{"id":"8c51fe28-7c12-4fe3-846b-f584cd191d44","arxiv_id":"2510.04700","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Repulsive interactions turn a half-filled Rashba-coupled Landau level proximitized by an s-wave superconductor into a topological superconductor.","lead":"Electrons confined to a Landau level and glued to an ordinary superconductor normally never form a topological superconductor. This paper shows, by exact numerical simulation, that adding repulsive electron-electron interactions flips the system into a topological superconducting state.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central claim overreaches: topological superconductivity is inferred from the unproven extension of Eq. (5) (parity–Chern correspondence) to the interacting ground state.","rationale":"The reader's weakest-assumption analysis correctly identifies the parity-Chern correspondence (Eq. 5) as the load-bearing inference rule. The paper is honest about the gap ('rigorous proof... lacking'), but the abstract and central claim state topological superconductivity as a result, not as a conjecture. The ED evidence for the odd-parity gapped phase is strong: fourfold degeneracy, robust parity, interaction-driven expansion of the phase, and p-wave winding are all observed. However, these are consistent with but do not prove a nonzero Chern number. The proposed entanglement-spectrum test would resolve the issue using the interacting ground state wavefunction, independent of the noninteracting theorem. Since the observed phase itself is likely real regardless of the topological label, the reader's CONDITIONAL verdict is appropriate; the central claim should be softened or the missing proof/invariant supplied. No ad hominem intended; the concern is purely about the logical step from numerical signatures to topology.","tokens_in":122246,"tokens_out":5638,"duration_ms":58111,"concrete_test":"Compute the bipartite entanglement spectrum of the fourfold-degenerate ground states (e.g., at Δ0/VC = 0.1, Nφ = 4×4) from the exact diagonalization. A chiral topological superconductor with half-integer c exhibits a low-lying entanglement branch whose counting matches the chiral Majorana edge theory (1,1,2,3,5,...), with the topological entanglement entropy consistent with c = 1/2. A trivial odd-parity superconductor would show no chiral branch and a flat, non-universal spectrum. This directly tests whether P = -1 implies the claimed topological property without relying on the noninteracting Eq. (5).","verdict_should_be":"UNCHANGED","load_bearing_attack":"The topological classification of the RID-TSC phase rests on the fermion parity P=-1 via Eq. (5), P=(-1)^N, proven only for noninteracting BdG Hamiltonians. The authors explicitly state that a rigorous extension to H̃_hybrid is lacking ('we expect ... half-odd integer c'). If that extension fails, the fourfold-degenerate odd-parity ground state could be a topologically trivial odd-parity superconductor. The boundary argument in the topology section would then not apply, and the central claim—that repulsive interactions produce TSC—would be unsupported. The momentum argument (Feature (ii), K away from inversion-invariant momenta) shows only that the state is not adiabatically connected to any BdG mean-field state of the form (4); it does not compute an interacting topological invariant. The numerical observables (degeneracy, parity, p-wave pair-amplitude winding) are solid evidence for an odd-parity gapped phase with chiral pairing correlations, but without the unproven parity-Chern correspondence they do not uniquely select a nonzero Chern number.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies a model of spinful electrons in a Rashba-coupled Landau level with a screened repulsive Coulomb interaction, proximitized by a type-II s-wave superconductor with a square Abrikosov vortex lattice. The lowest Rashba-split Landau level is projected and treated by full-Fock-space exact diagonalization on a torus. At half filling the authors find a quantum phase transition, as Δ0/VC is increased, from a composite Fermi liquid (even parity, twofold degenerate) to a fourfold-degenerate gapped state with odd fermion parity, total momenta K=(π/2,π/2) and (π/2,3π/2), and p±ip pair-amplitude winding. They interpret this as repulsive-interaction-driven topological superconductivity (RID-TSC), argue that it is not adiabatically connected to any BdG mean-field state, and propose that it can be viewed as proximity coupling a composite Fermi liquid to an s-wave superconductor.","tokens_in":122341,"tokens_out":4782,"duration_ms":41518,"significance":"The strength of the paper is its unbiased numerical approach: exact diagonalization in the full Fock space with all particle-number sectors, a phase diagram as a function of VC/Δ0 and μ, finite-size scaling with an extrapolated finite gap, and direct computation of pair amplitudes. There are no fitted parameters in the ED. If the topological interpretation is correct, the paper would establish a conceptually new route to topological superconductivity—repulsive interactions, not attraction, drive the phase—and would connect the half-filled Landau level problem to recent proposals for chiral superconductivity from fractional Chern insulators. The main weakness is that the topological label rests on an explicitly unproven extension of the Read-Green parity-Chern theorem to an interacting Hamiltonian; the numerical evidence is strong for an odd-parity gapped chiral paired phase, but weaker for the specific claim of nonzero Chern number and topological order.","major_comments":[{"comment":"The central topological claim hinges on the relation P=(-1)^N, Eq. (5), which is proved for noninteracting BdG Hamiltonians. The manuscript explicitly states: 'Although a rigorous proof of this extension to our interacting system is lacking, we expect that the RID-TSC phase is characterized by half-odd integer c.' This is load-bearing: without Eq. (5), the observed P=-1 fourfold-degenerate gapped state could be a topologically trivial odd-parity superconductor, and the boundary argument does not exclude that possibility, because fermion parity is not a topological invariant in an interacting system. I ask for either (i) a proof of Eq. (5) for H̃_hybrid, or (ii) a direct many-body topological invariant: many-body Chern number of the ground-state manifold, modular matrices, or edge/entanglement spectrum. Until then, the abstract and conclusion should say 'evidence for' rather than 'demonst","section":"Topological superconductivity section, after Eq. (5)"},{"comment":"The argument that K=(π/2,π/2) and (π/2,3π/2) lie away from inversion-invariant momenta, and hence cannot be adiabatically connected to any mean-field BdG state of Eq. (4), establishes that the phase is interaction-driven, not that it is topological. A trivial odd-parity superconductor in an interacting model could equally have non-IIM total momentum. Thus Features (i)-(iii) plus the momentum argument identify an odd-parity gapped phase with chiral pairing correlations, but the nonzero Chern number and topological order are an additional inference that requires independent support.","section":"Topological superconductivity section, Feature (ii)"},{"comment":"The winding of the p-wave pair amplitude F_{σ1σ2}(R,r̄) in real space is a correlation function, not a topological order parameter. The mapping to momentum-space winding in SM S6 is formulated for a noninteracting BdG structure; for the interacting ED ground state, a winding of the pair field around the origin does not by itself imply a nonzero Chern number—it could arise from vortex structure or phase texture. This is good supporting evidence for chiral p±ip pairing correlations, but it should not be presented as a direct proof of topological superconductivity.","section":"Fig. 5 and pair-amplitude analysis"}],"minor_comments":[{"comment":"The horizontal axis is labelled '1/Ne' while the text says 1/N_phi. Use a single notation consistently.","section":"Fig. 3(b)"},{"comment":"The caption states that the composite Fermi liquid appears at 'VC/Δc ≈ 50'; this should likely be 'VC/Δ0 ≈ 50'.","section":"Fig. 4 caption"},{"comment":"Given the unproven extension of Eq. (5), the phrase 'demonstrate topological superconductivity' is too strong. Consider 'provide numerical evidence for' or 'establish a phase consistent with' topological superconductivity.","section":"Abstract and title"},{"comment":"Define R and r̄ explicitly in the main text (center-of-mass and relative coordinates) and state their ranges; the caption of Fig. 5 is the only place where this is indicated.","section":"Pair amplitude definition, Eq. (6)"}],"recommendation":"major_revision","confidential_remarks":"The authors are transparent about the missing proof of the parity-Chern extension. My recommendation of major_revision reflects that the central claim can be salvaged either by adding a direct many-body topological invariant or by softening the language to 'evidence for topological superconductivity'. I would not reject the paper: the ED phase identification and the repulsive-interaction-driven mechanism are well supported within the model; it is the topological label that outruns the rigorous evidence."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. First, the central numerical finding—repulsive interactions turn a previously negative no-TSC proximity model into a gapped, fourfold-degenerate, odd-parity phase—is credibly established within the model. The ED is careful, the finite-size behavior is consistent, and the noninteracting limit reproduces the known negative result. Second, the paper's headline claim \"topological superconductivity\" is stronger than the evidence: the parity-Chern correspondence used to convert P=-1 into a nonzero Chern number is proven only for noninteracting BdG systems, and the authors concede the interacting extension is not proved.\n\nWhat is actually new: interactions reverse the no-TSC conclusion of Mishmash et al. and Chaudhary-MacDonald. That is a genuine conceptual step and will interest the FQH-proximity community. The phase diagram, level crossing, parity structure, and p-wave pair-amplitude winding are all compatible with an interaction-driven topological superconductor, and the screening rationale in footnote 71 is sensible. The paper is honest about its main gap—it explicitly says \"we expect\" for half-odd c—and it does not claim to have computed an interacting topological invariant.\n\nSoft spots, in proportion. The load-bearing inference is unproven. Equation (5) is a noninteracting BdG result; an interacting state with the same fermion parity could in principle be a topologically trivial odd-parity superconductor. The momentum argument shows the state is not adiabatically connected to any BdG mean-field ground state of the form in Eq. (4), but that is a statement about what the state is not, not a computation of what it is. The real-space p-wave winding is suggestive, not a bulk topological invariant. On the numerical side, four system sizes up to N_phi=32 is modest but normal for ED. The g_R to infinity simplification in the interaction matrix elements and the screening length set to l_B are stated modeling choices; they are not hidden, though they limit how literally one can take the parameter ranges. None of these makes the phase unlikely; together they make \"demonstrate topological superconductivity\" too strong.\n\nBottom line: a solid many-body calculation with a plausible but unproved topological interpretation. The abstract overclaims. This paper is for people working on hybrid FQH-superconductor systems, Majorana platforms, and composite-fermion pairing. It deserves a serious referee—not a desk reject. The right revision will either soften the claim to \"odd-parity phase consistent with TSC\" or add a direct many-body Chern number or entanglement signature. I would bring it to a reading group and would cite it if I worked in this area.","headline":"Careful exact diagonalization finds a credible interaction-stabilized odd-parity phase at half-filled Landau level, but the topological label rests on an unproven extension of the Read-Green parity argument; it still deserves a serious referee.","tokens_in":123043,"tokens_out":2048,"would_cite":true,"duration_ms":21508,"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":"At half filling, a repulsive interaction turns a proximitized Landau level into a topological superconductor, with fourfold-degenerate odd-parity ground states and p±ip pairing.","keywords":["topological superconductivity","repulsive interaction","Landau level","Rashba spin-orbit coupling","s-wave proximity effect","composite Fermi liquid","exact diagonalization","p±ip pairing"],"falsifier":"Thread a flux quantum through the torus for the RID-TSC ground state and compute the many-body Chern number by exact diagonalization; a zero invariant while the parity remains odd would falsify the topological claim despite the observed ground-state structure. A transport falsifier is thermal Hall conductance: the paper's half-odd-integer chiral central charge prediction would show up as a half-odd-integer quantized value, absent for a trivial odd-parity superconductor.","tokens_in":121962,"feed_emoji":"🧲","tokens_out":6660,"duration_ms":115697,"temperature":0.7,"pith_summary":"At half filling of the lowest Rashba-split Landau level, proximity to an ordinary s-wave superconductor does nothing topological for noninteracting electrons. This paper shows that adding a screened repulsive interaction between electrons turns the system into a gapped topological superconductor (RID-TSC) for a finite window of interaction-to-pairing ratios. The topological phase has fourfold-degenerate ground states with odd fermion parity, total momentum away from inversion-invariant points, and p±ip pairing correlations. Because the phase appears only at finite interaction strength and vanishes in the noninteracting limit, repulsion is not an obstacle to pairing here but the mechanism that creates topological superconductivity. The proposal is that a composite Fermi liquid proximity-coupled to an s-wave superconductor is the right physical picture.","feed_headline":"Repulsion alone creates topological superconductivity at half filling","feed_subtitle":"Proximity-coupling a half-filled Landau level to an s-wave superconductor turns repulsion into a topological pairing engine.","key_machinery":"The engine is the projected interacting Hamiltonian H̃_hybrid = H̃_int + H̃_Δ − μN, diagonalized exactly on a torus in the full Fock space. The diagnostic is the identity P = (−1)^N, which connects fermion parity to the parity of the Bogoliubov–de Gennes Chern number; with P = −1 it asserts a nonzero Chern number and hence a topological superconductor. The momentum selection rule — ground states at non-inversion-invariant momenta — is what prevents any adiabatic connection to a mean-field BdG ground state, marking the phase as intrinsically interaction-driven.","core_discovery":"On a torus with a square Abrikosov vortex lattice and Rashba spin-orbit coupling, exact diagonalization of the projected half-filled Landau level gives a ground state for Δ0/VC ≈ 0.1 that is fourfold degenerate, has fermion parity P = −1, momentum (π/2, π/2) and (π/2, 3π/2), and is separated by a gap whose finite-size extrapolation stays finite. The same features appear for several system sizes of the form n_x × n_y = 2s × 4t. The state emerges from the critical point at VC/Δ0 = 0 and expands as the interaction grows, before giving way to the composite Fermi liquid at even larger VC. Odd parity combined with the parity–Chern relation P = (−1)^N is used to identify the phase as topological, a","pith_inferences":["Editorial: The mechanism resembles anyon superconductivity in doped fractional Chern insulators: a repulsively correlated parent state (the composite Fermi liquid) plus pairing is converted by interaction into a topological superconductor. Testing this analogy by doping fractional Chern insulators with repulsive interactions could transfer the design principle to lattice systems.","Editorial: Comparing square versus triangular vortex lattices would isolate the role of pairing nodes: the square lattice's node positions dictate which non-inversion-invariant momenta are occupied; a triangular lattice with different nodes should shift or suppress the RID-TSC window.","Editorial: Because the phase has a finite critical pairing strength, it is not a weak pairing of composite fermions; this suggests the RID-TSC is a distinct state whose topological order, if any, can be probed by ground-state degeneracy on higher-genus surfaces, beyond the fourfold degeneracy observed here.","Editorial: If the parity–Chern extension fails, the RID-TSC phase would still be a novel interaction-induced odd-parity superconductor, and the dispute would be only about its topological label, not its existence."],"forward_implications":["A finite interaction strength converts a non-topological proximitized Landau level into a gapped topological superconductor; the extrapolated gap stays finite in the thermodynamic limit, unlike the rapidly collapsing composite-Fermi-liquid gap.","At fixed pairing, the RID-TSC phase appears only for VC > 0 and expands as VC/Δ0 grows, while the noninteracting system has only the vacuum and the ν = 1 integer quantum Hall state.","The fourfold-degenerate, odd-parity ground states at K = (π/2, π/2) and (π/2, 3π/2) cannot be connected adiabatically to any mean-field BdG superconducting ground state, establishing the phase as intrinsically interaction-driven.","Odd fermion parity together with the parity–Chern relation P = (−1)^N implies that the phase is topological with nonzero Chern number and gapless edge modes; the paper expects a half-odd-integer chiral central charge.","The p-wave channel of the induced pair amplitude winds once around the origin, giving p±ip pairing correlations in real space that map to momentum-space winding."],"fun_headline_variants":["Repulsion alone drives topological superconductivity at half filling","Half-filled Landau level: repulsion becomes topological pairing engine","Surprising repulsion effect: topological superconductivity in Landau level","s-wave coupling plus repulsion yields topological superconducting state","Repulsive interaction flips Landau level into topological superconductor"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The claim that the interacting P = −1 state is topological rests on assuming that the parity–Chern-number equality P = (−1)^N, which is proven for noninteracting Bogoliubov–de Gennes states, also applies to the interacting ground state; the paper states that a rigorous proof is lacking.","fun_headline_variants_meta":{"raw":{"variants":["Repulsion alone drives topological superconductivity at half filling","Half-filled Landau level: repulsion becomes topological pairing engine","Surprising repulsion effect: topological superconductivity in Landau level","s-wave coupling plus repulsion yields topological superconducting state","Repulsive interaction flips Landau level into topological superconductor"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000153,"raw_usage":{"total_tokens":1043,"prompt_tokens":741,"completion_tokens":302,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":485,"completion_tokens_details":{"reasoning_tokens":218}},"tokens_in":485,"tokens_out":302,"duration_ms":2531,"temperature":1.0,"reasoning_tokens":218,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T11:24:11.742746+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Thread a flux quantum through the torus for the RID-TSC ground state and compute the many-body Chern number by exact diagonalization; a zero invariant while the parity remains odd would falsify the topological claim despite the observed ground-state structure. A transport falsifier is thermal Hall conductance: the paper's half-odd-integer chiral central charge prediction would show up as a half-odd-integer quantized value, absent for a trivial odd-parity superconductor.","supporting_citations":[],"review_version":1}