{"id":"b5016997-5ab9-488d-a98a-af1190b49074","arxiv_id":"2608.11450","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"In rhombohedral graphene, the displacement field needed to reach the layer-polarized insulator increases with layer count, and six-layer devices show surface-state-dominated transport with gate-selective Landau levels.","lead":"Researchers measured how the number of graphene layers changes the phase diagram of rhombohedral multilayer graphene under an electric field. In six-layer graphene, they found transport dominated by decoupled surface states whose Landau levels can be controlled by one gate.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The r-6LG surface-state claim rests on a resistive peak that SI Sec. 7 itself explains by Drude mobility-density competition; separating that classical origin from surface-state transport is the key unaddressed step.","rationale":"The reader's weakest assumption identifies the same soft spot: the r-6LG surface-state interpretation is not cleanly separated from device-quality variations and a possible Drude origin of the resistive peak. My reading strengthens this with an internal piece of evidence: SI Sec. 7 explicitly offers the Drude competition between carrier density and mobility as a natural cause of a resistivity maximum, without quantitatively ruling it out for the peak later used as a surface-state signature. The concrete test proposed—using the already extracted two-band parameters to compute the classical rho_xx(D)—would settle whether the peak is genuinely anomalous. This is not a fatal flaw; the high-field Landau-level data and the screening calculation provide independent support, so conditional acceptance remains appropriate. The verdict should therefore remain unchanged from the reader's CONDITIONAL assessment, with the added condition that the classical Drude explanation be quantitatively excluded before the B = 0 peak is cited as evidence of surface-state-dominated transport.","tokens_in":15890,"tokens_out":7791,"duration_ms":76384,"concrete_test":"Re-analyze the B = 0 semimetal-phase peak using the two-band Drude formulas in SI Sec. 4, with the measured carrier densities and mobilities for r-6LG and for r-4LG/r-5LG, and compute rho_xx(D) at n = 0 over the same D range as Fig. 2a. Use a minimal model in which the band overlap (and hence n and p) decreases linearly with D while mobilities increase, as described in SI Sec. 7. If this Drude calculation reproduces the position, width, and layer-number contrast of the observed resistive peak to within about 20% without invoking surface states, then the B = 0 peak cannot serve as evidence for surface-state-dominated transport. If it does not reproduce the peak, the surface-state interpretation survives this specific check.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim includes 'surface-state-dominated transport emerges, with Landau levels (LLs) and resistive peaks selectively controlled by adjacent gates' (abstract and Sec. II.B). The weakest link is the interpretation of the B = 0 resistive peak in the semimetal phase of r-6LG. SI Sec. 7 states that as D increases, the band overlap shrinks (lowering electron and hole densities) while the bands become more dispersive (raising mobilities), and 'within a simple Drude picture, the competition between these two effects naturally leads to a maximum in the resistivity.' No quantitative analysis is presented to show that the observed peak is not this classical Drude maximum. The mobility contrast reported in SI Sec. 4 makes this concrete: r-6LG has carrier densities near 10^12 cm^-2 and substantially lower mobilities than r-4LG and r-5LG, so a layer-number-dependent classical peak could arise without invoking surface states. The adjacent-gate dependence of the peak and of the B = 4 T LLs (Fig. 3b-d) is the remaining evidence for the surface-state interpretation, but no controlled comparison rules out gate-specific contact or inhomogeneity effects in this single r-6LG device. Because the surface-state claim is used to support the enhanced-screening picture, this ambiguity is load-bearing; the high-field QH data are less affected but do not by themselves establish the B = 0 peak's origin.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports dual-gated electrical transport measurements on rhombohedral graphene with four, five, and six layers (plus one eight-layer device in the Supplementary Information) and maps the zero-magnetic-field phases at charge neutrality as a function of displacement field. It claims that the critical displacement field for the layer-antiferromagnet to semimetal transition is approximately constant from tetralayer to hexalayer graphene, whereas the critical displacement field for the semimetal to layer-polarized-insulator transition increases with layer number, and it attributes this to enhanced interlayer screening quantified by a self-consistent tight-binding calculation. The paper further claims that hexalayer graphene shows surface-state-dominated transport, evidenced by a resistive peak and Landau levels that respond selectively to the adjacent gate, with high-field quantum Hall data interpreted through layer-valley-locked Landau levels and dissipative states possibly arising from interlayer backscattering.","tokens_in":16069,"tokens_out":4400,"duration_ms":38739,"significance":"If the claims hold, the paper makes a valuable contribution by establishing layer number as a practical tuning parameter for correlated and topological phases in rhombohedral multilayer graphene. The experimental strengths include multi-temperature phase-boundary measurements, data from multiple pentalayer devices, and a self-consistent electrostatic tight-binding calculation that uses standard Slonczewski-Weiss-McClure parameters and is not fitted to the measured critical fields. The high-field Landau-level crossing patterns are also compared with explicit schematics, which is a useful diagnostic for layer counting. The main weakness is that the surface-state interpretation of the zero-field resistive peak in r-6LG is not quantitatively separated from a classical Drude mechanism that is acknowledged in the Supplementary Information; because that peak is central to the abstract and to the screening narrative, this ambiguity is load-bearing.","major_comments":[{"comment":"The resistive peak in the semimetal phase of r-6LG is presented as evidence for surface-state-dominated transport, but SI Sec. 7 states that within a simple Drude picture the competition between decreasing carrier density and increasing mobility with displacement field naturally leads to a resistivity maximum. The manuscript does not provide a quantitative calculation of the Drude rho_xx(D) using the measured n(D), p(D), mu_n(D), and mu_p(D) extracted in SI Sec. 4, nor does it demonstrate that the observed peak position, width, or magnitude disagrees with that classical prediction. Without this separation, the B = 0 peak cannot be uniquely attributed to surface states; indeed, the same mechanism could produce a layer-number-dependent peak because SI Sec. 4 reports that r-6LG has much larger carrier densities and substantially lower mobilities than r-4LG and r-5LG. This point is load-bearing for the abstract claim of surface-state-dominated transport.","section":"Sec. II.B, Fig. 3, SI Sec. 7"},{"comment":"The single-gate-controlled Landau-level features are demonstrated in one r-6LG device only, and the contrast with r-4LG and r-5LG devices is not controlled for device quality. SI Sec. 4 reports that r-6LG has substantially lower mobility than the thinner devices, so gate-specific contact effects or local inhomogeneity in this particular device could in principle produce similar-looking features. A quantitative comparison of device quality across the devices used for the contrast (for example, mobility, contact resistance, and residual charge inhomogeneity), or data from an additional r-6LG device, is needed to support the layer-number-dependent interpretation.","section":"Sec. II.B, Fig. 3b-d"},{"comment":"The central scaling trend of the semimetal-to-LPI critical field with layer number is based on one r-4LG and one r-6LG device in the main text, with additional r-5LG devices in the Supplementary Information, and no uncertainty estimates are given for the critical-field values. Because the phase boundaries are identified from crossing points of temperature-dependent resistivity traces, the authors should provide error bars or an explicit statement of the systematic uncertainty in identifying these crossings for each layer number; the significance of the claimed monotonic trend depends on these uncertainties.","section":"Sec. II.A, Fig. 2c"}],"minor_comments":[{"comment":"The sentence reporting carrier densities of approximately 10^12, 10^10, and 10^11 should state the units (cm^-2) and should include the fitting uncertainty in the extracted densities and mobilities.","section":"SI Sec. 4"},{"comment":"References 18 and 39 contain placeholder DOIs (10.1103/chsq-ndzs and 10.1103/j1zf-v3j5) that appear not to be valid Crossref identifiers; these should be corrected before publication.","section":"References 18 and 39"},{"comment":"The line cuts in Fig. 3c,d are not fully self-explanatory; the figure should state which color corresponds to which magnetic field and which gate is swept, along with the fixed values of the other gate.","section":"Fig. 3c,d"},{"comment":"The statement that LPI states are not observed in r-8LG should be presented in Fig. 2c as an upper limit or an unmeasured boundary rather than as a data point, so that the phase diagram is not misleading.","section":"SI Sec. 2"},{"comment":"The notation n_b and n_t is used for gate charge densities while n_j denotes layer charge densities; this is understandable but potentially confusing, and a brief definition of the subscript convention would improve clarity.","section":"Methods, Eqs. (5)-(6)"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The genuinely new thing here is the systematic layer-number sweep: Dc for the SM-to-LPI transition rises from r-4LG through r-6LG, while the LAF-to-SM boundary stays put, and the self-consistent tight-binding screening calculation captures that trend without fitting to the measured Dc. That part is solid and worth taking seriously. The r-6LG surface-state claim—adjacent-gate-controlled resistive peaks and Landau levels—is more of a stretch, and that's where the paper's weakest link sits.\n\nCredit where it's due: the experimental data are clean, the multi-temperature line cuts in Fig. 2a are convincing, and the screening calculation uses standard SWMC parameters with no free tuning to the phase boundaries. The high-field QH data in Fig. 4 are rich and the valley-layer-locked LL crossing analysis is a useful framework. The contrast with r-4LG and r-5LG devices is a reasonable argument for a layer-number effect, and the authors are careful to exclude moiré-aligned samples.\n\nSoft spots, in order of importance. First, the B = 0 resistive peak in r-6LG: the supplementary itself says that in a simple Drude picture, the competition between falling carrier density and rising mobility as D increases naturally produces a resistivity maximum. That is exactly the peak they interpret as surface-state-dominated transport. They never show quantitatively that the observed peak is larger or D-dependent in a way a two-band Drude model cannot reproduce. The gate-dependent asymmetry is suggestive, but with one r-6LG device and no controlled comparison to rule out contact or inhomogeneity effects, the surface-state interpretation remains plausible rather than proven. Second, the main-text phase diagram rests on one r-4LG and one r-6LG device each (additional r-5LG devices help), and there are no error bars on the Dc values. Third, the 'unscreened Coulomb interaction model' that the paper claims to defy is never spelled out in enough detail to know exactly what is being ruled out. These are fixable with quantitative analysis and more devices, not fatal flaws.\n\nWho gets value: experimentalists working on rhombohedral graphene and theorists modeling screening in multilayer stacks. The paper deserves a serious referee; it will likely be cited for the Dc trend even if the surface-state story gets revised. My recommendation: send it to peer review, but the referees should insist on a quantitative separation between the Drude and surface-state explanations for the r-6LG peak, and on error bars or at least device-to-device scatter for the phase boundaries.","headline":"Genuinely new layer-dependent phase diagram in rhombohedral graphene, with a plausible but not fully proven surface-state interpretation for r-6LG; worth a serious referee, but the biggest gap is ruling out a classical Drude origin for the B = 0 resistive peak.","tokens_in":16747,"tokens_out":1594,"would_cite":true,"duration_ms":16005,"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":"Rhombohedral graphene stacks of four to six layers show that layer number controls which insulating or metallic phase appears at charge neutrality: the field for the layer-polarized transition rises with thickness, and six-layer samples…","keywords":["rhombohedral multilayer graphene","layer-polarized insulator","layer-antiferromagnetic insulator","interlayer screening","surface states","Landau levels","quantum Hall effect","displacement field"],"falsifier":"Measure the same r-6LG semimetal phase in devices with mobility comparable to the best r-4LG and r-5LG devices and with contacts swapped or made symmetric: if the adjacent-gate-controlled peak and Landau levels persist, the screening interpretation is supported; if they vanish or track the contact asymmetry, the claim fails. A quantitative version is to fit $\\rho_{xx}(D)$ at $B=0$ in r-6LG with the two-band Drude model using measured carrier densities and mobilities as functions of $D$; if the resistive peak is fully reproduced by the density–mobility competition alone, no additional surface-screening mechanism is needed.","tokens_in":15603,"feed_emoji":"🧲","tokens_out":4956,"duration_ms":93025,"temperature":0.7,"pith_summary":"Rhombohedral graphene multilayers are stacks in which the lowest-energy electronic bands hug the top and bottom surfaces, making electron interactions strong. This paper reports that the layer number itself—four, five, or six layers—controls which symmetry-broken phase appears at charge neutrality and how easily a perpendicular electric field can switch between phases. The critical field separating the layer-antiferromagnetic insulator from the semimetal stays almost the same from four to six layers, while the field needed to reach the layer-polarized insulator grows steadily with layer number, which the authors attribute to stronger interlayer screening in thicker stacks. In six-layer samples, transport in the semimetal phase is carried by surface states whose Landau levels and a resistive peak respond to only the adjacent gate—a sign of surface states decoupled by screening. If true, thickness becomes a practical dial for engineering correlated and quantum-Hall phases in graphene without twist angles.","feed_headline":"Layer count turns rhombohedral graphene into a surface-state device","feed_subtitle":"In six-layer stacks, Landau levels follow only the adjacent gate—a sign that thickness tunes screening.","key_machinery":"The load-bearing object is the set of low-energy surface states in rhombohedral (ABC-stacked) multilayer graphene, whose kinetic energy scales as $E_k\\propto p^N$; in thicker stacks these states carry an increasing share of the low-energy density of states and screen the external displacement field before it reaches interior layers. The argument is carried by a self-consistent electrostatic tight-binding model, with a discrete Gauss-law relation coupling layer potentials to layer charge densities and an out-of-plane dielectric constant; it yields layer-resolved potentials, a screening factor $S = 1 - \\Delta U_{SC}/\\Delta U_{unscreened}$, and the critical field for the layer-polarized transition. In transport, the decisive signatures are adjacent-gate-controlled Landau levels and the fully lifted 24-fold degeneracy of the zeroth Landau level in hexalayer graphene, whose valley–layer locking allows the authors to assign each quantum-Hall state a flavor (filling factor, spin, valley, layer).","core_discovery":"The central claim is that layer number $N$ tunes the balance between electron-electron interactions and interlayer screening in rhombohedral multilayer graphene, producing two unconventional effects. First, the critical displacement field $D_c$ for the semimetal-to-layer-polarized-insulator transition increases monotonically from tetralayer to hexalayer (and beyond), contradicting the simplest unscreened two-surface-band model in which the gap should grow with thickness. Second, in hexalayer graphene a surface-state-dominated transport regime appears in the semimetal phase: a resistivity peak and, in a magnetic field, Landau levels that are controlled almost entirely by the gate on the same side as the surface state. At high field the 24-fold degenerate zeroth Landau level of the six-layer system is fully resolved, with valley locked to layer, and states with counter-propagating edge modes on the two surfaces become dissipative—attributed to interlayer backscattering. The paper explains both effects with self-consistent tight-binding calculations in which the external field is progressively screened by charge redistribution into surface-derived bands, with a screening factor exceeding 0.94 for six layers.","pith_inferences":["The same screening mechanism would predict that even thicker rhombohedral stacks (seven, eight layers) show yet stronger surface decoupling; the paper's own data hint that the layer-polarized onset moves to fields beyond the measured range, which is a direct testable extension.","If adjacent-gate control is intrinsic, then local gates could address individual surfaces independently, opening a route to electrically writable surface-state devices and valley-selective contacts without twist engineering.","A cleaner test of the screening story would be a direct measurement of the layer-resolved electrostatic potential (for example by scanning probe) across $N=4,5,6$ at fixed displacement field, compared against the calculated screening factor.","The dissipative states from interlayer backscattering suggest that at fractional fillings the decoupled surfaces may host interlayer coherent or fractional states, though that goes beyond the data presented here."],"forward_implications":["Layer number becomes a design knob: increasing $N$ suppresses the layer-antiferromagnetic phase beyond six layers and pushes the layer-polarized-insulator transition to higher displacement fields, so phase diagrams can be tailored by choosing thickness.","Hexalayer graphene's decoupled surface states act as a gate-tunable electron–hole bilayer: each surface's Landau levels respond to the adjacent gate, allowing selective population of one surface.","At high field, interlayer backscattering between counter-propagating edge modes can be switched on or off by the displacement field, giving electrically controlled dissipative versus quantized Hall states.","The high-field Landau-level crossing patterns provide a reliable way to identify the layer number of a rhombohedral graphene sample.","The screening-driven rise in $D_c$ means thicker rhombohedral stacks require larger external fields to reach layer-polarized insulating states, a practical constraint and opportunity for device design."],"supporting_citations":[{"why":"Supplies the interlayer-screening framework in graphene multilayers that the paper uses to interpret the layer-number-dependent $D_c$.","marker":"[3]"},{"why":"Reports the layer-antiferromagnetic insulator in tetralayer rhombohedral graphene, establishing the phase and measurement approach this paper extends.","marker":"[4]"},{"why":"Reports correlated insulating and Chern states in pentalayer rhombohedral graphene, providing the baseline for the layer-number comparison.","marker":"[5]"},{"why":"Shows that hBN alignment can modify phase onsets, supporting the paper's restriction to moiréless samples.","marker":"[14]"},{"why":"Provides STM/STS evidence for layer-dependent electronic structure and correlation strength that the paper's transport data connect to.","marker":"[27]"},{"why":"Uses the self-consistent tight-binding method for flat-band surface states in thick rhombohedral graphene, the basis of the screening calculations.","marker":"[30]"},{"why":"Establishes valley–layer locking of Landau levels in graphene multilayers, used to assign flavor labels to the quantum-Hall states.","marker":"[31]"},{"why":"Gives the electrostatic single-gate tracking formalism and Gauss-law relations used in the self-consistent screening model.","marker":"[39]"},{"why":"Provides the discrete Gauss-law electrostatic description of $N$-layer graphene that the calculations build on.","marker":"[40]"}],"fun_headline_variants":["Thick rhombohedral graphene reveals surface-state transport","Layer number tunes screening in rhombohedral graphene stacks","Hexalayer graphene: Landau levels obey just the nearby gate","Screening wins: thickness controls gap and surface states in graphene","Rhombohedral graphene: more layers, more surface control"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The strongest assumption is that the contrast between six-layer and thinner devices—the adjacent-gate-controlled resistive peak and Landau levels—reflects intrinsic layer-number-dependent screening, not device-to-device differences in mobility, contacts, or inhomogeneity; the six-layer device has notably lower mobility, and a Drude competition between carrier density and mobility can already produce a resistivity peak.","fun_headline_variants_meta":{"raw":{"variants":["Thick rhombohedral graphene reveals surface-state transport","Layer number tunes screening in rhombohedral graphene stacks","Hexalayer graphene: Landau levels obey just the nearby gate","Screening wins: thickness controls gap and surface states in graphene","Rhombohedral graphene: more layers, more surface control"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000517,"raw_usage":{"total_tokens":2529,"prompt_tokens":992,"completion_tokens":1537,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":608,"completion_tokens_details":{"reasoning_tokens":1454}},"tokens_in":608,"tokens_out":1537,"duration_ms":31439,"temperature":1.0,"reasoning_tokens":1454,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T14:12:31.213299+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the same r-6LG semimetal phase in devices with mobility comparable to the best r-4LG and r-5LG devices and with contacts swapped or made symmetric: if the adjacent-gate-controlled peak and Landau levels persist, the screening interpretation is supported; if they vanish or track the contact asymmetry, the claim fails. A quantitative version is to fit $\\rho_{xx}(D)$ at $B=0$ in r-6LG with the two-band Drude model using measured carrier densities and mobilities as functions of $D$; if the resistive peak is fully reproduced by the density–mobility competition alone, no additional surface-screening mechanism is needed.","supporting_citations":[{"cited_title":"In addition, t he gate -tunable surface states in r-6LG provide a platform for designer quantum Hall bilayers, where interlayer backscattering can be electrically switched","cited_arxiv_id":null,"evidence_quote":"Supplies the interlayer-screening framework in graphene multilayers that the paper uses to interpret the layer-number-dependent $D_c$."},{"cited_title":"Figure 1","cited_arxiv_id":null,"evidence_quote":"Reports the layer-antiferromagnetic insulator in tetralayer rhombohedral graphene, establishing the phase and measurement approach this paper extends."},{"cited_title":"The rhombohedral graphene domain is identified using scanning near-field infrared microscope and isolated in-situ using the AFM cutting","cited_arxiv_id":null,"evidence_quote":"Reports correlated insulating and Chern states in pentalayer rhombohedral graphene, providing the baseline for the layer-number comparison."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Shows that hBN alignment can modify phase onsets, supporting the paper's restriction to moiréless samples."},{"cited_title":"For the understanding of this peak, both carrier densities and mobilities of electrons and holes need to be taken into consideration","cited_arxiv_id":null,"evidence_quote":"Provides STM/STS evidence for layer-dependent electronic structure and correlation strength that the paper's transport data connect to."},{"cited_title":"As increasing the magnetic field, a crossover between the two regimes is expected to be observed","cited_arxiv_id":null,"evidence_quote":"Uses the self-consistent tight-binding method for flat-band surface states in thick rhombohedral graphene, the basis of the screening calculations."},{"cited_title":"0/3K” state is non -dissipative, whereas its neighboring “−1K′/4K","cited_arxiv_id":null,"evidence_quote":"Establishes valley–layer locking of Landau levels in graphene multilayers, used to assign flavor labels to the quantum-Hall states."}],"review_version":1}