{"id":"e9091df1-c253-4fe2-b7b7-7f78306ef170","arxiv_id":"2507.02114","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Chiral Andreev conversion at partially transparent graphene-superconductor interfaces is robust, not valley-degenerate, and can show interference oscillations from intervalley scattering at corners.","lead":"This paper computes how electrons arriving along the quantum Hall edge of a graphene nanostructure convert into holes where graphene meets a superconductor. The result is that this conversion is remarkably robust to partial interface transparency, unlike at zero magnetic field, and is controlled by valley scattering at corners.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Rounded-corner claim ('even when rounded') is asserted, not demonstrated: all Phe simulations use sharp corners, and the intervalley-scattering amplitude at smooth corners is left unquantified.","rationale":"Reader's weakest_assumption (abrupt B drop) is a legitimate modeling idealization, and the paper flags it. I do not see a contradiction there; the main numerical results would be largely unaffected qualitatively if the field decayed over a London depth. The more load-bearing gap is the rounded-corner extension because it is part of the abstract's headline claim (ii) and is not directly simulated anywhere. The sharp-corner results themselves are well-supported: the B=0 BTK agreement, the dense/sparse stitching consistency, the recovery of Eq. (1) at full transparency, and the data DOI are real independent checks. My concern is therefore a request for an additional computation, not a challenge to the internal correctness of the sharp-corner simulations. The appropriate verdict remains CONDITIONAL: the paper should be accepted subject to the rounded-corner claim being either directly verified or explicitly softened.","tokens_in":25713,"tokens_out":13497,"duration_ms":163408,"concrete_test":"Using the same tight-binding setup as Sec. IV B (Kwant, dense stitching, tNS/t=0.3, standard parameters), replace the two sharp 60-degree corners of the trapezoid by circular arcs of radius R intruding into the graphene, with the superconductor contact following the arc for a distance comparable to the sharp-corner contact. Compute Phe(µgr) for R/a = 2, 5, 10, 20. If the rapid oscillations of Fig. 2(b) persist with amplitude within a factor of ~2 of the sharp-corner case for R/a >= 10, the rounded-corner claim is validated; if the oscillation amplitude decays toward zero as R grows, the abstract's 'even when rounded' must be qualified to small radii only.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The abstract's claim (ii) that intervalley scattering occurs at the corners 'even when rounded' is not backed by any direct simulation. Every computed Phe(µgr) curve and scattering wavefunction in the paper (Figs. 2, 10, 11, 15, S2-S5) uses sharp corners; Sec. VI D extends to rounded corners via a qualitative argument: a locally armchair interval along a smooth corner acts as an intervalley-scattering corner. The extension assumes that the associated intervalley scattering amplitude is non-negligible for realistic corner radii. For a rounded corner with radius R much larger than the lattice constant, the direction of the edge changes over a length ~sqrt(R a) near the armchair direction, and the LLL edge state may follow the boundary adiabatically, making intervalley scattering far weaker than at a sharp corner. The paper neither simulates such corners nor estimates the amplitude; footnote [79] introduces a decay length d but does not evaluate it. Since the headline phenomenon is interference of hybrid modes 'even in the absence of disorder,' and the abstract explicitly states that this occurs 'even when rounded,' the rounded-corner generalization is the most load-bearing unsupported step. The abrupt-B-drop approximation (Sec. II A) is a separate qualitative idealization, but it is acknowledged, standard in the field, and would mainly shift quantitative values rather than remove the sharp-corner interference.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies Andreev conversion in clean graphene nanostructures in the quantum Hall regime coupled to a superconductor, using tight-binding Bogoliubov–de Gennes calculations implemented with Kwant. The central object is the probability Phe that an incoming electron from the upstream quantum Hall edge exits as a hole on the downstream edge, computed for the lowest Landau level in several zigzag and non-zigzag geometries. For fully transparent interfaces the authors recover the Akhmerov–Beenakker valley rule Phe = 0 or 1 depending on the edge types connected by the interface. For partially transparent interfaces they find that intervalley scattering at sharp corners can produce substantial Andreev conversion even when the electron-hole hybridization along the interface is weak, and that when both entrance and exit corners cause intervalley scattering, the two hybrid modes interfere, giving oscillations in Phe as a function of graphene chemical potential. They argue from boundary-condition considerations that this behavior extends to edges at arbitrary angles and to rounded corners. They also compare Andreev conversion as a function of interface transparency with the zero-field Blonder–Tinkham–Klapwijk result, finding that chiral quantum Hall Andreev conversion is considerably more robust and that it depends on the graphene filling.","tokens_in":25957,"tokens_out":5562,"duration_ms":63067,"significance":"The sharp-corner results are convincing and constitute the solid core of the paper. The tight-binding calculations are checked against two independent analytic limits: the B = 0 curve agrees remarkably well with the BTK expression, and the full-transparency limit reproduces the Akhmerov–Beenakker edge-type rule. The dense- and sparse-stitching calculations in the main text and the Supplemental Material cross-validate the conclusions with respect to the microscopic interface model, and the deposited data are a useful resource. If the rounded-corner generalization is confirmed, the paper would provide a concrete mechanism for robust Andreev conversion and disorder-free interference in quantum Hall–superconductor devices, which is directly relevant to recent downstream-resistance experiments. The main gap is that the rounded-corner claim, which appears prominently in the abstract, is not directly demonstrated by the numerical simulations.","major_comments":[{"comment":"The abstract states that intervalley scattering can occur at the corners 'even when rounded,' but this claim is not supported by any direct calculation in the manuscript. Every computed Phe(µgr) curve and scattering-state image (Figs. 2, 10, 11, 15, S2–S5) uses sharp corners. Section VI D extends to rounded corners through a qualitative argument: a locally armchair interval along a smooth corner is said to act as an intervalley-scattering corner, and footnote [79] introduces a decay length d without evaluating it or relating it to the corner radius or to the magnetic length. For a rounded corner with radius R much larger than the lattice constant, the edge direction changes over a length of order sqrt(R a) near the armchair direction, and the lowest-Landau-level edge state may follow the boundary adiabatically, making the intervalley-scattering amplitude much smaller than at a sharp corner. Since the central new claim of interference of hybrid modes 'even in the absence of disorder' depends on this rounded-corner generalization, I request either direct tight-binding simulations of rounded or smooth corners as a function of R, or a quantitative estimate of the intervalley-scattering amplitude of a locally armchair segment, before this claim can be considered demonstrated.","section":"Sec. VI D"},{"comment":"The general argument for arbitrary-angle sharp corners is built on the boundary-condition result of Ref. [54] for a 'minimal boundary,' a technical requirement that is explicitly set aside in footnote [77]. The numerical examples in Sec. VI B cover only two angle pairs (75°/75° and 45°/75°), so the classification of arbitrary corners as intervalley-scattering or valley-preserving is plausible but not systematically verified, especially for short edge segments or for angles close to the armchair boundary where reduced-zone folding can mix valleys. Because the rounded-corner discussion of Sec. VI D inherits this classification, I would like a statement explaining why the minimal-boundary caveat does not alter the valley assignments used in Eq. (1) and in Sec. VI C, or additional numerical validation for angles near 25° and 35° to test the stability of the classification.","section":"Sec. VI C"}],"minor_comments":[{"comment":"There is a typo in the introduction: 'Andreev refelction' should be 'Andreev reflection'.","section":"Sec. I.B"},{"comment":"The phrase 'as in a Mach-Zender interferometer' should read 'Mach-Zehnder interferometer'.","section":"Sec. V.B"},{"comment":"The caption contains the typo 'Zigzag parallelgram'; it should be 'Zigzag parallelogram'.","section":"Fig. 12"},{"comment":"The abrupt magnetic-field drop at the graphene-superconductor interface is acknowledged as an idealization, but a brief comment on how finite field penetration or Meissner screening would quantitatively modify the e-h skipping-orbit picture would help readers assess experimental applicability.","section":"Sec. II.A"},{"comment":"The transparency T is used throughout the paper but is precisely defined only in a footnote; consider moving the definition to the main text in Sec. II or Sec. V.","section":"Footnote 56"}],"recommendation":"major_revision","confidential_remarks":"The paper is well within the scope of cond-mat.mes-hall and the sharp-corner numerical results are of good quality. The main risk to the paper's central message is the rounded-corner generalization, which is stated in the abstract but not demonstrated. I believe major revision is appropriate: the authors should either add rounded-corner simulations or significantly soften the abstract and Sec. VI D claims. No concerns about citation or novelty disclosure beyond the normal expectation to compare with the cited experimental work."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First, the thing to know: the sharp-corner physics is real and well demonstrated. The paper shows that for a partially transparent graphene-superconductor interface in the QH regime, intervalley scattering at the corners of the nanostructure produces Andreev conversion even when the electron-hole hybridization along the interface is weak. When both corners scatter, the two hybrid modes interfere and make Phe oscillate as a function of chemical potential. That is a concrete mechanism that goes beyond the Akhmerov-Beenakker rule, which only applies to fully transparent interfaces. The numerical work is careful: tight-binding BdG with Kwant, and the checks are convincing. The zero-field limit matches the BTK curve across the whole transparency range, the full-transparency limit reproduces Eq. (1), and the dense/sparse stitching agreement in the supplement shows the result is not an artifact of the lattice match. I believe the central claim for sharp zigzag corners.\n\nWhere it gets soft: the rounded-corner claim. The abstract states intervalley scattering can occur at corners 'even when rounded', but every computed curve uses sharp corners. The extension in Sec. VI D is a qualitative argument: a locally armchair interval along a smooth corner acts like a scattering center. That is plausible, but the amplitude is never estimated, and for a large-radius corner the LLL edge state might follow the boundary adiabatically and suppress intervalley scattering. The footnote defines a decay length d but doesn't evaluate it. This is a real gap in the paper as written, and the stress-test note is right to call it the most load-bearing unsupported step. It is not fatal to the sharp-corner results, but it does mean the abstract overreaches slightly.\n\nOther soft spots are minor and mostly acknowledged. The abrupt drop of B at the interface is an idealization; the authors note it is not the case in recent experiments but has been used extensively. That would shift quantitative values, not remove the effect. The paper does not ship code but does provide a data DOI, which is decent.\n\nThe citation pattern looks fine; they build on their own previous work and the relevant literature. No red flags.\n\nWho this is for: people working on hybrid QH-superconductor transport, both experiment and theory. It deserves a serious referee. My recommendation: send it to review, but the referee should ask either for a direct simulation of rounded corners or for the abstract to be softened to 'may occur even when rounded'. The sharp-corner core is solid enough that the paper should be publishable even if the rounded-corner generalization stays heuristic, as long as it is framed as such.","headline":"Sharp-corner mechanism is solid and new; the 'even when rounded' claim in the abstract is the one load-bearing step that needs either a simulation or softer wording.","tokens_in":26501,"tokens_out":2575,"would_cite":true,"duration_ms":28169,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["73.43.-f","74.45.+c","73.63.-b","81.05.ue"],"model":"deepseek-v4-flash","headline":"For a partially transparent graphene–superconductor interface in the quantum Hall regime, intervalley scattering at the corners of the interface produces substantial Andreev conversion, and two such corners make the conversion probability…","keywords":["quantum Hall effect","graphene","Andreev conversion","superconductor","intervalley scattering","lowest Landau level","nanostructure","interference"],"falsifier":"Measure the downstream conductance (or Andreev conversion probability) as a function of gate voltage in a clean zigzag trapezoid graphene–superconductor junction with interface transmission around 20–30%: the paper predicts rapid periodic oscillations in $P_{he}$ across the lowest Landau level whenever both interface corners cause intervalley scattering. Alternatively, repeat the tight-binding calculation with a finite magnetic-field penetration depth in the superconductor and check whether the two hybrid modes remain non-degenerate and the corner-induced oscillations survive; if the oscillations disappear, the central interference claim fails.","tokens_in":25492,"feed_emoji":"⚛️","tokens_out":5972,"duration_ms":63784,"temperature":0.7,"pith_summary":"This paper claims that in clean graphene–superconductor nanostructures in the quantum Hall regime, the amount of electrons converted into holes at the superconducting contact is governed by valley scattering at the corners of the interface, not only by the edge type. The authors study the lowest Landau level with a tight-binding model and show that when the interface is only partially transparent, the two electron–hole hybrid modes along the interface are no longer valley-degenerate, and sharp or even rounded corners can scatter an electron between valleys. If both ends of the interface contain such intervalley-scattering corners, the two modes interfere like a Mach–Zehnder interferometer, making the Andreev conversion probability $P_{he}(\\mu_{gr})$ oscillate as the graphene chemical potential is tuned. This matters because it overturns the simple rule that Andreev conversion in this setting is decided solely by the type of graphene edge, and because the effect survives realistic partial transparency.","feed_headline":"Corner scattering drives Andreev conversion in quantum Hall graphene","feed_subtitle":"A partially transparent contact keeps electron-hole conversion strong and gate-tunable, unlike the zero-field case.","key_machinery":"The carriers of the argument are the two chiral electron–hole hybrid modes that live along the graphene–superconductor interface within the superconducting gap, together with the corners of the nanostructure. Near each valley ($K$ and $K'$) the interface supports one propagating hybrid mode; at partial transparency these modes are not degenerate, so they accumulate a phase difference as they propagate along the interface. A corner is intervalley-scattering when the graphene edge changes its effective zigzag type across the corner (for example, a 60-degree turn), forcing the edge state to switch valleys. Such a corner acts as a beam splitter when placed at the entrance or exit of the interface, and the interplay of the two modes along the interface forms an interferometer: scattering at one corner populates both modes and scattering at the other recombines them, producing oscillations in the Andreev conversion probability.","core_discovery":"The central discovery is that partial transparency of the graphene–superconductor interface changes the physics qualitatively. At full transparency the scattering state connects smoothly to a single electron–hole hybrid mode, and Andreev conversion is either complete or absent according to the Akhmerov–Beenakker rule comparing the effective zigzag type of the incoming and outgoing edges. At partial transparency, the two hybrid interfacial modes have different valley content and different propagation phases; a corner that changes the effective zigzag sublattice (a 60-degree corner in the zigzag case) forces intervalley scattering, which both populates both modes and couples strongly to the superconductor, producing what the paper calls Andreev intervalley scattering. With one such corner the conversion probability varies monotonically; with two, the modes interfere and $P_{he}(\\mu_{gr})$ oscillates rapidly. The paper further shows that the same rule applies to rounded corners, since almost all graphene edges behave as effective zigzag edges, and that chiral Andreev conversion in the quantum Hall regime is considerably more robust to reduced transparency than the zero-field Blonder–Tinkham–Klapwijk result.","pith_inferences":["If corner-induced intervalley scattering is as strong as the paper suggests, the same geometry should also shape the supercurrent of quantum Hall Josephson junctions, where the two hybrid modes carry the pairing correlations; a corner-controlled phase shift would appear as a magneto-oscillation distinct from the usual Fraunhofer pattern.","Because the effect depends only on the effective zigzag type of the edges, atomically controlled edge fabrication could be used to permanently set a device to either convert or not convert, turning the geometric classification into a design rule.","The robustness with respect to transparency suggests that part of the Andreev signal seen in experiments on disordered interfaces could be corner-induced rather than disorder-induced, a distinction that the clean-limit calculations make testable by comparing devices with deliberately different corner geometries."],"forward_implications":["With partial transparency, the value of $P_{he}$ is no longer pinned to 0 or 1 by edge type; corner geometry and interface quality control the conversion, so the simple edge-type rule applies only to nearly fully transparent contacts.","In structures where both ends of the superconducting interface are intervalley-scattering corners, the device acts as a Mach–Zehnder interferometer: $P_{he}(\\mu_{gr})$ oscillates, and the oscillations survive rounding of the corners.","Chiral Andreev conversion in the quantum Hall regime remains substantial for interface transparencies as low as roughly 10 percent, whereas zero-field Andreev reflection falls rapidly with transparency; devices should therefore tolerate poor-quality contacts.","A straight, smoothly connected interface with no intervalley corners gives $P_{he}=0$ even at partial transparency, identifying corner design as a practical on/off switch for downstream Andreev conductance.","Clean low-disorder graphene–superconductor interfaces, such as those that graphene–transition-metal-dichalcogenide heterostructures may provide, should display these corner-controlled oscillations directly."],"supporting_citations":[{"why":"Supplies the ideal-interface rule Eq. (1): electron-to-hole conversion is 1 or 0 depending on whether the incoming and outgoing edges are of the same effective zigzag type.","marker":"[36]"},{"why":"The authors' earlier work on infinite graphene-superconductor interfaces, showing that at non-ideal interfaces the propagating hybrid modes are not valley-degenerate and lack equal electron-hole weight; this paper builds on that.","marker":"[47]"},{"why":"The Blonder-Tinkham-Klapwijk result for Andreev reflection at zero field, against which the quantum-Hall robustness is benchmarked.","marker":"[57]"},{"why":"Provides the boundary condition for Dirac fermions on arbitrary graphene edges, used to argue that almost all edges behave like effective zigzag edges and to classify corners.","marker":"[54]"},{"why":"Shows that sharp corners in semiconductor nanostructures strongly affect Andreev conversion, motivating the geometric study here.","marker":"[44]"},{"why":"Identifies mechanisms of Andreev reflection in quantum Hall graphene including disorder and intervalley processes, providing context for the clean-limit corner mechanism.","marker":"[49]"}],"fun_headline_variants":["Partial transparency changes quantum Hall Andreev conversion","Even rounded corners scatter valleys at partial transparency","Andreev conversion in QH graphene robust to partial transparency","Hybrid modes lose valley degeneracy at partial transparency","Intervalley scattering at corners drives QH Andreev conversion"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The main load-bearing approximation is that the magnetic field drops abruptly to zero inside the superconductor, with the vector potential chosen as $\\mathbf{A}(x,y)=By\\,\\hat{x}\\,\\theta(-y)$, so that a clean Landau-level description applies; the paper notes this is not the situation in recent experiments, where field penetration and Meissner screening are present.","fun_headline_variants_meta":{"raw":{"variants":["Partial transparency changes quantum Hall Andreev conversion","Even rounded corners scatter valleys at partial transparency","Andreev conversion in QH graphene robust to partial transparency","Hybrid modes lose valley degeneracy at partial transparency","Intervalley scattering at corners drives QH Andreev conversion"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000492,"raw_usage":{"total_tokens":2460,"prompt_tokens":1031,"completion_tokens":1429,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":647,"completion_tokens_details":{"reasoning_tokens":1352}},"tokens_in":647,"tokens_out":1429,"duration_ms":12516,"temperature":1.0,"reasoning_tokens":1352,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T20:36:23.727675+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the downstream conductance (or Andreev conversion probability) as a function of gate voltage in a clean zigzag trapezoid graphene–superconductor junction with interface transmission around 20–30%: the paper predicts rapid periodic oscillations in $P_{he}$ across the lowest Landau level whenever both interface corners cause intervalley scattering. Alternatively, repeat the tight-binding calculation with a finite magnetic-field penetration depth in the superconductor and check whether the two hybrid modes remain non-degenerate and the corner-induced oscillations survive; if the oscillations disappear, the central interference claim fails.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the ideal-interface rule Eq. (1): electron-to-hole conversion is 1 or 0 depending on whether the incoming and outgoing edges are of the same effective zigzag type."},{"cited_title":"Transparent Graphene-Superconductor Interfaces: Quantum Hall and Zero Field Regimes","cited_arxiv_id":"2502.13307","evidence_quote":"The authors' earlier work on infinite graphene-superconductor interfaces, showing that at non-ideal interfaces the propagating hybrid modes are not valley-degenerate and lack equal electron-hole weight; this paper builds on that."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the boundary condition for Dirac fermions on arbitrary graphene edges, used to argue that almost all edges behave like effective zigzag edges and to classify corners."},{"cited_title":"Geometrical effects on the downstream conductance in quantum-Hall--superconductor hybrid systems","cited_arxiv_id":"2210.16867","evidence_quote":"Shows that sharp corners in semiconductor nanostructures strongly affect Andreev conversion, motivating the geometric study here."},{"cited_title":"Mechanisms of Andreev reflection in quantum Hall graphene","cited_arxiv_id":"2103.06722","evidence_quote":"Identifies mechanisms of Andreev reflection in quantum Hall graphene including disorder and intervalley processes, providing context for the clean-limit corner mechanism."}],"review_version":1}