{"id":"fe4728c0-993f-4d15-9756-f6e530b3331e","arxiv_id":"2504.19844","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Fully compensated ferrimagnets can produce electric-field- and Néel-vector-tunable topological superconductivity with Majorana modes in one, two, and higher-order three-dimensional geometries, without net magnetization.","lead":"This paper proposes using fully compensated ferrimagnets, magnetic materials with zero net magnetization, to create and switch Majorana bound states in superconducting heterostructures. A smart generalist should read it because it offers a path to tunable topological quantum devices that work without external magnetic fields.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central advantage, that zero net magnetization preserves the proximity-induced pairing, rests on an uncalculated uniform-Δ0 assumption; a self-consistent pairing calculation with the fFIM's staggered exchange is needed before the phase diagrams in Figs. 2–4 can be taken as physical predictions.","rationale":"The concrete band-structure calculations in the paper are internally consistent: the exact mapping to two Kitaev chains at μ=0 is a clean parameter-free derivation, the Chern number and Wilson loop results match finite-size edge spectra, and the higher-order edge theory with mass domain walls explains the corner modes. I therefore do not object to the model mathematics. The load-bearing concern is the physical premise that zero net magnetization preserves the proximity-induced pairing. The reader's weakest assumption identifies exactly this point: Δ0 is treated as uniform and unaffected by the fFIM's staggered exchange fields, and no microscopic demonstration is provided. This is not an objection to disagreement with consensus; it is a request for a missing computation that the argument itself needs. The secondary issue about the C=0 phase in Fig. 3 being labeled 'chiral' is a nomenclature problem, not a load-bearing correctness problem, so I do not elevate it. There is no machine-checked proof or publicly shipped code, but the analytical mappings and finite-size numerics provide real internal support. Since the reader already issued a conditional verdict based on the same weakest assumption, my read does not change the verdict; the appropriate action remains CONDITIONAL acceptance pending a self-consistent pairing check.","tokens_in":10352,"tokens_out":8590,"duration_ms":98470,"concrete_test":"In a slab geometry containing the fFIM and a superconducting layer with a local pairing interaction confined to the SC layer, solve the BdG equations self-consistently for the induced order parameter Δ(r), or equivalently Δ_A and Δ_B on the two fFIM sublattices, as a function of V0, V1, J0, and Néel orientation. Then recompute the 1D winding number, the 2D Chern number, and the corner-mode spectrum using this self-consistent Δ instead of the constant Δ0 assumed in Eqs. (2), (5), and (6). If the self-consistent Δ in the topological regions of Figs. 2–4 remains comparable to the assumed Δ0 with no nodes or sign reversal, the concern is resolved; if it is strongly suppressed or becomes momentum-dependent there, the physical phase diagrams differ qualitatively from those presented.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The proposal's main selling point is that fFIMs preserve the proximity-induced s-wave pairing because they have no net magnetization. This is asserted in the abstract and introduction, not derived. All three BdG models (Eqs. (2), (5), and (6)) take Δ0 as a fixed, uniform, momentum-independent input. But the fFIM is itself described by the two-sublattice Hamiltonian H(k) with opposite local moments J0 s·n τ_z. In a real heterostructure, the induced pair amplitude is determined by the microscopic proximity coupling across the fFIM–SC interface; it is not automatically the same on the two sublattices or in the nanowire/2DEG. Staggered exchange fields are pair-breaking for conventional s-wave pairing even at zero net magnetization: a Cooper pair with one electron on each sublattice sees opposite Zeeman fields, and antiferromagnetic superconductors generically acquire suppressed or spatially modulated gaps. The claimed topological phases in Figs. 2–4 require a finite, uniform Δ0 precisely in the parameter regions where V0 and V1 generate the spin splitting. If the self-consistent induced pairing is suppressed, becomes k-dependent, or changes sign in those regions, the phase boundaries shift and the topological regimes can disappear. The statement that zero net magnetization 'not only meets the fundamental requirements ... but also enables' the platform is therefore the least secure link in the argument. The delegations to the Supplemental Material validate the effective band structure against the full fFIM Hamiltonian, but they do not address pairing self-consistency.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes using fully compensated ferrimagnets (fFIMs) as a platform for topological superconductivity in three geometries: a 1D nanowire hosting Majorana zero modes, a 2D Rashba electron gas hosting chiral Majorana edge states, and a topological-insulator sandwich hosting higher-order Majorana corner modes. The authors introduce minimal BdG models, derive effective low-energy descriptions, compute winding numbers, Chern numbers, and edge-theory masses, and corroborate with numerical spectra. The central claim is that fFIMs' zero net magnetization avoids the usual pair-breaking trade-off while allowing electric-field (V0) and Néel-vector control of the topological phases.","tokens_in":10528,"tokens_out":9125,"duration_ms":99657,"significance":"If the predictions hold, this would be an important proposal for magnetic-field-free, electrically tunable topological superconductivity. The exact reduction of the 1D model to two Kitaev chains at μ=0, the mutual consistency between Chern numbers, Wilson loops, and edge spectra in 2D, and the edge-theory explanation of corner modes are all strengths. The proposed dual control (by V0 and by Néel vector orientation) is clearly formulated and experimentally testable. The main moderating factor is that the key advantage—that zero net magnetization preserves the proximity-induced superconductivity—is asserted rather than derived; the validity of the uniform-Δ0 assumption directly affects whether the phase diagrams of Figs. 2–4 are physical predictions.","major_comments":[{"comment":"The central claim that zero net magnetization in the fFIM 'preserves superconductivity' is not demonstrated. In all three models, the proximity-induced pairing Δ0 is a fixed, uniform, momentum-independent input. The fFIM substrate is described by a two-sublattice Hamiltonian with opposite exchange fields; how this staggered exchange modifies the induced pairing in the nanowire, 2DEG, or TI surface is not analyzed. If the effective Δ0 were suppressed, k-dependent, or altered in the parameter regions where V0 and V1 generate the topological phases, the phase boundaries in Figs. 2–4 would shift and the topological regimes could disappear. Please provide a microscopic justification or at least a quantitative estimate of the pair-breaking effect of the fFIM's staggered exchange (e.g., by considering a simple proximity model), or clearly state the conditions under which the uniform-Δ0 assumption holds.","section":"Abstract and Introduction; Eqs. (2), (5), (6)"},{"comment":"The paper assumes that the fFIM's low-energy spin-splitting term (V0 + V1(coskx − cosky)) s·n translates directly into an effective exchange term in an adjacent nonmagnetic layer. This step is not derived; it is an ansatz about the interfacial coupling. The text repeatedly refers to Supplemental Material validations against the full fFIM Hamiltonian, but no representative full-model result is shown in the main text. Please include at least one quantitative comparison between the effective-model and full-model phase diagrams (e.g., the 1D winding number or 2D Chern number), or summarize the full-model results in enough detail for the reader to judge whether the effective models faithfully capture the fFIM-induced spin splitting.","section":"Effective model and 1D/2D models; Eq. (1) vs. Eqs. (2) and (5)"},{"comment":"The exact Kitaev-chain mapping is demonstrated at μ=0, and the winding-number calculation in Fig. 2(b) is said to support the finite-μ results, but the text does not specify the value of μ used in Fig. 2(b) nor show how the topological phase boundaries evolve with μ. The phrase in the text, 'Introducing a finite chemical potential induces hybridization among two MZMs at the same end, leading to an energy splitting δE, that signals the transition to a trivial phase,' suggests that the νtot=2 regime is destroyed by arbitrarily small μ; it is unclear whether any other region of the parameter space remains topological at realistic μ. Please state the parameter values used for Fig. 2(b), and provide a representative μ-dependence of the winding number or of the topological gap so the practical applicability of the 1D proposal can be assessed.","section":"Eq. (3) and Fig. 2"}],"minor_comments":[{"comment":"There appears to be a typo in the fFIM term: '(V0 + V1(coskx − cosky)) s·n γz(0)' should likely be 'γz' without the '(0)'.","section":"Eq. (6)"},{"comment":"The phrase 'magnetic fields to induced the required spin splitting' should read 'to induce the required spin splitting.'","section":"Introduction, first paragraph"},{"comment":"Abbreviations 'MEM' (Majorana edge mode) and 'MES' (Majorana edge state) are used interchangeably; please define the preferred abbreviation and use it consistently.","section":"2D TSC section"},{"comment":"The captions do not specify the values of μ and Δ0 used in the numerical spectra; for reproducibility, please list the parameter values in the captions or note that they are given in the Supplemental Material.","section":"Figure captions (Figs. 2 and 3)"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is within the scope of the journal and addresses a timely topic. The main technical concern is the unproven uniform-Δ0 assumption, which is load-bearing for the paper's central marketing claim; I would not reject on that basis, but it needs to be addressed substantially. The authors should also make the validation against the full fFIM Hamiltonian more transparent in the main text, as the current reliance on the Supplemental Material weakens the reader's ability to assess the effective models. The relationship to prior altermagnet-based proposals (Refs. [29,30,53,54]) should be clarified to position the novelty of the fFIM platform explicitly."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's my take. The paper adapts well-established Majorana platform models (Rashba nanowire, chiral p+ip, HOTSC edge theory) to fully compensated ferrimagnets, adding electric-field (V0) and Néel-vector control. That combination is new, and the internal topological calculations look consistent. The 1D model exactly reduces to two Kitaev chains at μ=0; the 2D Chern numbers agree with Wilson loops and edge spectra; the HOTSC edge theory matches the corner-localized zero modes. Credit where due: the symmetry analysis connecting fFIM spin splitting to the low-energy models is careful, and the paper is honest about what is delegated to the SM.\n\nThe main soft spot is the pairing assumption. The abstract and introduction claim that zero net magnetization 'preserves superconductivity,' but the BdG Hamiltonians all take Δ0 as a uniform, momentum-independent input. A staggered exchange field can be pair-breaking even at zero net magnetization: a Cooper pair with one electron on each sublattice sees opposite Zeeman fields. No self-consistent or microscopic proximity calculation is provided. If the induced pairing is suppressed or becomes k-dependent in the parameter regions of interest, the phase boundaries in Figs. 2–4 shift and some topological phases may not survive. This is a load-bearing assumption, not a cosmetic detail. It is addressable—compute Δ(R) or a self-consistent gap for the fFIM/SC interface—but until then the prediction is conditional.\n\nMinor issues: the label 'chiral' for the C=0 phase with two counter-propagating edge modes is sloppy; and the heavy reliance on the SM for full-model validation makes the main text hard to check. Neither is fatal.\n\nOverall: this is a well-structured proposal worth serious refereeing. The reader's CONDITIONAL verdict is about right. The paper is for people working on Majorana platforms and compensated magnets, not a general audience. It deserves peer review, with pairing self-consistency as the main requested revision.\n\nRecommendation: send it to review. It is not a desk reject—internal consistency and the new platform make it worth the referee time.","headline":"Solid transfer of standard Majorana machinery to fFIMs, but the central claim that zero net magnetization preserves superconductivity rests on an uncalculated uniform-Δ0 assumption.","tokens_in":11216,"tokens_out":2232,"would_cite":true,"duration_ms":21452,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Fully compensated ferrimagnets, with zero net magnetization, can host Majorana zero modes, chiral edge states, and tunable corner modes across one, two, and higher dimensions, all controlled by electric fields and Néel-vector orientation.","keywords":["fully compensated ferrimagnet","Majorana zero modes","topological superconductivity","chiral Majorana edge states","higher-order topological superconductors","electric-field control","Néel vector","proximity-induced pairing"],"falsifier":"Compute the proximity pairing self-consistently in the fFIM–superconductor geometry; if the staggered exchange field suppresses or spatially modulates the induced pairing amplitude, the phase boundaries shift or the zero modes vanish. Experimentally, a nanowire on an fFIM at the predicted parameters should show a $2e^2/h$ zero-bias conductance peak only inside the computed $V_0$ windows, and its absence would falsify the central claim.","tokens_in":10011,"feed_emoji":"🧲","tokens_out":10817,"duration_ms":103323,"temperature":0.7,"pith_summary":"This paper argues that heterostructures built from a fully compensated ferrimagnet (fFIM)—a magnet whose opposite sublattice moments cancel to zero net magnetization—can support topological superconductivity in one, two, and higher dimensions. Because the fFIM has no net moment, the proximity-induced superconductivity is not weakened by stray fields, while an electric field tunes the spin splitting and drives transitions between trivial and topological phases. A rotating Néel vector is claimed to control the chirality of Majorana edge states and the spatial position of Majorana corner modes. If correct, this gives a magnetic-field-free, voltage-controlled route to Majorana bound states for quantum devices.","feed_headline":"Zero-magnet ferrimagnets host tunable Majorana modes","feed_subtitle":"Electric fields switch topological phases; rotating the Néel vector steers the Majorana modes—no magnetic field.","key_machinery":"The load-bearing object is the low-energy fFIM Hamiltonian $H_{\\text{eff}}(k) = 2t_0(\\cos k_x + \\cos k_y) - \\mu + (V_0 + V_1(\\cos k_x - \\cos k_y))\\,s\\cdot\\hat{n}$, where $V_0$ is an electric-field-controllable sublattice-staggered potential that converts the Fermi-surface spin splitting from d-wave symmetry at $V_0=0$ to s-wave symmetry at finite $V_0$. Placing this spin-splitting term into three BdG Hamiltonians—a nanowire, a Rashba electron gas, and a topological-insulator sandwich—each model admits a conserved quantity $s_x\\gamma_x$ that block-diagonalizes it. Each block maps onto a Kitaev chain or a chiral $p\\pm ip$ superconductor, so standard invariants (BDI winding number, class-D Chern number, and the Dirac masses of the edge theory) locate the Majorana modes and the phase boundaries where they appear.","core_discovery":"The paper claims that an fFIM-based heterostructure is a tunable topological superconductor in three distinct geometries. In the 1D nanowire, the BdG Hamiltonian decomposes at $\\mu = 0$ into two Kitaev chains, giving a $\\mathbb{Z}_2$ invariant $\\nu_{\\text{tot}} = \\nu_+ + \\nu_-$ and regions with two or four zero-energy Majorana end modes; the phase is controlled by gate voltage $V_0$ and by the Néel-vector orientation. In the 2D fFIM–Rashba–superconductor stack, the Chern number takes values $C\\in\\{-2,-1,0,1,2\\}$; nonzero Chern numbers give chiral Majorana edge modes, while in a zero-Chern region two counter-propagating chiral modes survive because the two conserved sectors carry opposite Chern numbers $C_+ = -C_-$. In the topological-insulator sandwich, edge theory gives Dirac masses whose sign changes across adjacent edges bind Majorana corner modes, and rotating the Néel vector by 90 degrees moves those corner modes between edges. The unifying claim is that zero net magnetization preserves the superconducting pairing while the sublattice-staggered potential $V_0$ provides all-electric control of the topological phase.","pith_inferences":["A self-consistent calculation of the proximity pairing, letting the superconducting order parameter respond to the opposite sublattice exchange fields, would reveal how robust the predicted phases are to realistic pair-breaking; this is a natural next step beyond the paper's fixed-$\\Delta_0$ models.","The $V_0$ mechanism should transfer to fFIMs with other crystal potentials, such as g-wave and i-wave, though the phase diagrams for those cases are not derived in this paper.","The zero-Chern two-dimensional region, with counter-propagating chiral modes, offers a natural setting for phase-biased Josephson interferometry that probes non-Abelian statistics without requiring a net Chern number."],"forward_implications":["A one-dimensional nanowire on an fFIM substrate should exhibit zero-energy Majorana end modes that can be switched on and off by a gate voltage, with the topological phase boundary given by the predicted $V_0$–$V_1$ diagram.","A two-dimensional fFIM–Rashba–superconductor stack should show chiral Majorana edge modes whose direction reverses when the Néel vector develops an out-of-plane component or when $V_0$ crosses a Chern-number boundary.","In the topological-insulator sandwich, Majorana corner modes should appear at corners where the edge Dirac mass changes sign, and rotating the Néel vector by 90 degrees should move them between distinct corners.","Because the fFIM has zero net magnetization, the superconducting proximity effect is not weakened by stray fields, so the platform avoids the usual trade-off between magnetic tunability and superconducting coherence."],"supporting_citations":[{"why":"Supplies the fFIM lattice Hamiltonian with d-wave crystal potential and establishes the electric-field-tunable spin splitting that all effective models inherit.","marker":"[35]"},{"why":"Contains the dimensional reduction, invariant derivations, and full-Hamiltonian checks that validate the 1D, 2D, and higher-order models.","marker":"[44]"},{"why":"Provides the Kitaev-chain mapping and Pfaffian formula used to identify the 1D Majorana zero modes and phase boundaries.","marker":"[52]"},{"why":"Defines the winding-number invariant for BDI-class spin-orbit coupled nanowires used for the 1D phase diagram.","marker":"[12]"},{"why":"Supplies the symmetry classification and Chern-number framework for class-D superconductors used for the 2D chiral edge states.","marker":"[51]"},{"why":"Gives the earlier altermagnet heterostructure edge theory whose Dirac-mass domain-wall mechanism is adapted to produce Majorana corner modes.","marker":"[53]"},{"why":"Establishes creation and manipulation of higher-order topological states by Néel-vector orientation, the control principle used for the corner modes.","marker":"[54]"},{"why":"Shows Majorana routes in zero-net-magnetization altermagnets, the compensated-magnet context the fFIM proposal extends.","marker":"[30]"}],"fun_headline_variants":["Zero-magnet ferrimagnets host electrically tunable Majorana modes","Neel-vector rotation and electric field steer Majorana modes","No magnetic field needed for ferrimagnet Majorana control","Ferrimagnet with zero net magnetization yields Majorana modes in 1D, 2D, 3D","Electric field tunes Majorana modes without magnetic field"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument assumes that the proximity-induced superconducting pairing has a uniform amplitude $\\Delta_0$ that is unaffected by the opposite exchange fields on the two fFIM sublattices; if those local exchange fields suppress or distort the pairing, the predicted topological phases could disappear.","fun_headline_variants_meta":{"raw":{"variants":["Zero-magnet ferrimagnets host electrically tunable Majorana modes","Neel-vector rotation and electric field steer Majorana modes","No magnetic field needed for ferrimagnet Majorana control","Ferrimagnet with zero net magnetization yields Majorana modes in 1D, 2D, 3D","Electric field tunes Majorana modes without magnetic field"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001688,"raw_usage":{"total_tokens":6707,"prompt_tokens":982,"completion_tokens":5725,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":598,"completion_tokens_details":{"reasoning_tokens":5630}},"tokens_in":598,"tokens_out":5725,"duration_ms":43819,"temperature":1.0,"reasoning_tokens":5630,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T05:42:30.136255+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the proximity pairing self-consistently in the fFIM–superconductor geometry; if the staggered exchange field suppresses or spatially modulates the induced pairing amplitude, the phase boundaries shift or the zero modes vanish. Experimentally, a nanowire on an fFIM at the predicted parameters should show a $2e^2/h$ zero-bias conductance peak only inside the computed $V_0$ windows, and its absence would falsify the central claim.","supporting_citations":[{"cited_title":"[2, 3, 12, 35, 51–53]","cited_arxiv_id":null,"evidence_quote":"Contains the dimensional reduction, invariant derivations, and full-Hamiltonian checks that validate the 1D, 2D, and higher-order models."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes creation and manipulation of higher-order topological states by Néel-vector orientation, the control principle used for the corner modes."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Shows Majorana routes in zero-net-magnetization altermagnets, the compensated-magnet context the fFIM proposal extends."}],"review_version":1}