{"id":"552f3995-28b1-4082-97bf-a10440710aeb","arxiv_id":"2509.02094","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"Valley splitting in doubly-gated silicon-on-insulator quantum wells is controlled by the electrostatic bias δn = nB - nF, reaching 6.3 meV, independent of total carrier density.","lead":"This study shows that in a silicon transistor with two gates, the energy splitting between the two electron valley states can be electrically tuned by the difference in gate-induced densities, reaching up to 6.3 meV independent of total electron density. This offers a clean control knob for valley-based quantum information processing in silicon.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Central 6.3 meV and n-independence claims rest on an unreviewed precoincidence/disorder analysis; without explicit selection criteria and error bars, the absolute values are unverified.","rationale":"The reader's weakest assumption correctly identifies the precoincidence/disorder analysis as the key vulnerability. I agree that the absolute valley-splitting values and the n-independence claim depend on an unreviewed supporting-information procedure. My concern is slightly more specific: the manuscript itself notes that disorder increases with δn, so the highest reported Δv values (up to 6.3 meV) are exactly where the disorder correction is largest. This makes it especially important to demonstrate that the extraction is robust to the disorder model and selection criteria. I do not see a fundamental flaw in the paper's logic; the method is established in prior work (Refs. 12, 13), and the qualitative trend of Δv increasing with δn is plausible. However, the quantitative central claim cannot be independently verified from the arXiv text alone, so the CONDITIONAL verdict is appropriate. If the SI were included and the proposed test passed, no change would be needed; if it failed, the verdict would move toward REJECT or at least require major revision. Thus I leave the reader's verdict unchanged while sharpening the condition.","tokens_in":7959,"tokens_out":4387,"duration_ms":53653,"concrete_test":"Obtain the supporting information (https://pubs.acs.org/doi/10.1021/acs.nanolett.5c03049) and re-analyze the raw Rxx maps with an automated, pre-registered criterion for precoincidence onset (e.g., a fixed threshold in ΔRxx/Rbkgd) rather than manual selection. Repeat the extraction with the disorder broadening Γ varied by ±20% around the SI's stated values. Then check: (1) Does the Δv vs δn trend, including the 6.3 meV point, survive within error bars? (2) At fixed δn, do points with different n remain consistent when the same automated criterion is applied? If varying Γ by ±20% shifts Δv at δn ≈ 9.2×10^12 cm^-2 by more than ~1 meV, or if fixed-δn points separate systematically with n, the central n-independence claim is not established.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central quantitative claim—valley splitting up to 6.3 meV at the buried SiO2 interface, tunable by δn and independent of n—is extracted from 'precoincidences' in the quantum Hall regime. The main text (Fig. 3a) reports 50 analyzed precoincidences but gives no selection criteria, no error bars, and no explicit disorder-broadening values. The method relies on a 'precise characterization of disorder' (Section III.B of the supporting information), but that supporting information is not included in the arXiv submission and is only available via an ACS link. This is especially concerning because the manuscript itself states that disorder increases as the wave function is pushed toward the interface with increasing δn, and that this makes locating the exact spectral coincidence nontrivial. The largest reported Δv values occur at the highest δn, where the disorder correction is largest. If the disorder model is inaccurate or the precoincidence selection is biased toward smooth trends, the apparent δn dependence could be overestimated and the claimed n-independence could be an artifact of selecting points that happen to collapse onto a single curve. The absence of error bars also makes the 'weak variation at fixed δn' statement unquantifiable. Thus the load-bearing assumption is not merely 'disorder matters'; it is that the disorder characterization is accurate enough to convert resistance onsets into absolute energy gaps across the full (n, δn) range.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript reports low-temperature magnetotransport measurements on doubly-gated silicon-on-insulator quantum wells. Using the quantum Hall coincidence method, the authors extract the valley splitting Δv and show that, at the buried thermal-oxide SiO2 interface, Δv increases with the electrostatic bias δn = n_B − n_F and reaches values as high as 6.3 meV, while being independent of the total carrier density n. They connect δn to the calculated wave-function probability at the interface and its penetration into the barrier, both of which are linear in δn, and compare their results with literature data for other silicon 2DEGs. Smaller valley splittings are reported near the front high-k interface.","tokens_in":8314,"tokens_out":3807,"duration_ms":45311,"significance":"If the quantitative extraction is robust, the paper provides a compelling demonstration of electrical valley-splitting tunability in a technologically relevant SOI platform, with a clean separation of total density and vertical electric field. The strengths include the independent double-gate control, the wide (n, δn) range, the use of tilted-field coincidence measurements, the Poisson-Schrodinger simulations of wave-function quantities, and the cross-system comparison with literature data. However, the central Δv values rely on a 'precoincidence' analysis whose disorder characterization is deferred to the supporting information, which is not included in the arXiv submission. This makes the absolute values and the n-independence claim difficult to assess from the main text alone.","major_comments":[{"comment":"The central values of Δv are obtained from 'precoincidences', but the main text gives no selection criteria for the 50 analyzed precoincidences, no disorder-broadening parameters, and no explicit formula converting resistance onsets into energy gaps. The reader is referred to Section III.B of the supporting information, which is not included in the arXiv submission. This is load-bearing because the largest reported Δv values occur at the largest δn, exactly where disorder is stated to be largest. Please make the full procedure available to reviewers and report the disorder characterization, selection criteria, and a representative example of the conversion.","section":"Section III.B of the SI; paragraph 'We now turn to quantitative extraction of Δv'"},{"comment":"No error bars or uncertainty estimates are provided for Δv. The claim that Δv is 'independent of the total carrier concentration' is supported only by colored data points; the scatter at fixed δn is not quantified. Please provide error bars (or an equivalent uncertainty quantification) and, if possible, report the residual n-dependence at fixed δn as a slope with uncertainty.","section":"Fig. 3(a)"},{"comment":"The manuscript states that disorder increases as the wave function is pushed toward the interface, so locating the true spectral coincidence is nontrivial. The precoincidence method is said to require a 'precise characterization of disorder', but the disorder model is not described in the main text. Because the highest Δv values occur at the highest δn, a systematic error in the disorder model could inflate the apparent δn dependence and artificially collapse the n-independence. Please show how the disorder characterization is validated, how sensitive the extracted Δv values are to the assumed disorder parameters, and how selection bias among precoincidences is excluded.","section":"Paragraph 'We now turn to quantitative extraction of Δv'"},{"comment":"The x-axis in Fig. 3(a) is the calculated |Ψ(zi)|², and Figs. 3(b,c) present calculated wave-function quantities, but the simulation parameters (effective masses, barrier heights, numerical method, and input density/gate voltages) are only referenced to Section IV of the SI. Since the quantitative comparison across samples and the claim that |Ψ(zi)|² is linear in δn and independent of n depend on these calculations, please include the simulation details and an estimate of their uncertainty in the main text or a fully available appendix.","section":"Fig. 3(a)-(c) and SI §IV"}],"minor_comments":[{"comment":"Typo: 'uncomplete' should be 'incomplete'.","section":"Abstract/Introduction"},{"comment":"'M.O. Georbig' is likely 'M.O. Goerbig'.","section":"Acknowledgments"},{"comment":"The color maps in Fig. 1(b,c) are described with resistance values and percentages in the caption, but the figures themselves do not show color bars. Please add color bars or define the full scale.","section":"Fig. 1"},{"comment":"The 'precoincidence' and 'coincidence' terms are introduced in the text but not defined in a figure legend or in a dedicated equation. Consider adding a schematic of the precoincidence condition and a formal definition, even if the quantitative details are in the SI.","section":"Fig. 2(b-f)"},{"comment":"Ref. 8 is missing the author list; Ref. 12 repeats a similar measurement style but could be more clearly distinguished from Ref. 13 in terms of method and sample type.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The main concern is the absence of the supporting information from the arXiv submission, especially Section III.B describing the precoincidence analysis. Please ensure that the editor and reviewers receive the SI, and that the disorder characterization and selection criteria are described in a verifiable way. If the precoincidence analysis is confirmed, the paper would be a valuable contribution to valley engineering in silicon; the current main text alone is insufficient to verify the central quantitative claims."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a solid transport study of valley splitting in doubly-gated SOI MOSFETs. The genuinely new piece is the systematic separation of the electrostatic bias δn = nB − nF from the total density n, showing experimentally that the splitting tracks δn (and the computed wavefunction penetration into the barrier) rather than n. The two-interface comparison within a single device—large splitting at the buried SiO2, smaller at the high-k top interface—adds useful support to the idea that the interface controls the effect. The connection to Saraiva et al.'s wavefunction-overlap quantities is sensible, and the Poisson-Schrödinger calculations in Fig. 3b,c corroborate the experimental trend.\n\nThe soft spot is the quantitative extraction. The main text reports 50 'precoincidences' with no error bars and no explicit selection criteria, and refers to the SI for the disorder characterization that converts resistance features into energy gaps. The stress-test concern is fair: disorder grows toward the interface, so the largest reported splittings are exactly where the correction is biggest, and if that model is off, the absolute values and the n-independence claim shift. The manuscript itself flags that locating the true spectral coincidence is nontrivial. That does not sink the paper, but it means the central numbers are not fully verifiable from the arXiv version. A referee will need to see the SI and, ideally, the authors should add error bars and selection criteria to the main text. The qualitative trend and the wavefunction argument are likely robust; the exact magnitude is less certain.\n\nThe citation pattern is appropriate—earlier SIMOX work by the same team is properly cited, and Saraiva et al. is used for interpretation, not fitted. No circularity. And the paper is honest about the disorder difficulty.\n\nFor whom? People working on silicon spin qubits or valleytronics will want to read this. It is a subfield improvement, not a paradigm shift. But it deserves a serious referee: the experiment is careful, the parameter disentanglement is valuable, and the concerns are addressable with the SI and added detail. I'd send it to peer review with a request for the missing material.\n\nRecommendation: accept for peer review; conditional on seeing the SI and a response about error bars.","headline":"Fresh evidence that the gate imbalance δn, not total density, controls valley splitting in SOI, but the headline 6.3 meV and n-independence claim rest on a precoincidence analysis that is fully documented only in the SI.","tokens_in":8758,"tokens_out":2238,"would_cite":true,"duration_ms":24689,"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 doubly gated silicon-on-insulator quantum wells, the valley splitting increases with gate imbalance δn = nB − nF, reaching 6.3 meV independent of total carrier density.","keywords":["valley splitting","silicon-on-insulator","doubly gated MOSFET","quantum Hall effect","electrostatic bias","Si/SiO2 interface","valleytronics","Landau level coincidence"],"falsifier":"A sample with the same Si/SiO2 interface but substantially lower disorder, measured at fixed δn while sweeping n over the accessible range, would falsify the independence claim if ΔV changes with n. Alternatively, an independent gap measurement such as thermal activation of resistance minima at one δn that disagrees with the precoincidence-extracted ΔV would question the absolute scale.","tokens_in":7910,"feed_emoji":"⚡","tokens_out":6727,"duration_ms":68611,"temperature":0.7,"pith_summary":"This paper shows that the valley splitting—the energy gap between the two degenerate conduction-band valleys of a silicon quantum well—can be controlled by the electrostatic bias between two gates, independent of the total electron density. In a doubly gated silicon-on-insulator transistor, the authors find that increasing the gate imbalance δn pushes the electron wavefunction against the buried thermal-oxide interface and into the barrier, and that the measured valley splitting grows with that wavefunction contact, reaching 6.3 meV. The same device shows a smaller valley splitting at the front high-k interface, so a single sample can cover a wide range of valley splittings. The paper argues that this makes δn, not density or raw electric field, the natural experimental control parameter for valleys in silicon and a route toward electrically tunable valleytronics.","feed_headline":"Gate imbalance tunes silicon valley splitting to 6.3 meV","feed_subtitle":"Not total density but the imbalance between two gates sets the valley gap—up to 6.3 meV in one device.","key_machinery":"Valley splitting in a [100] silicon quantum well is the energy separation between the two degenerate conduction-band valleys, lifted by intervalley scattering at the confining interface. The paper's control parameter is the electrostatic bias δn = nB − nF, which is shown to control the wavefunction modulus at the interface |Ψ(zi)|^2 and its penetration ∫Ψ(z>zi)^2 dz. The extraction machinery is the Landau-level coincidence/precoincidence method, which converts resistance features into comparisons of cyclotron, spin, and valley gaps. The proportionality of |Ψ(zi)|^2 and the barrier penetration to δn, independent of n, is what makes δn the natural knob.","core_discovery":"At low temperatures and in magnetic fields, the authors track longitudinal resistance in the quantum Hall regime while independently sweeping front- and back-gate voltages. They convert gate voltages to three quantities: total electron density n = nF + nB, electrostatic bias δn = nB − nF, and the perpendicular and total magnetic fields. When a spin and valley Landau level coincide, the resistance pattern changes, and the paper uses these 'precoincidences' to extract the valley gap ΔV. The central result is a monotonic increase of ΔV with δn, up to 6.3 meV at δn ≈ 9.2 × 10^12 cm^-2, with points at the same δn but different n giving nearly equal ΔV. Poisson-Schrödinger simulations show that at","pith_inferences":["If the mapping from δn to |Ψ(zi)|^2 is universal, singly gated MOSFET data should collapse onto the same ΔV versus |Ψ(zi)|^2 trend once their wavefunctions are computed, making the comparison a quantitative test of the underlying theory.","A direct test would be to vary the barrier material or thickness while keeping δn fixed: the theory predicts the splitting should follow the calculated penetration into the barrier, not the gate voltages themselves.","The different slopes seen between samples imply that a single universal curve may not exist; each interface may need its own microscopic parameter, which could be probed by controlled interface roughness or strain.","One could use the demonstrated tunability to operate a single device as a switch between nearly unpolarized and strongly valley-polarized regimes."],"forward_implications":["Electrostatic bias δn, not total density, is the control parameter for valley splitting in doubly gated silicon quantum wells; this allows independent tuning of valley energy while keeping carrier concentration fixed.","Valley splittings up to 6.3 meV at the buried thermal-oxide interface are reachable, while the same sample can show smaller splittings near the high-k interface, giving a single-device range from roughly 1–2 meV to 6.3 meV.","Comparisons of valley splitting across different silicon systems should use the interface wavefunction modulus and barrier penetration as the relevant variables rather than raw electric field or density.","Because the valley splitting can approach a sizable fraction of the Fermi energy, gate-bias control can produce large valley polarization at low temperatures.","The double-gas regime could host two spatially distinct 2DEGs with different valley splittings in one device, a possible building block for valley-based devices."],"supporting_citations":[{"why":"Supplies the interface-induced intervalley-coupling theory whose two microscopic quantities—wavefunction modulus at the interface and penetration into the barrier—are computed and linked to δn.","marker":"[9]"},{"why":"Introduces the coincidence method in Si 2D electron gases that the paper adapts to extract valley gaps from Landau-level crossings.","marker":"[10]"},{"why":"Demonstrates valley splitting control in doubly gated SiO2/Si/SiO2 quantum wells, the prior system this work extends.","marker":"[12]"},{"why":"Provides the precoincidence/disorder-based extraction procedure and zero-field valley polarization data on which the present quantitative analysis builds.","marker":"[13]"},{"why":"Gives singly gated MOSFET valley splitting data used in the comparison plot against interface wavefunction modulus.","marker":"[11]"},{"why":"Supplies valley splitting data from another doubly gated silicon system for comparison on the same |Ψ(zi)|^2 axis.","marker":"[20]"}],"fun_headline_variants":["Gate imbalance dials silicon valley splitting to 6.3 meV","Valley gap in silicon tuned by two-gate imbalance","Doubly gated silicon: control valley splitting to 6.3 meV","Electrical tuning of valley splitting hits 6.3 meV","How to set valley splitting in silicon: gate imbalance"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The reported energy gaps rest on identifying 'precoincidences' in disordered transport and converting them to valley splittings using a disorder model; if that model is wrong, or if the selected precoincidences are unrepresentative, the absolute values and the claimed independence from total density could be off.","fun_headline_variants_meta":{"raw":{"variants":["Gate imbalance dials silicon valley splitting to 6.3 meV","Valley gap in silicon tuned by two-gate imbalance","Doubly gated silicon: control valley splitting to 6.3 meV","Electrical tuning of valley splitting hits 6.3 meV","How to set valley splitting in silicon: gate imbalance"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000138,"raw_usage":{"total_tokens":992,"prompt_tokens":746,"completion_tokens":246,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":490,"completion_tokens_details":{"reasoning_tokens":171}},"tokens_in":490,"tokens_out":246,"duration_ms":2829,"temperature":1.0,"reasoning_tokens":171,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T11:51:50.928976+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A sample with the same Si/SiO2 interface but substantially lower disorder, measured at fixed δn while sweeping n over the accessible range, would falsify the independence claim if ΔV changes with n. Alternatively, an independent gap measurement such as thermal activation of resistance minima at one δn that disagrees with the precoincidence-extracted ΔV would question the absolute scale.","supporting_citations":[{"cited_title":"L.; Calder\\'on, M","cited_arxiv_id":null,"evidence_quote":"Supplies the interface-induced intervalley-coupling theory whose two microscopic quantities—wavefunction modulus at the interface and penetration into the barrier—are computed and linked to δn."},{"cited_title":"Solid State Communications 1980, 34, 51--55","cited_arxiv_id":null,"evidence_quote":"Introduces the coincidence method in Si 2D electron gases that the paper adapts to extract valley gaps from Landau-level crossings."},{"cited_title":"Valley splitting control in SiO _ 2 / Si/SiO _ 2 quantum wells in the quantum Hall regime","cited_arxiv_id":null,"evidence_quote":"Demonstrates valley splitting control in doubly gated SiO2/Si/SiO2 quantum wells, the prior system this work extends."},{"cited_title":"Valley Polarization in Si(100) at Zero Magnetic Field","cited_arxiv_id":null,"evidence_quote":"Provides the precoincidence/disorder-based extraction procedure and zero-field valley polarization data on which the present quantitative analysis builds."},{"cited_title":"S.; Scappucci, G","cited_arxiv_id":null,"evidence_quote":"Gives singly gated MOSFET valley splitting data used in the comparison plot against interface wavefunction modulus."},{"cited_title":"T.; Fujiwara, A.; Fujisawa, T.; Muraki, K.; Hirayama, Y","cited_arxiv_id":null,"evidence_quote":"Supplies valley splitting data from another doubly gated silicon system for comparison on the same |Ψ(zi)|^2 axis."}],"review_version":1}