{"id":"31a643c9-abb7-4abc-b520-5b837156b4cf","arxiv_id":"2601.14364","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"Reentrant superconductivity in non-circular Corbino Josephson junctions has a period set by the number of corners, and this period is halved on topological insulator surfaces.","lead":"Non-circular Corbino Josephson junctions show superconductivity re-appearing at specific magnetic flux values, with a period set by the number of corners. In junctions made on topological insulators, that period is halved, offering a possible experimental fingerprint of topological superconductivity.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Period halving rests on a single numerical realization with no N-convergence or parameter-sweep support","rationale":"The conventional reentrant condition (nv = m nc) is proven analytically, so the novel part of the paper is the topological period halving. That claim depends entirely on the numerical observation that the tight-binding model produces nonzero critical current at half-integer multiples of nc. The paper gives no analytic derivation of the sin(2ϕ) current-phase component from the low-energy model (6), only a consistency check in the Supplemental Material. The numerical evidence is a single point in parameter space with no convergence study, so the half-integer signals might be artifacts of the lattice discretization or the ad hoc energy cutoff. The reader's weakest assumption (narrow-junction validity) is also legitimate, but it is an external applicability condition; the numerical robustness concern is more directly load-bearing for the internal correctness of the central claim. Because the paper would be strengthened by adding convergence checks and parameter sweeps, the CONDITIONAL verdict remains appropriate; our concern does not change it.","tokens_in":10509,"tokens_out":16413,"duration_ms":177546,"concrete_test":"Recompute the topological square-junction critical current in the ladder model for N=100, 200, 400, 800, 1600 (keeping t0=1, t1=0.6, t2=0.3, Δ=0.2) and for Δ=0.1 and 0.3 at N=400. If the normalized Ic at nv=2 does not converge to a nonzero value as N increases, or vanishes for some Δ, then the period halving is a finite-size/parameter artifact and the central claim fails. As a complementary check, remove the |E|<5Δ cutoff and recompute; if the nv=2 signal changes by orders of magnitude, the cutoff is driving the result.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The period-halving claim for topological Corbino junctions is the central new prediction, but it rests on a single numerical realization of the tight-binding model (N=400, t0=1, t1=0.6, t2=0.3, Δ=0.2). The Supplemental Material shows that a sin(2ϕ) component in the current-phase relation would produce the halving, yet no analytic derivation shows that Hamiltonian (6) has such a component; its existence is inferred solely from the same simulation. The half-integer reentrance signals (e.g., nv=2 for a square) are weak, below the 10^-3 cutoff relative to Ic(0), and could be finite-size or cutoff artifacts. Without a convergence study in N and parameter variation around the gapless point, the nonzero Ic at half-integer multiples is not established. This is a correctness risk internal to the model, independent of the acknowledged narrow-junction validity conditions.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies Corbino (annular) Josephson junctions formed by two superconductors separated by a normal region on the surface of a three-dimensional topological insulator (3DTI) or on a conventional metal. The authors first show analytically, using a single-harmonic phase model, that for a conventional non-circular junction reentrant superconductivity occurs only when the number of threaded flux quanta n_v is an integer multiple of the number of corners n_c [Eqs. (4)-(5)]. They then generalize to the topological case by modeling the 3DTI surface as two counter-propagating Majorana modes coupled by a phase-dependent term [Eq. (6)], regularized by a two-leg Majorana ladder [Eqs. (7)-(8)]. Using numerical diagonalization for a square geometry, they find that the topological junction has nonzero I_c for all even n_v, in contrast to the conventional case where only multiples of four contribute; this is described as a halving of the reentrance period. The Supplemental Material shows that such a period halving is consistent with a sin(2φ) contribution to the current-phase relation. The paper also mentions a Josephson diode effect when inversion symmetry is broken and discusses experimental implications.","tokens_in":10725,"tokens_out":6588,"duration_ms":67848,"significance":"If the period-halving prediction is correct, it would provide an experimentally accessible and geometry-specific signature of the helical Majorana surface modes in 3DTI-superconductor hybrid junctions. The conventional part of the paper is clean: the Fourier selection rule leading to n_v = m n_c is elegant and matches the exact-phase numerics. The paper is also honest in listing limitations. However, the central topological claim is currently supported by a single numerical realization without convergence tests or an independent analytic derivation; the SI consistency check does not prove that the sin(2φ) component exists. The significance is therefore conditional: the idea is attractive, but the evidence as presented is not yet at the level of a demonstrated 'theory'.","major_comments":[{"comment":"The central prediction of period halving rests on a single tight-binding realization with N=400 and the fixed parameters t0=1, t1=0.6, t2=0.3, Δ=0.2. No convergence in N, no sweep of Δ or t1−2t2, and no check of the cutoff dependence are provided. In the log-scale figures the half-order peaks (e.g., n_v=2 for n_c=4) appear at the 10^-3 (main text) or 5×10^-3 (SI) floor, so it is unclear whether the plotted values are resolved currents or clamped artifacts. Since the claim \"the topological junction shows I_c ≠ 0 for all even n_v\" is precisely the existence of these weak peaks, this numerical evidence is load-bearing. Please provide tabulated I_c values before the cutoff, N-convergence data (e.g., N=200, 400, 800, 1600), and parameter sweeps around the gapless point.","section":"Topological Corbino junctions"},{"comment":"The period-halving explanation assumes a nonzero I_0^{(2)} in the current-phase relation and shows that a sin(2φ) term yields the observed selection rule. However, the paper does not derive from Hamiltonian (6) why a sin(2φ) component should be present; the only evidence for it is the same numerical diagonalization. This is a consistency check, not an independent derivation. Given the title and abstract promise a theory, the mechanism for half-periodicity remains unexplained. An analytic estimate or a perturbative argument showing that the Majorana coupling generates I_0^{(2)} would substantially strengthen the claim.","section":"SI Sec. I"},{"comment":"The low-energy Hamiltonian (6) is stated to be valid in the narrow-junction limit W < ξ, but no estimate of W/ξ for the simulated geometry is given, and the ladder parameters are not mapped to continuum quantities. The redundant Majorana modes and the mixed periodic/anti-periodic boundary conditions are a specific regularization choice; the circular topological result (zero I_c for all n_v > 0) is a nontrivial consequence of this model and is not checked against a continuum solution. These omissions do not disprove the claim, but they increase the risk that the small half-order signals are lattice or boundary artifacts rather than a robust topological effect.","section":"After Eq. (6), Outlook"}],"minor_comments":[{"comment":"The caption lists n = 1, 2, 5, 20, but the panels are labeled n = 1, 2, 10, 40. Please correct the mismatch.","section":"SI Fig. S1"},{"comment":"The sentence contains a typo: \"where and J_m is the mth Bessel function\" should read \"where J_m is the mth Bessel function.\"","section":"After Eq. (5)"},{"comment":"The main text states a 10^-3 cutoff while the SI uses 5×10^-3. Clarify whether the plotted points at the floor are actual data or clamped; if clamped, state so explicitly and give the unresolved values in a table.","section":"Fig. 2, SI Fig. S3"},{"comment":"The Josephson diode effect is asserted without any numerical or analytical demonstration. If this result is part of the paper's claims, please include at least one illustrative calculation or figure; otherwise, move it to the outlook discussion.","section":"Topological Corbino junctions"}],"recommendation":"major_revision","confidential_remarks":"The conventional Corbino analysis is sound and likely publishable. The topological period-halving claim is the main selling point but is under-supported: one numerical realization, no convergence, and no analytic mechanism. I would like the authors to provide the missing numerical evidence and an independent argument before acceptance. Also note that Ref. [37] is an overlapping-author preprint used as partial support for the diode effect; the editor may want to ensure that this does not create a reporting issue."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. The reentrant-superconductivity selection rule n_v = m n_c for conventional non-circular Corbino junctions is clean and, as far as I can tell, new; the Fourier derivation in Eq. (5) is transparent and matches the exact phase integration numerically. The topological period-halving claim (n_v = (m/2) n_c for even n_c) is a concrete, falsifiable prediction, and the absence of halving for odd n_c plus the presence in square, hexagonal, and two-corner shapes is internally consistent. The paper is also honest about its limitations, including the narrow-junction Majorana description and the stated possibility of alternative mechanisms for halving.\n\nThe soft spots are in the numerical evidence for the halving. It rests on one tight-binding realization: N=400, t0=1, t1=0.6, t2=0.3, Delta=0.2. No convergence study in N, no variation around the gapless point, no code or data. The SI shows that a sin(2φ) component in the current-phase relation would produce the halving, but it does not derive that component from Hamiltonian (6); that is a gap between the continuum model and the numerics. The half-integer signals (e.g., n_v=2 for a square) are small in the log-scale plots, and the 10^-3 cutoff makes it hard to judge whether they are robust or finite-size noise. The stress-test concern that this could be a numerical artifact is fair, though the effect appearing across several geometries with the expected parity behavior counts as some evidence against a pure artifact. The narrow-junction assumption is reasonable for state-of-the-art 3DTI hybrids but is not quantitatively validated.\n\nThe conventional selection rule holds up analytically and is the strongest part of the paper. The topological prediction is worth testing but is not yet established to the same standard. The reference to the upcoming experiment [37] is opaque, so I cannot judge that consistency claim.\n\nThis paper deserves a serious referee. A revision that adds N-convergence, parameter sweeps around the gapless point, and preferably a derivation of the sin(2φ) term would put the central prediction on firmer ground. I would send it to review and ask for those additions.","headline":"A clean analytic selection rule for conventional Corbino junctions, plus a topological period-halving prediction that is promising but numerically under-supported.","tokens_in":11233,"tokens_out":4092,"would_cite":true,"duration_ms":37516,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":null,"created_at":"2026-08-03T09:14:22.534746+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":null,"supporting_citations":[],"review_version":1}