{"id":"b0245fe9-a917-44e5-9dc5-ab161d0a272c","arxiv_id":"2502.04785","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Strong proximity superconductivity persists in the flat-band limit of twisted bilayer graphene, with critical current decoupled from normal-state conductance and a Josephson diode effect in flat-band domes.","lead":"Using NbTiN superconducting contacts on twisted bilayer graphene, the authors measured supercurrents through samples with different twist angles, from dispersive to flat bands. They found surprisingly strong proximity superconductivity in the flat-band limit and a critical current that does not follow the normal-state conductance, pointing to interaction and quantum geometry effects.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Concern: The claim that interactions cause an excess critical current in the flat-band domes is not uniquely established because the Dynes–Fulton analysis in Supplementary L shows the supercurrent is edge-dominated, so the measured bulk G_N may not be the correct non-interacting baseline.","rationale":"The reader's weakest_assumption precisely identifies the same load-bearing concern: the measured bulk GN may not be the correct baseline for the non-interacting supercurrent, given the edge-dominated supercurrent profile shown in Supplementary L. My independent reading of the main text and supplement confirms this is the most vulnerable point of the central explanatory claim. The empirical observations (strong flat-band supercurrents, the Ic-GN anomaly, and the Josephson diode effect) are well supported by the data and control devices, but the attribution of the anomaly to interaction-induced excess current is not uniquely established. The paper's own Supplementary L provides the evidence that a spatially inhomogeneous, edge-channel-dominated supercurrent exists exactly in the domes where the anomalous scaling is reported, and no spatially resolved conductance baseline is provided. The Ginzburg-Landau estimate is explicitly an order-of-magnitude check with parameters chosen to match experiment, and the monotonic relation between the computed correlator phi_R and Ic is an assumption. Because the reader's verdict is already CONDITIONAL, which appropriately captures the uncertainty in the explanatory mechanism, my stress-test does not move the verdict. However, the concrete test I propose would settle whether the anomalous Ic-GN scaling survives a spatially resolved, non-interacting baseline, and is worth running before elevating the central claim to a definitive statement.","tokens_in":30433,"tokens_out":2474,"duration_ms":21590,"concrete_test":"Perform a spatially resolved conductance measurement or simulation that separates edge and bulk contributions at the fillings of the D2 dome (nu ~ -2 to -3.5). Specifically, measure or compute GN_edge and GN_bulk separately, and test whether a non-interacting, edge-dominated Josephson junction model that uses the edge conductance (or a weighted combination of edge and bulk conductances) as the baseline reproduces the observed Ic(GN) dome without invoking I_c^int. If the non-interacting edge-channel model reproduces the deviation from the bulk-GN scaling, the excess-current interpretation is weakened. A simpler analytical check: re-derive the predicted I_c vs. GN relation for a junction whose supercurrent density profile is the measured edge-peaked J_s(x) from Supplementary L, and compare it to the measured Ic-GN dome.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central explanatory claim is that the violation of the Ic-GN scaling in the flat-band domes signals an interaction-induced excess critical current, I_c^int, which is independent of GN. This hinges on using the measured two-terminal GN as the correct baseline for the conventional, non-interacting supercurrent. However, the authors' own Dynes-Fulton analysis (Supplementary L, Figs. S25-S26) shows that precisely in the filling range where the anomalous scaling is claimed (e.g., the nu ~ -2 to -3.5 dome in D2), the supercurrent is strongly concentrated at the edges of the junction rather than in the bulk. A two-terminal conductance GN measures the total conductance through all parallel channels, including edge and bulk contributions, but the relevant baseline for the proximity effect is the conductance of the specific channels that carry the supercurrent, weighted by their Andreev transparency. If the edge channels have higher transparency or different filling dependence than the bulk, then Ic and GN can decouple without any interaction-induced excess term. The paper does not rule out this possibility: it does not provide a spatially resolved GN profile, nor a comparison of the edge-vs-bulk conductance at the relevant fillings, nor a model of how a non-interacting, spatially inhomogeneous junction would scale Ic with a properly weighted GN. The Ginzburg-Landau estimate of I_c^int (Supplementary E) is explicitly an order-of-magnitude check with parameters chosen to match the data (U ~ 10 ueV, xi ~ 40 nm), and the monotonic relation between the computed correlator phi_R and Ic is assumed but untested. Thus the empirical finding of strong flat-band supercurrents is solid, but the attribution of the anomalous Ic-GN relation to interactions is conditional at best.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports transport measurements of NbTiN/TBG/NbTiN Josephson junctions at three twist angles (0.94°, 1.00°, 1.24°) and compares them with control devices at larger twist angles and with monolayer graphene. The central empirical findings are (i) that the critical current remains substantial in the flat-band limit, forming dome-shaped superconducting regions near half-filling and near the band edges, and (ii) that Ic does not scale with the two-terminal normal-state conductance GN in the flat bands, in contrast to the dispersive bands and to the control devices. The authors attribute this anomalous scaling to an interaction-induced excess critical current I_c^int, and support the interpretation with Ginzburg-Landau estimates and with continuum-model calculations of a superconducting pair correlator that separates dispersion, quantum-geometric, and multiband contributions. They also report a Josephson diode effect in the flat-band domes and attribute it to inversion-symmetry breaking in the TBG weak link.","tokens_in":30680,"tokens_out":5321,"duration_ms":56387,"significance":"If the interpretation is correct, the paper provides the first systematic evidence that flat-band weak links can sustain proximity supercurrents with strength comparable to dispersive-band junctions, and that interactions can decouple the critical current from the normal-state conductance. The dataset is substantial: three magic-angle devices, three larger-twist TBG controls, one graphene control, magnetic interference patterns, and temperature and field dependence. The continuum-model correlator calculations offer a useful framework for separating dispersion, quantum-geometric, and multiband contributions. However, the central explanatory claim rests on an assumption about the spatial structure of the normal-state conductance that the paper itself shows to be violated, and the quantitative estimate of I_c^int is fitted rather than predicted. The empirical observations are solid and deserve publication; the interpretation needs to be strengthened or reframed.","major_comments":[{"comment":"The claim that the violation of the Ic-GN scaling in the flat-band domes signals an interaction-induced excess critical current assumes that the two-terminal conductance GN is the correct non-interacting baseline. Supplementary L shows, however, that in the very same filling range (e.g., the ν = -2 to -3.5 dome of D2, Fig. S26) the supercurrent is strongly edge-dominated, with the left edge carrying up to three times the bulk supercurrent (Fig. S26d). Because GN is measured across all parallel channels while the supercurrent flows primarily through edge channels, a non-interacting junction with spatially varying channel transparency or filling-dependent edge conductance could produce the observed decoupling between Ic and GN. The manuscript does not provide a spatially resolved GN profile nor a model of how a non-interacting inhomogeneous junction would scale Ic with a properly weighted conductance. This alternative should be ruled out or incorporated before the interaction interpretation is presented as the conclusion.","section":"Section II.B and Supplementary L (Figs. S25-S26)"},{"comment":"The quantitative support for I_c^int is not independent. The Ginzburg-Landau formula is taken from the self-cited preprint arXiv:2410.23121, and the parameters U ~ 10 micro-eV and xi_q = 40 nm are chosen to reproduce the measured Ic ~ 50 nA; the paper itself labels this an order-of-magnitude check. As such, the calculation cannot be adduced as evidence for the interaction origin of the excess current. The authors should either derive I_c^int from a microscopic model of TBG with realistic parameters or provide a distinct experimental signature that discriminates the interaction mechanism from the inhomogeneous-baseline alternative.","section":"Supplementary E"},{"comment":"The comparison between the computed pair correlator phi_R and the measured critical current is heuristic: the paper assumes a monotonic relation between phi_R and Ic without deriving the current from the correlator. As the authors note in Supplementary F, the correlator is a response function, not the supercurrent. The qualitative agreement with dome positions is suggestive, but the calculation should be framed as a qualitative indicator rather than as a test of the quantum-geometric and multiband mechanisms, or it should be extended to compute Ic directly.","section":"Section II.C and Supplementary F"}],"minor_comments":[{"comment":"The displayed equation for I_c^int is garbled by missing division bars; it should read I_c^int = (8e/ℏ)(W L_ξ/A_m)(Δ_S^2/U)(1 - U/(4 k_B T)) exp(-L/L_ξ).","section":"Supplementary E"},{"comment":"The phrase 'the first detailed study of the SC proximity effect in the flat-band limit' should be qualified with respect to the gate-defined TBG Josephson junctions in Refs. [28,29], whose geometry differs but which also probe proximity in flat bands.","section":"Abstract"},{"comment":"The error bars on the diode efficiency are shown but their derivation is not described; Supplementary K discusses extraction but not the error estimate.","section":"Fig. 5d-e"},{"comment":"In the sentence 'this is seen in Fig. 1f, were we measure the differential resistance', 'were' should be 'where'.","section":"Section II.A"}],"recommendation":"major_revision","confidential_remarks":"The empirical core of the paper is strong and appropriate for the journal. The main concern is that the interpretation hinges on two self-cited theory papers (arXiv:2404.09211 and arXiv:2410.23121) that are not yet peer-reviewed, and the fit of U and xi_q to the data reduces the evidential weight. Given the overlapping authorship, the authors should be encouraged to temper the causal claim or to provide stronger independent support. The edge-transport finding in Supplementary L is sufficiently important that it should be integrated into the main-text discussion of the Ic-GN scaling rather than appearing only in the context of the diode effect."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This is a careful transport study of NbTiN/TBG/NbTiN Josephson junctions, twist-tuned from dispersive (66 meV bandwidth) to flat-band (<10 meV) limits. The headline empirical result—flat-band proximity effect survives with Ic only a factor of five below the dispersive value, and Ic fails to scale with GN—is well supported and is the first systematic look at this crossover. The paper also does a lot of things right: three magic-angle-adjacent devices plus off-magic TBG and monolayer graphene controls, Fraunhofer patterns with the expected periodicity, and a Josephson diode effect with proper symmetry checks (Ic+(B) = |Ic-(-B)|). The control devices showing conventional Ic-GN correlation strengthen the claim that the flat-band behavior is special.\n\nThe soft spot is the interpretation. The authors attribute the anomalous scaling to an interaction-induced excess critical current Ic_int, using a Ginzburg-Landau estimate from a self-cited preprint with parameters (U ~ 10 ueV, xi_q ~ 40 nm) chosen to match the data. That would be fine as an order-of-magnitude check, but their own Dynes-Fulton analysis (Supp. L) shows that in the domes where the anomaly appears, the supercurrent is strongly edge-dominated. The measured two-terminal GN is the total across all channels; if the edge channels carrying the supercurrent have different transparency or filling dependence than the bulk, Ic and GN can decouple without any interaction effect. The paper does not provide a spatially resolved conductance or model an inhomogeneous non-interacting junction, so the interaction claim is not uniquely established. This is a genuine gap, not a manufactured one.\n\nMinor points: the computed pair correlator phi_R is assumed to be monotonically related to Ic, which is plausible but untested. The JDE symmetry-breaking discussion (sublattice polarization) is appropriately speculative.\n\nOverall: the empirical core is solid and deserves publication; the explanation should be treated as conditional. I would send this to peer review and ask the authors to address the edge-baseline alternative, either by modeling inhomogeneous GN or by additional measurements. I'd cite it for the experimental findings.","headline":"Careful experiment with a real anomaly in Ic-GN scaling, but the interaction-driven explanation is underdetermined because the supercurrent is edge-dominated in the relevant domes.","tokens_in":31410,"tokens_out":2573,"would_cite":true,"duration_ms":25817,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["74.50.+r","74.45.+c","73.22.Pr"],"model":"deepseek-v4-flash","headline":"Even in twisted bilayer graphene's flattest bands, the superconducting proximity effect remains strong and the critical current decouples from normal-state conductance.","keywords":["twisted bilayer graphene","flat-band superconductivity","Josephson junction","proximity effect","critical current","quantum geometry","Josephson diode effect","moiré materials"],"falsifier":"Make a junction whose supercurrent path and conductance probe coincide, for instance a narrow gate-defined channel with wide superconducting contacts, and compare $I_c$ and $G_N$ across the flat-band dome: if the decoupling disappears, the interaction-induced excess current is not the explanation, while if it persists, the claim survives.","tokens_in":30198,"feed_emoji":"⚡","tokens_out":14436,"duration_ms":140564,"temperature":0.7,"pith_summary":"Twisted bilayer graphene is two graphene layers stacked at a small twist angle, creating moiré bands that can be made nearly flat, with a width below 10 meV. This paper asks whether those flat bands can still carry a supercurrent when placed between two superconducting electrodes, and it argues that they can: critical currents in the flattest devices are only about a factor of five below those in the dispersive bands, and the $I_c R_N$ product reaches comparable values. It also claims that inside the flat bands the critical current $I_c$ stops following the normal-state conductance $G_N$, which is what would be expected if an interaction-induced excess supercurrent, independent of $G_N$, contributes alongside the usual transport term. If correct, this would mean flat-band weak links are not inherently dead for proximity superconductivity, and that quantum geometry and multiband pairing help determine where superconducting domes form.","feed_headline":"Supercurrent stays strong in graphene's flattest bands","feed_subtitle":"Critical current stops tracking normal conductance in flat-band junctions, signaling an interaction-driven excess current.","key_machinery":"The load-bearing object is the contact-induced pair correlator $\\phi_{\\mathbf R}=\\int_{\\mathrm{u.c.}} da\\,\\langle c_{\\downarrow,-}(\\mathbf R+a)\\cdot c_{\\uparrow,+}(\\mathbf R+a)\\rangle$, a response function of the twisted bilayer graphene bands to the pairing field imposed by the superconducting lead. Computed in a two-band continuum model of twisted bilayer graphene, it splits into a kinetic factor $\\phi^{\\mathrm{disp}}$ that encodes band dispersion and a Bloch-overlap factor $\\phi^{\\mathrm{QG}}$ determined by the quantum metric, so the calculation can isolate single-band atomic, single-band geometric, multiband, and interband contributions. For the interaction-induced current, a free-energy expansion around an exact flat band yields $I_c^{\\mathrm{int}}\\propto \\Delta_S^2/U\\, e^{-L/L_Q}$ with the coherence length set by the averaged minimal quantum metric $\\xi_Q$, and no dependence on the normal-state conductance; this is the mechanism the paper invokes to explain the $I_c$-$G_N$ decoupling. An inversion of the measured interference patterns is used to show that the supercurrent is edge-concentrated in the diode regions.","core_discovery":"On the paper's own terms, the central discovery is that the superconducting proximity effect remains strong in the flat-band limit of twisted bilayer graphene: even for a junction with bandwidth $w<10$ meV the measured critical current reaches $I_c\\sim65$ nA, compared with $\\sim350$ nA in the dispersive bands, and $I_c R_N$ is comparable at specific fillings. The accompanying anomaly is that $I_c$ and $G_N$ decouple inside the flat bands: as doping moves away from the charge-neutrality point, $G_N$ keeps rising while $I_c$ peaks and falls, and in the domes between $\\nu=\\pm2$ and $\\nu=\\pm4$ the current is larger than the small normal conductance would suggest. The paper attributes this excess to strong electron interactions, which produce a critical-current contribution $I_c^{\\mathrm{int}}$ that scales with the attractive interaction and not with $G_N$, and it shows that a free-energy estimate gives the observed tens of nanoamperes. Interference patterns at the domes also show a Josephson diode effect, with $I_c^+(B)\\neq|I_c^-(B)|$ and $I_c^+(B)=|I_c^-(-B)|$, which the paper reads as spontaneous breaking of $C_{2z}$ and spinless time-reversal symmetry, consistent with a sublattice-polarized state.","pith_inferences":["If the decoupling mechanism is generic, the same $I_c$-$G_N$ breaking should appear in other flat-band weak links, such as small-angle twisted trilayer graphene or kagome metals, whenever an interaction-induced term dominates.","Because the diode appears only in the flat-band domes and the supercurrent there is edge-concentrated, a natural experiment is to vary edge termination or width: if the diode efficiency tracks the edge-to-bulk ratio, the edge channel plays a causal role, whereas if it tracks filling only, the bulk correlated state is responsible.","The pair-correlator calculation suggests that the dome positions shift toward the band edges as the bandwidth decreases; mining the existing dataset of intrinsic twisted bilayer graphene superconductors for the same trend would test whether proximity domes and intrinsic domes share a geometric origin.","A quantitative theory that includes interactions ought to reproduce both the dome shape and the integer-filling suppression; if it does, the same formalism may connect the diode's symmetry-broken state to the ground states identified in other twisted bilayer graphene experiments."],"forward_implications":["If the flat-band proximity effect is as strong as reported, flat-band Josephson junctions can serve as superconducting elements even where the Fermi velocity is essentially zero.","The collapse of the $I_c\\propto G_N$ rule in flat bands means future estimates of critical currents in moiré superconductors cannot be based on normal-state conductance alone.","The quantum-geometric and multiband contributions that reproduce dome-shaped $I_c$ regions suggest why intrinsic superconducting domes in twisted bilayer graphene appear between half-filling and the band edges.","The programmable Josephson diode, switchable by reversing the magnetic field, makes the observed flat-band domes a candidate platform for superconducting diode devices.","The correlation between the diode efficiency and the $I_c$ dome implies that the symmetry-broken phase and the enhanced supercurrent share the same filling range, which a complete theory of interactions in twisted bilayer graphene will need to explain."],"supporting_citations":[{"why":"It supplies the theoretical prediction that the quantum metric contributes to the critical current of flat-band Josephson junctions, framing the geometry term.","marker":"[12]"},{"why":"It provides the theory of flat-band junctions in which an interaction-induced critical current independent of $G_N$ appears, including the order-of-magnitude estimate used here.","marker":"[13]"},{"why":"It establishes the geometric origin of superfluidity in flat-band lattices, the basis for invoking quantum geometry in the proximity effect.","marker":"[10]"},{"why":"It reports experimental evidence for flat-band superconductivity enabled by quantum geometry in moiré graphene, giving context for the geometric enhancement.","marker":"[16]"},{"why":"It provides the continuum model used for all band-structure, bandwidth, and pair-correlator calculations.","marker":"[34]"},{"why":"It demonstrated unconventional superconductivity in magic-angle graphene and set the filling range for the intrinsic domes compared with the proximity domes.","marker":"[17]"},{"why":"It mapped the correlated insulator, superconducting, and orbital-magnet phases of magic-angle bilayer graphene, providing the phase-diagram context around fillings $\\nu=\\pm2$ to $\\pm4$.","marker":"[18]"},{"why":"It reported symmetry-broken Josephson junctions and superconducting diodes in magic-angle twisted bilayer graphene, the direct comparison for the diode effect seen here.","marker":"[30]"},{"why":"It shows the conventional $I_c$-$G_N$ scaling in monolayer graphene Josephson junctions, serving as the control for the decoupling claim.","marker":"[32]"},{"why":"It derives an anomalous coherence length in superconductors with a quantum metric, used for the length scale entering the interaction-induced current.","marker":"[33]"}],"fun_headline_variants":["Flat-band graphene junctions keep supercurrent strong","Supercurrent persists in graphene's flat bands","Critical current decouples from conductance in flat bands","Interaction-driven excess supercurrent in flat-band graphene","Flat bands don't suppress supercurrent in graphene junctions"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument assumes that the measured two-terminal normal-state conductance $G_N$ is the correct baseline for the noninteracting supercurrent, so that the observed mismatch with $I_c$ can be attributed to an interaction-driven excess current rather than to the actual edge-dominated supercurrent path having a different conductance than the bulk value.","fun_headline_variants_meta":{"raw":{"variants":["Flat-band graphene junctions keep supercurrent strong","Supercurrent persists in graphene's flat bands","Critical current decouples from conductance in flat bands","Interaction-driven excess supercurrent in flat-band graphene","Flat bands don't suppress supercurrent in graphene junctions"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001057,"raw_usage":{"total_tokens":4496,"prompt_tokens":1065,"completion_tokens":3431,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":681,"completion_tokens_details":{"reasoning_tokens":3360}},"tokens_in":681,"tokens_out":3431,"duration_ms":28662,"temperature":1.0,"reasoning_tokens":3360,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T21:27:59.622008+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Make a junction whose supercurrent path and conductance probe coincide, for instance a narrow gate-defined channel with wide superconducting contacts, and compare $I_c$ and $G_N$ across the flat-band dome: if the decoupling disappears, the interaction-induced excess current is not the explanation, while if it persists, the claim survives.","supporting_citations":[{"cited_title":"Julku, S","cited_arxiv_id":null,"evidence_quote":"It establishes the geometric origin of superfluidity in flat-band lattices, the basis for invoking quantum geometry in the proximity effect."},{"cited_title":"Tian et al., Evidence for Dirac flat band superconductivity enabled by quantum geometry, Nature 614, 440 (2023)","cited_arxiv_id":null,"evidence_quote":"It reports experimental evidence for flat-band superconductivity enabled by quantum geometry in moiré graphene, giving context for the geometric enhancement."},{"cited_title":"Bistritzer and A","cited_arxiv_id":null,"evidence_quote":"It provides the continuum model used for all band-structure, bandwidth, and pair-correlator calculations."},{"cited_title":"Lu et al., Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene, Nature 574, 653 (2019)","cited_arxiv_id":null,"evidence_quote":"It mapped the correlated insulator, superconducting, and orbital-magnet phases of magic-angle bilayer graphene, providing the phase-diagram context around fillings $\\nu=\\pm2$ to $\\pm4$."},{"cited_title":"Díez-Mérida et al., Symmetry-broken Josephson junctions and superconducting diodes in magic-angle twisted bilayer graphene, Nat","cited_arxiv_id":null,"evidence_quote":"It reported symmetry-broken Josephson junctions and superconducting diodes in magic-angle twisted bilayer graphene, the direct comparison for the diode effect seen here."}],"review_version":1}