{"id":"fb0e323f-fcb7-45dc-b9ab-90d240fc5b75","arxiv_id":"2509.03295","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Transport measurements show several superconducting states in rhombohedral tetra- and pentalayer graphene, including three that are enhanced or induced by magnetic fields and survive in-plane fields up to 8.5 T.","lead":"Researchers measured electrical transport in four-layer and five-layer rhombohedral graphene and found several superconducting states, some of which get stronger when a magnetic field is applied. The results point to unconventional superconductivity that survives fields far above the usual Pauli limit, and puts the material forward as a platform for topological quantum devices.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"SC3's boost by a small perpendicular field may be a Josephson-junction/Fraunhofer artifact; the paper's qualitative counterarguments do not rule it out, so the central 'field-boosted SC' claim for SC3 is not yet secured.","rationale":"The reader's weakest assumption (SdH-based parent-state identification) is a legitimate concern, but it is not the most load-bearing: the field-enhanced and field-induced phenomenology, which is the paper's central contribution, would survive even if the parent-state spin/valley assignment were revised. The same cannot be said for a Josephson-array artifact. The paper itself reports Fraunhofer interference near the SC3 phase boundary and states that the mechanism of the B_perp boost is not yet clarified. The two arguments given to exclude the Josephson-network explanation are qualitative: (n,D)-independence of the optimum B_perp is also expected if the loop area is set by a fixed disorder length scale, and agreement between two devices made in the same laboratory does not establish a universal intrinsic behavior. Consequently, the 'SC3 boosted by a small out-of-plane field' claim, one of the three headline unconventional responses, is not yet secured. I recommend keeping the reader's CONDITIONAL verdict: acceptance should require either the geometry-dependence test proposed above or a quantitative model showing why the observed Fraunhofer fringes do not extend into the SC3 region of the phase diagram. No verdict-category change is needed because the reader's CONDITIONAL already anticipates missing checks; this concern sharpens the condition rather than moving the verdict.","tokens_in":14502,"tokens_out":10064,"duration_ms":99426,"concrete_test":"Fabricate a second R5G Hall bar with the same crystalline quality but with the contact separation L changed by at least a factor of two, and map the critical current Ic versus B_perp inside SC3. If the B_perp at maximum Ic scales inversely with the contact-defined loop area (flux quantum divided by area), the enhancement is a Fraunhofer/Josephson-network effect; if it remains at ~1.8 mT despite the geometry change, the intrinsic scenario survives.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing unsecured step is the interpretation of SC3's enhancement by a small perpendicular field as an intrinsic property of a uniform unconventional superconductor. Extended Data Fig. 5i reports Fraunhofer-like interference fringes 'adjacent to the phase boundary of SC3,' and the main text ends the discussion with 'We believe further studies are needed to clarify the underlying mechanism.' That is a red flag: the same critical-current-versus-B-perp data that show Ic doubling at ~1.8 mT are also the signature of a Josephson-junction network whose loop frustration is relieved by a small applied flux. The authors' only counterarguments are that the optimal B_perp is independent of (n,D) and comparable in two devices. Neither is quantitative: a fixed loop area set by disorder or by device geometry would also give an (n,D)-independent optimum, and two devices fabricated by the same process can share the same characteristic island size. If the B_perp boost is a Fraunhofer or pi-junction network effect, then SC3 is not an intrinsically field-boosted superconductor, and the PVR > 35 estimate for SC3 loses its interpretation. This concern does not directly affect SC2 and SC4, but it weakens the central claim of a family of unconventional superconductivities.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports transport measurements on rhombohedral tetralayer and pentalayer graphene, identifying several superconducting states. Three of these (SC2, SC3, SC4) are claimed to be unconventional: SC2 is strengthened by an in-plane magnetic field, SC3 is boosted by a small out-of-plane field, and SC4 is induced by an in-plane field. All three remain superconducting up to 8.5 T in-plane, with nominal Pauli-limit-violation ratios exceeding 35 for SC3 and about 65 for SC4. Shubnikov-de Haas analysis assigns the parent states of SC2 and SC3 to valley-unpolarized, spin-polarized half-metals with annular Fermi surfaces, and the absence of anomalous Hall effect is used to infer zero valley polarization. A separate R4G/WSe2 device shows that proximitized spin-orbit coupling produces additional superconducting states. The authors interpret these observations as evidence for a family of unconventional superconductors in a clean, gate-tunable material platform.","tokens_in":14698,"tokens_out":5005,"duration_ms":46478,"significance":"If the interpretations hold, this work would establish a clean, crystalline, gate-tunable platform for unconventional superconductivity, with field-enhanced and field-induced superconducting states that are rare in any material. The paper's strengths include the mutual consistency of several superconducting diagnostics (vanishing Rxx, nonlinear dV/dI, suppression by millitesla out-of-plane fields, BKT scaling), the reproduction of the SC3 field-enhancement in a second device, and the clean-limit context (xi/l << 1). However, two load-bearing points need additional support before the central claims can be considered secure: the intrinsic nature of the SC3 enhancement under a small perpendicular field, and the robustness of the fermiology-based assignment of parent states for SC2 and SC3. These concerns do not undermine the existence of superconductivity, but they directly affect the interpretation of the field-enhancement and the claimed half-metal parentage.","major_comments":[{"comment":"The paper reports Fraunhofer-like interference fringes in the critical current near the phase boundary of SC3 (Extended Data Fig. 5i), and the main text concludes this section with 'We believe further studies are needed to clarify the underlying mechanism.' This admission, together with the presence of such fringes, leaves open the possibility that the observed enhancement of Ic and TBKT under a small perpendicular field arises from a Josephson-junction network (e.g., superconducting islands with pi junctions) rather than an intrinsic property of a uniform superconductor. The authors' counterarguments—that the optimal B_perp is independent of (n, D) and comparable in two devices—are qualitative; a fixed loop area set by disorder or by device geometry would also give an (n, D)-independent optimum. To secure the central claim that SC3 is an intrinsically field-boosted superconductor, the paper should provide a quantitative analysis of the Fraunhofer period in Extended Data Fig. 5i, a direct test that rules out percolative/junction effects (e.g., multi-terminal or noise measurements), or an explicit demonstration that the enhancement persists when the normal-state resistance away from SC3 is unchanged.","section":null},{"comment":"The parent-state identification for SC3 rests on the frequency relations f1−f2≈1/2 and f1−f3≈1/2, yet the low-frequency branch is explicitly described as 'unclear' within the density range of SC3. The branch is identified only at the two ends of the SC3 region, and the normalized frequency f_nu depends on gate capacitances calibrated from Landau fans. If the frequency assignments are not unique, the conclusion that SC3 emerges from a valley-unpolarized half-metal with an annular Fermi surface is not secured; consequently, the exclusion of an orbital-magnetism mechanism for the B_perp enhancement also loses support. A similar concern applies to SC2 (Fig. 2d), where the relation f1−(f2+f3)≈1/2 is used. Please provide a more thorough evaluation of the SdH branches, including uncertainty estimates and a comparison with band-structure calculations, so that the half-metal parentage and the spin-polarized interpretation rest on firmer ground.","section":null}],"minor_comments":[{"comment":"The equation for the coherence length is garbled in the provided manuscript; please ensure that all equations, especially the expression for ξ, are typeset correctly.","section":null},{"comment":"The definitions of n and D appear to be missing a factor or a division by ε0; please verify that the formulas as written are consistent with the units used in the figures (V/nm).","section":null},{"comment":"The text says 'Compared to bare R4G as shown in Fig. 1a' but Fig. 1a is the R5G map; Fig. 1b is the R4G map. Please correct the figure reference.","section":null},{"comment":"The naming of the new states in the R4G/WSe2 device (SC3–SC7) may be confusing because SC3 in the bare R5G device is a different state; please add a clarifying note or use distinct labels.","section":null},{"comment":"The statement that the sample could not be cooled as efficiently at 8 T as at 5 T is important for interpreting the high-field data; please include this caveat in the main text where the B|| = 8 T data are compared with B|| = 5 T.","section":null}],"recommendation":"major_revision","confidential_remarks":"The paper reports striking and potentially important observations, and the superconducting nature of the zero-resistance states is well supported by conventional diagnostics. The main risk is that the unusual field-enhancement of SC3 and the SdH-based parent-state assignments are not yet securely established. Given the authors' own admission that the mechanism of the B_perp enhancement is unclear, and the presence of Fraunhofer-like fringes in the same data, the SC3 claim needs a quantitative alternative-interpretation check. The fermiology concern is also substantive because it is the basis for the spin-polarized half-metal picture and the exclusion of orbital mechanisms. These issues are addressable in revision, so I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear X,\n\nThe headline is that this paper reports genuinely new superconducting states in clean rhombohedral multilayer graphene: SC2, which is strengthened by an in-plane field, SC4, which is induced by an in-plane field, and SC3, which is boosted by a small out-of-plane field. The first two are convincing. The diagnostics are mutually consistent—zero Rxx, nonlinear dV/dI, suppression by millitesla-scale perpendicular fields, BKT scaling—and SC3 is reproduced in a second device. The clean-limit estimate (xi << l) is credible, and the Pauli-limit violation ratios, while computed from TBKT rather than mean-field Tc and therefore inflated, are still notable for survival to 8.5 T in-plane.\n\nThe soft spot is SC3's out-of-plane enhancement. The authors report Fraunhofer-like fringes adjacent to the SC3 phase boundary, and they close the discussion with 'We believe further studies are needed to clarify the underlying mechanism.' That is precisely where a Josephson-junction network artifact could hide. Their counterargument—optimal B_perp independent of (n,D) and comparable in two devices—is not quantitative; a fixed loop area from disorder or device geometry would give the same constant optimum. So the intrinsic field-boosted SC3 claim is not yet secured. This does not affect SC2 or SC4, but it weakens the central 'family of unconventional superconductivities' framing.\n\nThe parent-state identification for SC2/SC3 as spin-polarized, valley-unpolarized half-metals relies on SdH frequency relations where the low-frequency branch is described as unclear. That is a real caveat, but not a circular step—the parent state is inferred from independent data. The lack of raw data is a problem for verification.\n\nThis paper is for anyone working on graphene superconductivity or unconventional pairing. It deserves a serious referee, and I would send it to review. The referee should ask for raw data and a more careful treatment of the SC3 enhancement, ideally a direct test that distinguishes a uniform superconductor from a junction network.\n\nRecommendation: engage with it, but treat SC3 as an open question rather than an established field-enhanced superconductor.","headline":"Genuinely new field-enhanced and field-induced superconducting states in clean rhombohedral graphene, with SC2 and SC4 convincing and SC3's intrinsic out-of-plane boost still an open question.","tokens_in":15389,"tokens_out":2795,"would_cite":true,"duration_ms":24795,"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 clean rhombohedral graphene, the authors identify superconducting states that are enhanced or induced by magnetic fields and survive in-plane fields far beyond the BCS Pauli limit.","keywords":["rhombohedral multilayer graphene","unconventional superconductivity","Pauli limit violation","field-enhanced superconductivity","field-induced superconductivity","Shubnikov-de Haas oscillations","half-metal parent state","spin-orbit proximity effect"],"falsifier":"A direct spin-sensitive measurement of the normal states of SC2 and SC3 would settle the parent-state claim: if no net spin polarization is found, or if a higher-resolution Shubnikov-de Haas measurement fails to reproduce the frequency relations $f_1 - (f_2 + f_3) \\approx 1/2$ and $f_1 - f_2 \\approx 1/2$, $f_1 - f_3 \\approx 1/2$, the half-metal interpretation collapses. On the superconducting side, observing that the small out-of-plane field no longer enhances SC3 in a device with different contacts or after a different cooling procedure would point to a non-intrinsic, percolative origin.","tokens_in":14276,"feed_emoji":"🧲","tokens_out":12941,"duration_ms":106536,"temperature":0.7,"pith_summary":"This paper reports electrical transport measurements on hole-doped rhombohedral tetralayer and pentalayer graphene and argues that these clean carbon crystals host a family of superconducting states, several of which behave in ways ordinary Bardeen-Cooper-Schrieffer superconductors cannot. In pentalayer graphene, one superconducting state (SC2) is strengthened by an in-plane magnetic field, another (SC3) is strengthened by a small out-of-plane field, and a third (SC4) appears only when an in-plane field is applied; all three remain superconducting in in-plane fields up to 8.5 tesla, far beyond the nominal Pauli limit for a conventional superconductor. The paper also reports that putting a WSe2 layer next to tetralayer graphene produces several new superconducting states while keeping the graphene in the clean limit. If the interpretation is right, rhombohedral multilayer graphene is a tunable, low-disorder testbed for superconductivity with broken symmetries and a plausible platform for engineering non-Abelian quasiparticles.","feed_headline":"Magnetic fields boost, even switch on, graphene superconductors","feed_subtitle":"Unconventional superconducting states in clean graphene get stronger, or appear, under magnetic fields.","key_machinery":"The load-bearing objects are the ordered parent states of the superconducting phases, identified by spin and valley structure and diagnosed with Shubnikov-de Haas oscillations. The central signatures are frequency relations among the oscillation branches: $f_1 - (f_2 + f_3) \\approx 1/2$ for SC2 and $f_1 - f_2 \\approx 1/2$, $f_1 - f_3 \\approx 1/2$ for SC3, which the paper reads as evidence for an annular Fermi surface (a ring-shaped Fermi surface) in a half-metal (a conductor with only one spin species at the Fermi level). Superconductivity itself is established by vanishing $R_{xx}$, nonlinear current-voltage curves, critical-current peaks that respond to a small out-of-plane field, and BKT scaling with $V_{xx} \\propto I^3$; the clean limit is quantified through coherence length $\\xi$ and mean free path $l$ with $\\xi/l \\ll 1$. The Pauli-limit-violation ratio, the measured in-plane critical field divided by the Pauli limit, is what turns the survival of SC3 and SC4 up to 8.5 T into a quantitative argument for unconventional pairing.","core_discovery":"The central discovery is that clean, hole-doped rhombohedral tetra- and penta-layer graphene host not one but several superconducting states, and three of them respond to magnetic fields in ways a conventional spin-singlet superconductor should not. SC2, whose normal state is identified as a valley-unpolarized (both valleys equally occupied), spin-polarized half-metal with an annular Fermi surface, has its critical current and Berezinskii-Kosterlitz-Thouless transition temperature increased when an in-plane field is applied. SC3, identified from Shubnikov-de Haas data as a half-metal with an annular Fermi surface, is boosted by an out-of-plane field of about 1.8 mT and is still superconducting in an in-plane field of 8.5 T, corresponding to a nominal Pauli-limit-violation ratio above 35. SC4 does not exist at zero field and is induced only by a large in-plane field, surviving to at least 8.5 T with a nominal Pauli-limit-violation ratio around 65. The paper argues that these effects come from the spin-polarized isospin structure of the parent states rather than from Ising spin-orbit coupling, because bare graphene has very weak spin-orbit coupling.","pith_inferences":["An extension the paper does not pursue is a direct test of triplet pairing: measuring the angular anisotropy of the upper critical field of SC4 in the plane would distinguish a spin-triplet state from an extrinsic or multi-band effect.","The nearly identical optimal out-of-plane field for SC3 in two devices resembles an Aharonov-Bohm period of a small loop; testing whether the enhancement survives with different contact geometries would separate a phase-sensitive mechanism from a density-of-states effect.","If the spin-polarized half-metal assignments are right, rhombohedral graphene offers a rare example of possible spin-polarized superconductivity without magnetic dopants, which could clarify what kind of pairing glue is needed.","The low displacement fields at which several of these superconductors appear would make it practical to combine them with quantum anomalous Hall regions in split-gate devices, because gate leakage is less of a risk at low fields."],"forward_implications":["Rhombohedral multilayer graphene becomes a clean, gate-tunable platform for studying superconductivity without the twist-angle disorder that complicates moiré devices.","The in-plane-field robustness of SC2, SC3, and SC4, with nominal Pauli-limit-violation ratios above 35, would require pairing mechanisms beyond the conventional Pauli limit, such as spin-triplet or other broken-symmetry pairing.","Because the same rhombohedral stacks already host quantum anomalous Hall states, superconducting regions and topological regions could be combined in one material to pursue Majorana or parafermion quasiparticles.","Proximitized spin-orbit coupling from WSe2 creates additional superconducting states while preserving the high mean free path, suggesting interface engineering as a practical way to enlarge the superconducting phase diagram."],"supporting_citations":[{"why":"establishes that unconventional superconductivity is vulnerable to impurities, motivating the clean-limit requirement that rhombohedral graphene satisfies.","marker":"3"},{"why":"reported superconductivity in rhombohedral trilayer graphene and supplies the SC1 comparison and the coherence-length/mean-free-path estimate used to put these devices in the clean limit.","marker":"37"},{"why":"reported spin-polarized superconductivity and a $B_{\\parallel}$-induced superconducting state in Bernal bilayer graphene, the state SC4 is compared with and distinguished from.","marker":"33"},{"why":"documented correlated insulators and Chern insulators in pentalayer rhombohedral graphene, providing the isospin-broken parent-state landscape from which SC2 and SC3 are claimed to emerge.","marker":"4"},{"why":"documented broken-symmetry insulators and metals in tetralayer rhombohedral graphene, the parent-state context for SC1 and SC2 in the four-layer devices.","marker":"5"},{"why":"reported chiral superconductivity in rhombohedral graphene; its orbital-magnetic-moment mechanism is the one the paper argues against for the out-of-plane-field enhancement of SC3.","marker":"47"},{"why":"defines the Pauli limit used to compute the nominal Pauli-limit-violation ratios quoted for SC3 and SC4.","marker":"6"},{"why":"showed a large quantum anomalous Hall effect in spin-orbit-proximitized rhombohedral graphene, the topological states the paper proposes to combine with the superconductors for non-Abelian quasiparticles.","marker":"8"}],"fun_headline_variants":["Magnetic fields boost, even switch on, graphene superconductivity","Field-enhanced superconductivity in rhombohedral graphene","Graphene's unconventional superconducting states strengthen under magnetic fields","Magnetic fields unlock unconventional superconductivity in graphene","Rhombohedral graphene superconductors respond strongly to magnetism"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument rests on reading the Shubnikov-de Haas frequencies as proving that SC2 and SC3 emerge from spin-polarized, valley-unpolarized half-metals with ring-shaped Fermi surfaces; the paper itself notes that the low-frequency branch in the SC3 density range is unclear, so a misassignment would weaken the spin-polarized interpretation and the exclusion of orbital-magnetism mechanisms for the out-of-plane-field enhancement.","fun_headline_variants_meta":{"raw":{"variants":["Magnetic fields boost, even switch on, graphene superconductivity","Field-enhanced superconductivity in rhombohedral graphene","Graphene's unconventional superconducting states strengthen under magnetic fields","Magnetic fields unlock unconventional superconductivity in graphene","Rhombohedral graphene superconductors respond strongly to magnetism"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001294,"raw_usage":{"total_tokens":5357,"prompt_tokens":1095,"completion_tokens":4262,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":711,"completion_tokens_details":{"reasoning_tokens":4184}},"tokens_in":711,"tokens_out":4262,"duration_ms":30177,"temperature":1.0,"reasoning_tokens":4184,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T16:31:34.292622+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A direct spin-sensitive measurement of the normal states of SC2 and SC3 would settle the parent-state claim: if no net spin polarization is found, or if a higher-resolution Shubnikov-de Haas measurement fails to reproduce the frequency relations $f_1 - (f_2 + f_3) \\approx 1/2$ and $f_1 - f_2 \\approx 1/2$, $f_1 - f_3 \\approx 1/2$, the half-metal interpretation collapses. On the superconducting side, observing that the small out-of-plane field no longer enhances SC3 in a device with different contacts or after a different cooling procedure would point to a non-intrinsic, percolative origin.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"establishes that unconventional superconductivity is vulnerable to impurities, motivating the clean-limit requirement that rhombohedral graphene satisfies."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"reported superconductivity in rhombohedral trilayer graphene and supplies the SC1 comparison and the coherence-length/mean-free-path estimate used to put these devices in the clean limit."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"reported spin-polarized superconductivity and a $B_{\\parallel}$-induced superconducting state in Bernal bilayer graphene, the state SC4 is compared with and distinguished from."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"documented correlated insulators and Chern insulators in pentalayer rhombohedral graphene, providing the isospin-broken parent-state landscape from which SC2 and SC3 are claimed to emerge."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"documented broken-symmetry insulators and metals in tetralayer rhombohedral graphene, the parent-state context for SC1 and SC2 in the four-layer devices."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"reported chiral superconductivity in rhombohedral graphene; its orbital-magnetic-moment mechanism is the one the paper argues against for the out-of-plane-field enhancement of SC3."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"defines the Pauli limit used to compute the nominal Pauli-limit-violation ratios quoted for SC3 and SC4."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"showed a large quantum anomalous Hall effect in spin-orbit-proximitized rhombohedral graphene, the topological states the paper proposes to combine with the superconductors for non-Abelian quasiparticles."}],"review_version":2}