims that hopping networks change character with gate voltage, being carried by crystallites at band edges and by defects near the Fermi energy.","feed_headline":"Matching fingerprints, 100,000-fold different conductance","feed_subtitle":"A simulated amorphous carbon in an insulator's descriptor region conducts like the ordered form — morphology alone cannot predict…","key_machinery":"The load-bearing object is the variable-range hopping network. Each thermally accessible tight-binding molecular orbital is converted into one or more hopping sites with a position and radius, using density-weighted k-means clustering; sites whose effective radius exceeds the largest crystalline inclusion in the ensemble are deleted as numerical artifacts. The hopping rate between sites $i$ and $j$ is written as $\\omega_{ij} = \\omega_0 e^{-\\xi_{ij}}$, where $\\xi_{ij}$ combines the site separation, the Gaussian overlap of the two site wavefunctions, and the site energies. Percolating a cluster that connects left and right edges of each 40 nm sample defines a critical $\\xi_c$, and the ensemble conductance is the integral of $e^{-\\xi}$ over the distribution of $\\xi_c$. The second diagnostic object is the crystallinity $\\chi$ of a site, the fraction of its electronic density lying on crystalline hexagons, which reveals where in the energy spectrum the conduction network lives.","core_discovery":"The paper's central discovery is that a unique map between $(\\log \\eta_{\\mathrm{MRO}}, \\rho_{\\mathrm{sites}})$ and conductance does not exist for amorphous monolayer carbon. Its evidence is the sAMC-q400 ensemble: those structures occupy nearly the same descriptor coordinates as the experimentally insulating AMC-400, yet the percolation calculation puts their ungated conductance at $(2.51 \\pm 0.40)\\times 10^{-5}$ S, comparable to the ordered sAMC-300 ensemble. A second claim is that conduction networks are not controlled by atomic structure alone: variable-range hopping sites near the band edges sit preferentially on crystalline inclusions, while sites near the Fermi energy sit preferentially on defects. Because a gate voltage shifts the chemical potential through these regimes, the morphology of the conducting network can be changed while leaving the film itself unchanged.","pith_inferences":["A natural extension is that any low-dimensional morphology descriptor space will underdetermine transport in disordered two-dimensional carbons; descriptors that capture defect clustering rather than total defect fraction may restore a useful, though possibly multi-valued, structure-property relation.","If defect-localized Fermi-energy states really carry the current, then deliberate defect patterning by irradiation, strain, or growth conditions could route current along engineered paths, a possibility the paper does not test.","The predicted crystallite-to-defect crossover could be tested directly by spectrally resolved local density-of-state measurements at different gate voltages; if the crossover is absent, the k-means site construction is the likely culprit.","The protocol's $a_{\\max}$ cutoff is set by the largest crystalline inclusion in each ensemble, so the model implicitly assumes real localization radii never exceed that scale; samples with very large ordered domains might violate that assumption and shift the Fermi-energy conductance."],"forward_implications":["The five-order-of-magnitude conductance gap between sAMC-300 and sAMC-500 reproduces the experimental gap, indicating that the percolation-based variable-range hopping model captures the dominant transport physics in these films.","Because the same $(\\log \\eta_{\\mathrm{MRO}}, \\rho_{\\mathrm{sites}})$ point can host both insulating and conducting samples, experimental classification of AMCs should include ring statistics and crystallite-size distributions, not just the two standard order parameters.","Gate voltage can modulate conductance by selecting band-edge crystalline hopping networks or Fermi-energy defect networks, without any change to the atomic structure.","The Fermi-energy preference for defects implies that ungated conductance is controlled by the defect network's density and connectivity, so defect engineering should be as effective as global crystallinity in designing conductive AMCs.","The combination of gate-tunable electronic transport with low thermal conductance positions AMCs as potential thermoelectric materials, once their absolute conductivities are raised toward useful levels."],"supporting_citations":[{"why":"Provides the experimental AMC-300, AMC-400, and AMC-500 morphologies and conductance data that the simulations reproduce and whose descriptor-to-conductance map the paper challenges.","marker":"Ref. 12"},{"why":"Introduced the Morphological Autoregressive Protocol used to generate the mesoscale amorphous graphene ensembles.","marker":"Ref. 13"},{"why":"Supplies the C-GAP-17 machine-learned interatomic potential that produced the training structures for the MAP model.","marker":"Ref. 15"},{"why":"Establishes the variable-range hopping picture and the two-dimensional Mott law on which the transport model rests.","marker":"Ref. 19"},{"why":"Provides the percolation-theory treatment of hopping conductivity that the numerical implementation adapts to amorphous carbon.","marker":"Ref. 20"},{"why":"Supplies the semi-empirical tight-binding parametrization used to construct the electronic Hamiltonian.","marker":"Ref. 22"},{"why":"Provides the companion tight-binding parametrization and photophysics context that the Hamiltonian parameters are adapted from.","marker":"Ref. 23"},{"why":"Provides the Lanczos algorithm used to partially diagonalize the large sparse tight-binding Hamiltonians.","marker":"Ref. 24"},{"why":"Shows how to estimate hopping conductance from percolation in finite-size systems, the approach followed for the ensemble-averaged conductance calculation.","marker":"Ref. 35"},{"why":"Documents edge-state and bulk-localization behavior in amorphous graphene nanojunctions that motivates the gate-voltage metamorphosis analysis.","marker":"Ref. 42"}],"fun_headline_variants":["Same morphology metrics, 100,000-fold different conductance","Amorphous carbon conductance defies morphology predictors","Gate voltage can control conduction network in amorphous carbon","Morphology alone fails to explain amorphous carbon conductance","Amorphous carbon: similar structure, dissimilar conductivity"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The results stand on the assumption that the protocol for turning delocalized tight-binding orbitals into hopping sites, namely k-means partitioning into high-density pockets followed by deletion of sites larger than the largest crystalline inclusion, does not systematically bias which morphologies receive sites or how those sites conduct.","fun_headline_variants_meta":{"raw":{"variants":["Same morphology metrics, 100,000-fold different conductance","Amorphous carbon conductance defies morphology predictors","Gate voltage can control conduction network in amorphous carbon","Morphology alone fails to explain amorphous carbon conductance","Amorphous carbon: similar structure, dissimilar conductivity"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00028,"raw_usage":{"total_tokens":1604,"prompt_tokens":830,"completion_tokens":774,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":446,"completion_tokens_details":{"reasoning_tokens":701}},"tokens_in":446,"tokens_out":774,"duration_ms":7167,"temperature":1.0,"reasoning_tokens":701,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T11:34:38.308193+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the conductance of a real AMC film whose ring statistics match sAMC-q400 (crystalline hexagons more abundant than isolated hexagons) rather than AMC-400: if it is insulating, the claimed non-uniqueness of the descriptor map would fail. Alternatively, recompute sAMC-q400 Fermi-energy conductance after varying the k-means localization thresholds (grid resolution, density cutoff, 20 \\AA{} pocket separation, and the $a_{\\max}$ cutoff) and check whether the $\\approx 2.5\\times 10^{-5}$ S prediction survives.","supporting_citations":[],"review_version":1}