{"id":"ef8d5215-1020-4524-b464-6fe0f8e1a6f6","arxiv_id":"2411.18156","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Zigzag germanene nanoribbons thinner than about two nanometers lose their 2D topological edge states and instead develop mirror-and-time-reversal-protected zero-dimensional end states, claimed as the first 1D topological insulator with strong spin-orbit coupling.","lead":"Experiments on ultrathin germanene nanoribbons show that their electronic edge states disappear below a width of about two nanometers, while a localized state appears at the ribbon ends. The authors interpret this as the first one-dimensional topological insulator with strong spin-orbit coupling, a platform that could matter for future topological quantum devices.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 1D-TI claim rests on an assumed mirror-symmetric termination and an unverified parameter regime; without atomically resolving the end and testing whether MxT survives on the Pt/Ge(110) support, a trivial end state is not excluded.","rationale":"The paper has real strengths: the wide-ribbon edge states and their reversible electric-field switching provide independent evidence for the 2D quantum spin Hall behaviour, and the tight-binding LDOS calculations reproduce the trend of edge-state disappearance with width. However, the 0D end-state evidence is not yet at the same level. The MxT protection argument in SI §2.2 is valid for the idealized Hamiltonian, but the SI itself notes that armchair terminations lack the symmetry, so the actual end termination is decisive. The manuscript also contains an unreconciled parameter discrepancy (Ms=+0.02t in the main text versus MS=−0.04t in the SI), and the SI's width assignment is partly inferred from the same LDOS peak used to claim topology. These are not indications that the claim is false; they are unverified conditions in an otherwise plausible chain. The proposed DFT/STM check would settle whether the observed end peak is the predicted MxT-protected mode or a trivial termination state. The reader's CONDITIONAL verdict therefore remains appropriate.","tokens_in":18120,"tokens_out":13225,"duration_ms":132640,"concrete_test":"Acquire atomic-resolution STM images of both ends of the 2-hexagon ribbon that hosts the end state, determine the number of hexagons across the width and the exact end termination, and feed this geometry with the Pt/Ge(110) substrate and Rashba SOC into spin-polarized DFT. Then check whether the MxT mirror plane is an exact symmetry of the relaxed supported structure and whether the Zak-phase invariant of SI Eq. 4 remains ν=1. If the termination differs from the model or MxT is broken, the observed end peak is not protected and the central claim would need revision.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that the ~75 meV end-localized state in the ~1 nm ribbon is an MxT-protected 0D topological end state rather than a trivial termination state. Three conditions are necessary: (i) the ribbon is exactly 2 hexagons wide with the mirror-symmetric zigzag termination used in SI Fig. S6; (ii) the combined mirror-time-reversal symmetry MxT survives in the Pt/Ge(110)-supported sample; and (iii) the staggered mass and Rashba terms place the system in the ν=1 phase. None of these is directly established. Atomic-resolution STM resolves the long edges but not the end cut, and SI §2.1 explicitly neglects Rashba while the substrate is expected to induce it. The model parameters are inconsistent between the main text (Ms=+0.02t) and the SI (MS=−0.04t); the SI also infers the 2-hex width from the matching LDOS peak, making the width assignment partly circular. Since the topological invariant (SI Eq. 4) is meaningful only when MxT quantizes the Zak phase and the Hamiltonian is in the calculated topological regime, the experimental evidence does not yet exclude a trivial geometry-dependent end state.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports STM/STS measurements on germanene nanoribbons grown on Pt/Ge(110) and tight-binding calculations for zigzag-terminated nanoribbons. It claims a width-driven crossover: above a critical width of about 2 nm the ribbons show 2D quantum spin Hall edge states, while the thinnest (nominally 2-hexagon-wide) ribbon shows a 0D end-localized state near 75 meV and an absence of such a state in a 3-hexagon ribbon. The end states are interpreted as topologically protected by the combined action of mirror and time-reversal symmetry, and the authors claim this constitutes the first realization of a 1D topological insulator with strong spin-orbit coupling. The theoretical analysis uses a Kane-Mele-type model with intrinsic SOC, a staggered mass, and longer-range hopping, and defines a Zak-phase-based invariant nu to identify the topological phase.","tokens_in":18369,"tokens_out":9139,"duration_ms":84255,"significance":"If the central claim is correct, the paper is significant: it would demonstrate a 2D-to-1D topological transition in a single material platform, realize a 1D topological crystalline phase with strong spin-orbit coupling, and provide a pathway toward dense arrays of topologically protected states. The tight-binding and Zak-phase calculations are clearly presented and appear internally consistent, and the spatial mapping of an end-localized state is a valuable experimental observation. The significance is, however, conditional: the topological interpretation rests on symmetry and parameter assumptions that are not directly verified, and the experimental evidence is based on very few ribbons without statistical or control measurements.","major_comments":[{"comment":"The value of the staggered mass MS is inconsistent between the main text and the Supplementary Information. The main text states that the calculations use lambda_SO = 0.3t, MS = 0.02t, t3 = 0.3t, while SI §2.3 states 'we compared the experimental results to the theoretical ones obtained for the parameters lambda_SO = 0.3t and MS = -0.04t', and the phase diagram in SI Fig. S7d uses MS = -0.04t. The sign and magnitude of MS determine whether the 2-hexagon ribbon is in the nu = 1 phase and the 3-hexagon ribbon is trivial (SI Figs. S7-S8). Since MS is not measured independently, the theory-experiment comparison is not robust to this ambiguity and the central claim is not yet well constrained.","section":"Main text (p. 5, 'To understand this') and SI §2.3"},{"comment":"The assignment of the thinnest measured ribbon as 2 hexagons wide is made from the LDOS peak: 'Therefore, we conclude that it is likely that the thinnest experimental ribbons are only 2-unit cells wide.' This makes the width assignment partly circular because the same spectroscopic signature is used both to identify the width and to validate the topological model. The width should be determined from atomically resolved STM topography of the ribbon and its end termination, independent of the dI/dV peak. The main-text inset of Fig. 3h does not provide atomic resolution of the end, so this circularity remains unresolved.","section":"SI §2.3 ('A direct comparison...')"},{"comment":"The topological invariant nu defined by SI Eq. (4) is quantized only if the combined mirror-time-reversal symmetry MxT is preserved (SI §2.2). The experimental ribbons sit on a Pt/Ge(110) substrate, which can break mirror symmetry, and the model neglects Rashba spin-orbit coupling, which the authors themselves state is 'likely present' in the experiments (SI §2.1). No experimental evidence is provided that MxT survives in the measured ribbons—for instance, no atomically resolved image of the end termination that would establish a mirror-symmetric cut, and no test of robustness against symmetry-breaking perturbations. Until this is shown, the observed end-localized state could be a trivial termination state, and the topological protection claim is not established.","section":"SI §2.1 and §2.2"},{"comment":"The central experimental evidence consists of single dI/dV spectra from apparently single ribbons of each width (Fig. 3e-h). No error bars, number of ribbons, or repeated measurements are reported, and no control experiments are presented (e.g., ribbons with different end terminations, different lengths, or different tip conditions). For a claim as strong as 'the first realization of a 1D topological insulator with strong spin-orbit coupling', this statistical and control basis is too thin. At minimum, the authors should report the number of ribbons measured and show that the 2-hexagon end state and the 3-hexagon absence are reproducible.","section":"Fig. 3e-h and main text"}],"minor_comments":[{"comment":"The phrase 'contrary to the tenfold way classification' is misleading: class AII in 1D is trivial in the tenfold way, but the proposed phase is protected by the additional mirror symmetry MxT, making it a topological crystalline phase rather than a violation of the tenfold way. The wording should be adjusted.","section":"Abstract and main text"},{"comment":"The caption mentions 0D end states marked in the inset of a band structure for a 2-hexagon ribbon. Since a band structure with periodic boundary conditions along x cannot contain end states, the inset likely shows the open-boundary spectrum; please state this explicitly.","section":"Fig. 2g inset"},{"comment":"The notation for SOC strength is inconsistent: the Hamiltonian (1) uses lambda_SO/(3sqrt(3)) in the hopping term, while the text often writes 'lambda_SO = 0.3t'. Please define the convention once and use it consistently throughout the main text and SI.","section":"SI §2.1"},{"comment":"The closing statement that end states are 'akin to Majorana zero modes' and involve 'fractionalized electrons' is not supported by the measurements or by the class-AII-with-mirror model presented; this overreach should be toned down or removed.","section":"Conclusion"},{"comment":"The data availability statement only offers data 'upon reasonable request'; for a claim of this significance, providing raw STS spectra and the tight-binding code would improve reproducibility.","section":"Data availability"},{"comment":"The buckling upper bound of 0.35 Å is given without an associated measurement uncertainty or a statement of how many line profiles were averaged; please report typical values and sample-to-sample spread.","section":"Fig. 1g"}],"recommendation":"major_revision","confidential_remarks":"The paper is likely to attract attention given the germanene platform and the 1D-TI claim, but the experimental evidence is quite thin and the MS parameter inconsistency is a serious concern. If the authors can provide more statistics, atomically resolved end terminations, and reconcile the main-text and SI parameter values, the result would be much stronger. There is also a novelty question relative to Traverso et al. (Ref. 37) and earlier graphene nanoribbon predictions; the authors should clarify what is new beyond these predictions. No concerns about citation manipulation."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First thing to know: this is the most credible experimental claim so far for a 1D topological insulator with strong spin-orbit coupling. The key observation is that zigzag germanene nanoribbons on Pt/Ge(110) show a width-driven transition: wide ribbons have edge states, ~2 nm ribbons lose them, and ~1 nm ribbons show a sharp state localized at the ends. The authors back this with a Kane-Mele tight-binding model and a Zak-phase invariant quantized by a combined mirror-time-reversal symmetry. That combination is new, and the even/odd width dependence (2-hex topological, 3-hex trivial) follows the Haldane-model prediction, which is the right theoretical lens.\n\nThe experimental work is careful in many ways: they demonstrate that the edge states in wide ribbons are reversibly destroyed by an electric field, which is a good control. They also show the end-state localization in topography and dI/dV maps. The tight-binding phase diagrams are thorough, and the LDOS calculations reproduce the main features.\n\nThe soft spots are real but not disqualifying. First, the staggered mass is quoted as +0.02t in the main text and -0.04t in the SI when comparing to experiment. That inconsistency matters because the topological phase depends on it, and the SI uses the experimental matching to infer both the mass and the ribbon width. Second, the argument that the end state is topological relies on MxT symmetry surviving in the Pt/Ge(110)-supported sample. The authors explicitly neglect Rashba spin-orbit coupling, which the substrate is likely to induce. If that symmetry is broken, the Zak phase is no longer quantized and the end state could be a trivial termination state. Third, the statistical basis is thin: a handful of spectra, no error bars, no systematic study of end-term geometry. Atomic-resolution images show the long edges but not the exact termination of the ends.\n\nNone of these flaws breaks the central claim, but they do mean the paper is not airtight yet. The main result—that an ultrathin germanene ribbon hosts a sharp end state that appears and disappears with width—is likely to hold. The topological interpretation needs one more experimental step: direct evidence that the state is symmetry-protected (e.g., dependence on termination, or comparison with a ribbon where the symmetry is intentionally broken) or at least a direct measurement of the staggered mass and Rashba terms.\n\nFor peer review: yes, this deserves a serious referee. The subject is important, the theoretical framework is appropriate, and the experimental claim is specific enough to be tested. I would recommend major revision, not rejection, with emphasis on clarifying parameters, providing more statistics, and addressing the mirror-symmetry concern head-on.\n\nA colleague reading this in a group should take it as a high-quality preprint with a plausible but not yet proven topological claim. Worth citing for the width-driven transition, worth discussing in detail at the next journal club.","headline":"A credible first shot at a 1D topological insulator, but the topological claim rests on an unverified symmetry and a parameter inconsistency; deserves a serious referee.","tokens_in":18987,"tokens_out":4238,"would_cite":true,"duration_ms":34395,"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":"Ultrathin germanene nanoribbons realize a one-dimensional topological insulator with protected end states.","keywords":["germanene","nanoribbons","one-dimensional topological insulator","quantum spin Hall effect","topological end states","Zak phase","mirror symmetry","spin-orbit coupling"],"falsifier":"Compute a 2-hexagon zigzag germanene ribbon with a first-principles model that includes the Pt/Ge(110) substrate and Rashba spin-orbit coupling; if the mirror-time-reversal Zak phase is no longer quantized to 0 or $\\pi$ (so $\\nu$ is not 1 for the experimental geometry), the observed end state cannot be topologically protected. On the experimental side, deliberately breaking mirror symmetry at one ribbon end, for example by placing a single adatom on one edge, should destroy the protected end state while leaving a trivial termination state in place.","tokens_in":17944,"feed_emoji":"⚛️","tokens_out":14041,"duration_ms":114992,"temperature":0.7,"pith_summary":"The paper claims that germanene nanoribbons undergo a width-driven topological transition: when a ribbon narrows below roughly 2 nm, the helical edge states of the two-dimensional quantum spin Hall phase disappear and sharply localized states appear at the two ends of the ribbon. These 0D end states are argued to be topologically protected by a combined mirror and time-reversal symmetry, making the ultrathin ribbons the first experimentally realized one-dimensional topological insulator with strong spin-orbit coupling. The case rests on scanning tunneling spectroscopy of ribbons with widths from about 1 to 6 nm, matched ribbon-by-ribbon to tight-binding calculations of the Zak phase. If correct, the result locates the lower-dimensional limit of a known two-dimensional topological phase and supplies a concrete platform in which protected boundary states can be packed into dense arrays and toggled by an electric field.","feed_headline":"Germanene ribbons turn into 1D topological insulators below 2 nm","feed_subtitle":"A width-driven crossover swaps edge states for protected end states, a first in 1D spin-orbit topology.","key_machinery":"The central object is the combined symmetry $M_x T$, mirror reflection across the ribbon axis composed with time reversal, which forces the Wilson-loop eigenvalues of a zigzag nanoribbon to be real and therefore quantizes the Zak phase to either 0 or $\\pi$. The Zak phase is the Berry phase accumulated by the occupied Bloch states across the one-dimensional Brillouin zone. It is computed from a tight-binding Hamiltonian of Kane-Mele type, with intrinsic spin-orbit coupling $\\lambda_{SO}$, a staggered mass $M_S$, and longer-range hopping, solved in a ribbon geometry for widths from one to fourteen hexagon cells. The paper defines the invariant $\\nu \\equiv (\\varphi - \\varphi_{M_S \\to \\pm\\infty})/\\pi \\bmod 2$, where $\\varphi_{M_S\\to\\pm\\infty}$ is the Zak phase of the trivial large-mass limit; $\\nu = 1$ signals two exponentially localized end states inside the minigap that opens in the edge-mode spectrum of sufficiently thin ribbons. This machinery also accounts for the even/odd hexagon-count dependence: even-width ribbons are topological in certain parameter windows while odd-width ribbons are not.","core_discovery":"The paper reports the first experimental realization of a one-dimensional topological insulator with strong spin-orbit coupling, in zigzag-terminated germanene nanoribbons grown on Pt/Ge(110). For ribbons wider than about 2 nm, the nanoribbons behave as two-dimensional quantum spin Hall strips with helical edge states, consistent with earlier germanene measurements. Below that width, the edge modes fail to traverse the bulk gap and instead open a minigap, and two zero-dimensional states localize at the ribbon ends. The authors show by computing the Zak phase that these end states are not trivial termination modes: the combined mirror and time-reversal symmetry quantizes the Zak phase to 0 or $\\pi$, giving a nontrivial invariant $\\nu=1$ for the 2- and 6-hexagon-wide ribbons and $\\nu=0$ for the 3-hexagon-wide ribbon, in agreement with the spectroscopy. In one dimension the time-reversal-symmetric class alone has no topological phase, so the protection must come from the additional mirror symmetry; the paper thus identifies a width-driven transition from a 2D class-AII insulator to a 1D topological crystalline phase.","pith_inferences":["If the central claim holds, the same width-driven crossover should appear in other honeycomb nanoribbons with strong spin-orbit coupling, such as silicene, stanene, or bismuthene, whenever the zigzag termination preserves the mirror-time-reversal symmetry; the STM recipe used here can be applied directly to those materials.","The even/odd hexagon-count dependence hints at a general parity selection rule for mirror-symmetric honeycomb nanoribbons; the paper's own phase diagram shows re-entrant topological windows at larger even widths, so a systematic experimental scan of widths beyond six hexagons could test whether end states reappear at those larger widths.","Because the end states sit in a minigap whose size shrinks with width, gating or substrate engineering that tunes the staggered mass could switch individual ribbons in and out of the 1D topological phase in situ, enabling addressable arrays of protected end states.","The authors compare the end states to Majorana-like zero modes; a stronger test would be to measure the end-state spin polarization or to couple two ribbons end-to-end and look for nonlocal correlations, which would distinguish a symmetry-protected charge mode from a genuine topological-superconductor end mode."],"forward_implications":["Nanoribbons narrower than about 2 nm lose their conducting edge channels, leaving only 0D end states, so the material behaves as a 1D topological insulator rather than a 2D quantum spin Hall strip.","The end states are protected only while the combined mirror and time-reversal symmetry is intact, so a perturbation that breaks the mirror symmetry of the zigzag termination should destroy them; this gives a sharp experimental signature for checking the claim.","The 6-hexagon ribbon is an intermediate case with both edge and end states, so the 2D-to-1D crossover is gradual, and the measured critical width of about 2 nm defines the practical packing limit for 1D edge channels in germanene nanoribbon arrays.","Because the topology depends on ribbon width and on whether the width is an even or odd number of hexagon cells, the same growth method can in principle pattern arrays in which selected ribbons are topological and selected ribbons are trivial."],"supporting_citations":[{"why":"Supplies the Kane-Mele model of the quantum spin Hall effect in a honeycomb lattice, the starting point for the nanoribbon tight-binding calculations.","marker":"[1]"},{"why":"Defines the Z2 topological characterization of the quantum spin Hall effect, the 2D topology whose lower-dimensional limit the paper probes.","marker":"[2]"},{"why":"Earlier experimental confirmation of the 2D topological phase in germanene and of the substrate-enhanced gap, the platform the present ribbons are built from.","marker":"[20]"},{"why":"Predicts topological bound states in thin zigzag nanoribbons of a Haldane-type model, which the paper uses to explain the even/odd hexagon-count dependence.","marker":"[37]"},{"why":"Provides the dispersion of germanene topological edge states at zigzag and armchair edges, used to interpret the STS lineshape of the edge states.","marker":"[45]"},{"why":"Describes the segregation-based growth of aligned Ge nanoribbons on a metal/Ge(110) template, the method adapted here to fabricate the samples.","marker":"[46]"},{"why":"Defines the Zak phase used as the 1D topological invariant whose quantization to 0 or pi signals the 0D end states.","marker":"[55]"}],"fun_headline_variants":["First 1D topological insulator from germanene nanoribbons","Below 2 nm, germanene ribbons switch to 1D topology","Width-driven crossover yields protected 1D end states","1D topological insulator realized in germanene ribbons","Ultrathin germanene ribbons host 1D topological phase"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The topological identification of the end states assumes the combined mirror and time-reversal symmetry stays exact in the experimental nanoribbons even though the Pt/Ge(110) substrate and the neglected Rashba spin-orbit coupling could each break it.","fun_headline_variants_meta":{"raw":{"variants":["First 1D topological insulator from germanene nanoribbons","Below 2 nm, germanene ribbons switch to 1D topology","Width-driven crossover yields protected 1D end states","1D topological insulator realized in germanene ribbons","Ultrathin germanene ribbons host 1D topological phase"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000174,"raw_usage":{"total_tokens":1313,"prompt_tokens":1004,"completion_tokens":309,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":620,"completion_tokens_details":{"reasoning_tokens":224}},"tokens_in":620,"tokens_out":309,"duration_ms":3254,"temperature":1.0,"reasoning_tokens":224,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T11:27:20.669593+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute a 2-hexagon zigzag germanene ribbon with a first-principles model that includes the Pt/Ge(110) substrate and Rashba spin-orbit coupling; if the mirror-time-reversal Zak phase is no longer quantized to 0 or $\\pi$ (so $\\nu$ is not 1 for the experimental geometry), the observed end state cannot be topologically protected. On the experimental side, deliberately breaking mirror symmetry at one ribbon end, for example by placing a single adatom on one edge, should destroy the protected end state while leaving a trivial termination state in place.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the Z2 topological characterization of the quantum spin Hall effect, the 2D topology whose lower-dimensional limit the paper probes."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Earlier experimental confirmation of the 2D topological phase in germanene and of the substrate-enhanced gap, the platform the present ribbons are built from."},{"cited_title":"& Traverso Ziani, N","cited_arxiv_id":null,"evidence_quote":"Predicts topological bound states in thin zigzag nanoribbons of a Haldane-type model, which the paper uses to explain the even/odd hexagon-count dependence."},{"cited_title":"J., Klaassen, D","cited_arxiv_id":null,"evidence_quote":"Provides the dispersion of germanene topological edge states at zigzag and armchair edges, used to interpret the STS lineshape of the edge states."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Describes the segregation-based growth of aligned Ge nanoribbons on a metal/Ge(110) template, the method adapted here to fabricate the samples."},{"cited_title":"Berry’s phase for energy bands in solids","cited_arxiv_id":null,"evidence_quote":"Defines the Zak phase used as the 1D topological invariant whose quantization to 0 or pi signals the 0D end states."}],"review_version":1}