{"id":"530cad19-b471-4ac9-97c5-37e847f56b28","arxiv_id":"2602.12223","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Using exact tight-binding calculations, the authors show kagome edge states are termination-dependent in the pristine lattice, become termination-independent helical modes with Kane-Mele spin-orbit coupling, and form Chern-insulating chiral edge states under Zeeman/Rashba or non-coplanar magnetic or","lead":"This paper maps how the edges of a kagome lattice, a honeycomb-like arrangement of corner-sharing triangles, host electronic states depending on how the lattice is cut and whether spin-orbit coupling or magnetism is added. Because kagome materials are promising for topological electronics, the catalog could guide experiments looking for edge-state signatures.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Slab width used for all termination-dependent edge-state calculations is never reported or converged, so the in-gap state inventories in Figs. 2–7 could be finite-size artifacts; Eq. (19) also has a typo making the quoted Jc inconsistent.","rationale":"The paper's central claim is a catalog of edge states and topological invariants across several tight-binding models. All results come from finite-width slab calculations, yet the manuscript never reports the number of sites or unit cells in the finite direction, nor shows any convergence test. The only statement, in Sec. IV, that 'we keep the slab width large enough to avoid any hybridization between edge states' is an assertion without quantitative evidence. This matters because the termination-resolved edge-state counts in Figs. 2–7 are the basis for the central claims: that flat termination suppresses edge states, that mixed terminations support a specific number of modes, and that chiral edge-mode counts match bulk Chern numbers. If the slab is too narrow, edge states from opposite boundaries can hybridize and split, or spurious discrete modes can appear in the gaps, changing the reported inventories. The flat-termination case is especially delicate: an absence of edge states in a narrow slab could simply mean the edge-state wavefunctions from opposite edges overlap and move into the bulk. A convergence test with increasing width would rule this out. In addition, Eq. (19) contains a clear typo: as typeset it gives Jc≈2.646 at θ=π/3, while the text quotes 1.51, which corresponds to 2/√(1+3cos²θ). This inconsistency affects the subcritical/supercritical classification in Sec. VI, though it is likely a typesetting error and does not undermine the existence of the Chern phases. The reader's weakest_assumption coincides with the slab-width issue, and I agree that this is the most load-bearing concern. Therefore the verdict should remain CONDITIONAL pending the requested convergence details and the typo correction.","tokens_in":21312,"tokens_out":11358,"duration_ms":103352,"concrete_test":"For each termination in Figs. 2 and 3, repeat the slab diagonalization with at least two slab widths W and 2W (e.g., 20 and 40 unit cells in the finite direction) and verify that the number, dispersion, and LDOS of the in-gap states are unchanged. Pay particular attention to the flat termination: if any edge-localized state appears at larger W, the claim that flat termination completely suppresses edge modes is a finite-size artifact. Also re-evaluate the Jc value by recomputing the Chern-number transition around J/t=2 at θ=π/3 to confirm the quoted Jc≈1.51.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper never reports the slab width (number of sites or unit cells) for any of the slab calculations in Sections III–VI, nor provides a convergence test. Section IV only states that 'we keep the slab width large enough to avoid any hybridization between edge states' with no quantitative support. This is the most load-bearing concern because the termination-resolved edge-state inventories in Figs. 2–7 and the matching of edge-mode counts to Chern numbers depend critically on the assumption that opposite-edge states do not hybridize and that no spurious finite-size modes appear. If the chosen widths are inadequate, the claim that the flat termination completely suppresses edge states (Fig. 2(b)) and the specific edge-state counts for mixed terminations could be artifacts. Additionally, Eq. (19) as typeset gives Jc/t = 2√(1+3cos²θ) ≈ 2.646 at θ=π/3, inconsistent with the quoted Jc≈1.51, which corresponds to 2/√(1+3cos²θ). This undercuts the subcritical/supercritical classification in Section VI, though it is likely a mechanical typo rather than a deep physics error.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript presents a numerical tight-binding study of a two-dimensional kagome lattice in slab geometry. It first identifies four lattice terminations (zigzag, armchair, cove, flat) and reports that in the pristine limit the existence and number of localized in-gap states depend strongly on termination, with the flat edge hosting no edge states. It then adds Kane–Mele spin–orbit coupling, computes the Z2 index via Wilson-loop winding, and reports spin-polarized helical edge states in a quantum spin Hall phase that are insensitive to edge termination. Breaking time-reversal symmetry by an out-of-plane Zeeman field plus Rashba spin–orbit coupling gives quantum anomalous Hall phases with Chern numbers resolved from Berry curvature, Hall conductivity, and edge-mode counting, with Kane–Mele coupling further modifying the Chern phases. Finally, non-coplanar q=0 magnetic order with scalar spin chirality is shown to produce subcritical and supercritical exchange regimes with multiple Chern phases. The central claim is a termination-resolved map of kagome edge states and topology across these models.","tokens_in":21532,"tokens_out":5436,"duration_ms":54603,"significance":"If the reported identification is correct, the work provides a useful systematic catalogue of boundary-sensitive and boundary-insensitive edge states in a widely studied model. It connects termination-dependent spectral features to experimental observations in kagome materials and gives concrete model predictions for Chern and Z2 edge-mode counts. The methods are standard and the manuscript is transparent about importing the critical-exchange expression from Ref. [45]. I find no fitting-to-data circularity: parameters are hand-chosen, and the Wilson-loop and Berry-curvature invariants are evaluated with independent standard tools. The main obstacle is that the finite-slab evidence is not yet quantitatively supported; once slab widths and convergence tests are provided, and the Eq. (19) typo is fixed, the central conclusions are likely to hold.","major_comments":[{"comment":"No slab width (in unit cells or sites) is reported for any slab calculation, and no convergence test is given. Section IV only says that the width is kept 'large enough to avoid hybridization' without quantitative support. This is load-bearing: the termination-resolved edge-state inventories of Fig. 2, the complete suppression for flat termination, and the matching of chiral edge-mode counts to Chern numbers in Figs. 4–7 all depend on the chosen finite width. I request per-termination and per-gap widths, BZ sampling, and a short convergence study showing that the in-gap states and their splittings stabilize with increasing width.","section":"Sections III–VI, Figs. 2–7"},{"comment":"As typeset, J_c(θ)/t = ±2√(1+3cos²θ) gives J_c/t ≈ 2.646 at θ=π/3, inconsistent with the quoted J_c/t ≈ 1.51. The quoted value corresponds to J_c/t = ±2/√(1+3cos²θ). Since J_c separates the subcritical and supercritical regimes used throughout Section VI, especially in Figs. 6 and 7, the formula must be corrected and the numerical values and phase assignments re-verified. If the reciprocal form is intended, the manuscript should state this explicitly.","section":"Section VI, Eq. (19)"}],"minor_comments":[{"comment":"Typographical errors: 'anihilates' after Eq. (1) should be 'annihilates'; 'egeinvalue' in the Wilson-loop discussion should be 'eigenvalue'.","section":"Sec. II and Sec. IV"},{"comment":"The position-weighted amplitude ρ_{n,a}(k) uses r·ê_a, but r is not defined as the position vector in the slab coordinate system. Please clarify the origin and normalization of r, and add color bars to the slab band-structure figures showing the position expectation value.","section":"Eq. (8) and Figs. 3–7"},{"comment":"The middle panels show energy levels versus 'state index'; the ordering of the state index and the counting of degenerate edge states should be explained in the caption or text.","section":"Fig. 2 captions"},{"comment":"The text notes that chiral modes appear twice because of the projected BZ period. This should be made explicit in the caption at first occurrence to avoid confusion about edge-mode counting.","section":"Fig. 4(c)"},{"comment":"Figures SF1 and SF2 lack axis labels and color bars for spin polarization and position expectation; please add them for completeness.","section":"Supplemental Material"}],"recommendation":"major_revision","confidential_remarks":"To the editor: The technical core is standard and the conclusions are plausible, but the missing convergence information and the Eq. (19) typo are exactly the kind of load-bearing issues that should be fixed before publication. I do not see a circularity or novelty-disclosure problem; the critical-exchange formula is attributed to Ref. [45]. The paper is within the journal's scope and is suitable for revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper gives you a systematic, termination-resolved map of kagome edge states across pristine, Kane-Mele, Zeeman+Rashba, and non-coplanar magnetic configurations. That combined catalog is genuinely new, even though each ingredient has been studied separately. The methods are standard exact diagonalization plus Wilson-loop and Berry-curvature calculations, and the displayed bands and Chern numbers do line up: the Z2 phase shows termination-independent helical states, the Chern phases show matching chiral edge-mode counts, and the pristine flat termination suppressing edge states is a clean, striking result. I don't see a load-bearing physics error.\n\nThe soft spots are real but manageable. First, the slab width is never reported. Section IV just says 'large enough to avoid any hybridization between edge states,' with no number of sites or unit cells and no convergence test. That matters most for the terminating-dependent inventories in Figs. 2-7, and especially for the claim that flat termination completely gets rid of edge states. The logic is plausible, but the reader can't verify that the in-gap states aren't finite-size artifacts. Second, Eq. (19) as typeset gives Jc(pi/3)/t = 2.646, while the text quotes 1.51, which matches 2/sqrt(1+3cos^2(theta)). That looks like a typo, but it undercuts the subcritical/supercritical classification in Sec. VI until corrected. Third, no code or data is provided, which makes independent verification harder than it needs to be for a catalog paper.\n\nI don't agree with any harsher skepticism. The circularity burden is low: these are hand-chosen model parameters, not fits to data, and the bulk-boundary correspondence and Wilson-loop method are external standards, not inputs that imply the conclusions. The citation pattern looks fair, including the attribution of Jc to ref. [45]. The paper is not trying to be more than it is: a competent, useful catalog with a few reproducible qualitative claims. It doesn't settle a big open question, but it gives experimentalists a clearer vocabulary for interpreting termination-dependent STM/ARPES on Co3Sn2S2, FeGe, and similar materials.\n\nWho should read it: anyone doing kagome edge-state engineering or interpreting termination-dependent surface spectra. Deserves a serious referee, but I'd send it back for revision: report slab widths, add a convergence check, fix the Jc typo, and ideally release the code or at least the key geometry parameters. With those changes I'd be comfortable citing it.","headline":"A useful termination-resolved catalog of kagome edge states, built with standard methods and internally consistent results, but the missing slab-width reporting and a likely typo in Jc need fixing before I'd trust the details.","tokens_in":22119,"tokens_out":1091,"would_cite":true,"duration_ms":11773,"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":"This paper claims that kagome edge states are governed by lattice termination, spin-orbit coupling, and magnetic order: flat cuts suppress them, Kane-Mele coupling makes helical edge states termination-independent, and magnetism yields Cher","keywords":["kagome lattice","edge states","lattice termination","Kane-Mele spin-orbit coupling","quantum spin Hall effect","Chern insulator","quantum anomalous Hall effect","scalar spin chirality"],"falsifier":"Repeat the slab calculations of Figs. 3–5 and 7 for a systematic series of slab widths (e.g., 10 to 100 unit cells) and track the number, degeneracy, and dispersion of the in-gap edge states; if any of the reported edge modes appears, disappears, or changes its degeneracy as the width grows, the termination-resolved classification is a finite-size artifact rather than a bulk property. Alternatively, on the experimental side, a flat-terminated surface of a pristine kagome material surveyed by scanning tunneling spectroscopy should show no localized edge-state signal near the Fermi level, while","tokens_in":21107,"feed_emoji":"🧲","tokens_out":6526,"duration_ms":56190,"temperature":0.7,"pith_summary":"Using tight-binding slab calculations, this paper asks when a two-dimensional kagome lattice—a net of corner-sharing triangles—carries localized electronic states at its edges. It finds that in the pristine lattice the answer is decided by the boundary geometry: zigzag, armchair, and cove terminations host one to five edge states, while a flat termination completely removes them. Adding Kane-Mele spin-orbit coupling opens bulk gaps and produces a Z2 topological insulator with helical, spin-polarized edge states that appear for every termination, making the topological edge modes insensitive to the boundary details that control trivial edge states. When time-reversal symmetry is broken, either by a Zeeman field plus Rashba coupling or by a non-coplanar magnetic texture with finite scalar spin chirality, the system enters Chern insulating phases; the number of chiral edge modes seen in the slab matches the computed Chern number in each gap. If these results hold, they give a termination-resolved recipe for engineering edge transport in kagome materials, and explain why different cleaved or terraced surfaces of the same compound can show very different edge spectra.","feed_headline":"Flat cuts kill kagome edge states","feed_subtitle":"Spin-orbit coupling restores termination-independent helical modes; magnetism adds chiral Hall channels.","key_machinery":"The argument runs on exact diagonalization of tight-binding Hamiltonians on kagome slabs, and the central objects are the four line-cut terminations (zigzag, armchair, cove, flat) that define the boundary geometry. The topological classification is carried by two invariants: the Z2 index, computed from the odd winding of Wilson-loop eigenvalue phases across half the Brillouin zone (the signature of the Kane-Mele quantum spin Hall phase), and the Chern number, computed from integrated Berry curvature and matched to the number of chiral edge modes in each bulk gap. The magnetic mechanisms are the Zeeman plus Rashba combination, which lifts spin degeneracy to open Chern gaps, and scalar spin ch","core_discovery":"The paper's central claim is a termination-resolved map of edge states in a single-orbital tight-binding model of the kagome lattice. In the pristine limit, edge-state existence and multiplicity are highly sensitive to the boundary: out of the four line-cut terminations considered—zigzag, armchair, cove, and flat—only the flat termination completely suppresses localized edge modes, while mixed terminations combine the edge states of their constituents. Kane-Mele spin-orbit coupling changes the picture qualitatively: it opens bulk gaps at the Dirac point and near the flat band, and the system becomes a Z2 topological insulator whose helical edge states are spin-polarized, counter-propagating,","pith_inferences":["A testable extension: STM measurements on flat-terminated versus armchair-terminated terraces of a real kagome material (e.g., FeGe or Co3Sn2S2) should show an absence of edge-state LDOS at flat steps and clear edge-state peaks at zigzag or armchair steps, isolating the termination effect in a material with finite spin-orbit coupling.","The paper's results suggest termination can be used as a design parameter for valley-selective or orbital-angular-momentum-carrying edge channels; the triangular LDOS pattern at armchair edges implies a net orbital angular momentum that could be read out in orbital Hall or optospintronic experiments.","The critical exchange field Jc and the phase diagram's sensitivity to Kane-Mele coupling imply that alloying or strain, which modifies intrinsic SOC, could drive a kagome magnet across a topological transition; this is an inference about materials control that the paper does not claim directly.","The finding that KMSOC transforms chiral modes into helical-like modes at higher coupling (mentioned for the non-coplanar case) suggests a general competition between Chern and spin-Hall orderings that could appear in other frustrated lattices with both intrinsic SOC and non-coplanar order."],"forward_implications":["Flat-terminated kagome surfaces should show no pristine edge states; any edge conductance observed there must come from spin-orbit or magnetic effects, not from the bare lattice.","In the Kane-Mele regime, edge channels are helical and termination-independent, so transport along arbitrarily cut edges of a Z2 kagome insulator should be backscattering-free.","In the Zeeman+Rashba and non-coplanar regimes, measuring the quantized anomalous Hall conductance sigma_xy = C e^2/h directly counts the number of chiral edge modes, providing a sharp experimental test of bulk-boundary correspondence.","Kane-Mele coupling acts as a switch: it can create new Chern phases (C=-1 from non-coplanar order), flip the sign of an existing phase (C=1 to C=-1 in the Zeeman+Rashba case), or destroy all Chern phases, so tuning intrinsic SOC is a practical knob for controlling the direction and presence of chiral edge transport.","The sign changes of the anomalous Hall conductivity at van Hove singularities (Lifshitz transitions) connect the Hall response to Fermi-surface topology, meaning that Hall measurements can track Lifshitz transitions in kagome metals."],"fun_headline_variants":["Kagome edges: termination decides, SOC saves","Flat cuts kill kagome edge states, SOC revives them","Termination quenches kagome edge modes; SOC and magnetism restore","Kagome edge states: cut-dependent, SOC-protected"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The load-bearing premise is that the slab widths used in the exact-diagonalization calculations — stated only as 'large enough to avoid hybridization between edge states' — are genuinely large enough that the reported in-gap edge modes survive the thermodynamic limit and are not finite-size artifacts.","fun_headline_variants_meta":{"raw":{"variants":["Kagome edges: termination decides, SOC saves","Flat cuts kill kagome edge states, SOC revives them","Termination quenches kagome edge modes; SOC and magnetism restore","Kagome edge states: cut-dependent, SOC-protected"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000807,"raw_usage":{"total_tokens":3357,"prompt_tokens":701,"completion_tokens":2656,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":445,"completion_tokens_details":{"reasoning_tokens":2585}},"tokens_in":445,"tokens_out":2656,"duration_ms":18169,"temperature":1.0,"reasoning_tokens":2585,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-02T23:53:53.614529+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Repeat the slab calculations of Figs. 3–5 and 7 for a systematic series of slab widths (e.g., 10 to 100 unit cells) and track the number, degeneracy, and dispersion of the in-gap edge states; if any of the reported edge modes appears, disappears, or changes its degeneracy as the width grows, the termination-resolved classification is a finite-size artifact rather than a bulk property. Alternatively, on the experimental side, a flat-terminated surface of a pristine kagome material surveyed by scanning tunneling spectroscopy should show no localized edge-state signal near the Fermi level, while","supporting_citations":[],"review_version":1}