{"id":"65c2f3c3-cc59-4a8e-91c7-96b35712bb21","arxiv_id":"2501.00554","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Al13Os4 is a bulk weak-coupling superconductor at 5.47 K and is predicted by DFT to be a Z2 nontrivial topological metal with saddle-point van Hove singularities near the Fermi level.","lead":"Al13Os4, a periodic approximant of a decagonal quasicrystal, becomes a bulk superconductor at about 5.47 K, the highest transition temperature seen in any quasicrystal or approximant so far. The paper combines resistivity, magnetization, specific heat, muon spin rotation, and density-functional calculations to argue the material also has a nontrivial Z2 electronic topology with spin-polarized surface states.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The Z2=1 claim applies the Fu-Kane parity criterion to a gapless metal without proving its validity; the parity product depends on an arbitrary choice of occupied bands and is therefore not a well-defined topological invariant.","rationale":"The reader's weakest_assumption is exactly the point I consider most load-bearing: the topological invariant is computed with a method whose assumptions are not met. The superconductivity claim has independent support from resistivity, magnetization, specific heat, and muSR, and none of my concerns affect that evidence. The combined headline claim, however, is 'superconductivity in a nontrivial Z2 approximant quasicrystal'; without a valid Z2 invariant, the paper becomes a solid superconducting-metal report rather than a demonstration of topological superconductivity. The parity-based argument in the text and Fig. 3(d) is not a minor technicality: the parity product over arbitrarily chosen 'valence bands' can yield different values depending on the energy cutoff, and the statement that 'either γ2 or γ3' works is itself evidence that the result is not unique. In a metal with multiple Fermi sheets, there is no natural occupied manifold for the Fu-Kane formula unless a global gap is proved. The proposed check directly tests whether the invariant is stable under an extended or shifted set of bands. Since the reader already conditioned the verdict on this concern, my finding does not change the verdict.","tokens_in":11115,"tokens_out":5511,"duration_ms":57531,"concrete_test":"Recompute the parity eigenvalues for all eight time-reversal-invariant momenta using the full set of occupied bands determined by the Fermi level (not the preselected γ1-3 set), and repeat with the Fermi level shifted by ±10 meV. If the resulting parity product changes, or if the number of occupied bands is not identical at all TRIM points, the Z2 invariant is cutoff-dependent and the claim of a well-defined Z2=1 is invalid. An independent cross-check is to compute the non-Abelian Wilson-loop spectrum for the full manifold of bands crossing the Fermi level; a gapless Wilson spectrum would show that the parity computation does not define a valid topological invariant.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central topological claim, Z2=1 for Al13Os4, is derived in the section on electronic structure and topology by applying the Fu-Kane parity criterion [28] to a set of bands labeled γ1-3. That criterion is proven for inversion-symmetric insulators, where a global gap separates occupied and empty states and the number of occupied bands is constant throughout the Brillouin zone. In Al13Os4, however, the same section states explicitly that four bands (γ1-4) cross the Fermi level and form open Fermi sheets. The system is a metal; there is no global gap, and the number of occupied bands changes across the Fermi surface. The paper asserts that spin-orbit coupling gaps out nodal crossings and yields a continuous local bandgap at each k-point, but a local gap between particular pairs of bands does not define a filled subspace that can be used in the parity formula. The authors then state that the product yields Z2=1 when either γ2 or γ3 bands are considered as valence bands, revealing the cutoff-dependence: in a metal, attribution of a band as 'valence' is arbitrary. If the parity product changes when γ4 is included or when the chemical potential is shifted, the invariant is not a property of the material. Consequently, the nontrivial Z2 and the interpretation of the observed surface states as topological are not established by the presented calculation, even though the bulk superconductivity evidence is independent and convincing.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"Meena et al. report the discovery of superconductivity in the monoclinic decagonal-quasicrystal approximant Al13Os4. The paper presents resistivity, magnetization, specific heat, and muon spin rotation/relaxation data showing a bulk superconducting transition at Tc = 5.47(2) K, a weak-coupling fully gapped superconducting state with gap ratios Δ(0)/kBTc = 1.72(1) and 1.78(6) from specific heat and TF-μSR, respectively, and preserved time-reversal symmetry from ZF-μSR. First-principles calculations are used to propose that the material is a Z2 nontrivial metal with spin-polarized surface states and 3D saddle-point van Hove singularities near the Fermi level. The authors conclude that Al13Os4 is the first decagonal approximant combining bulk superconductivity with nontrivial topology.","tokens_in":11482,"tokens_out":10346,"duration_ms":101378,"significance":"The experimental superconductivity evidence is strong and internally consistent: four independent bulk probes give consistent transition temperatures, the specific-heat and TF-μSR gap ratios agree with each other and with weak-coupling BCS, and ZF-μSR directly addresses the time-reversal-symmetry question. If the topological part is correct, the paper would report the highest Tc among quasicrystals/approximants and a rare combination of bulk superconductivity and nontrivial topology, making Al13Os4 a promising platform for studying proximity-induced topological superconductivity. The DFT work also identifies an interesting saddle-point van Hove structure near Ef. The main weakness is that the Z2=1 claim is not rigorously justified for a gapless metal; this is a load-bearing part of the central claim as stated and needs to be either strengthened or explicitly softened.","major_comments":[{"comment":"The derivation of Z2=1 is not rigorous for a gapless metal. The text states that four bands γ1–γ4 cross the Fermi level and form open Fermi sheets, so the system has no global gap and no constant number of occupied bands across the Brillouin zone. The Fu–Kane parity criterion [28] is proven for inversion-symmetric insulators, where the occupied subspace is a well-defined vector bundle. A 'continuous bandgap at each k-point' between selected pairs of bands does not define a filled subspace suitable for the parity formula. The authors' own statement that the product gives Z2=1 'when either γ2 or γ3 bands are considered as valence bands' reveals a cutoff dependence, and the table in Fig. 3(d) omits γ4, which also crosses EF. To support this claim, the authors must either compute a well-defined topological invariant for a metal (for example, Wannier charge centers or Wilson loops with an explicit and robust energy window) or provide a rigorous argument that the parity product over all occupied bands is well defined and independent of the arbitrary choice of valence bands. Without this, the nontrivial Z2 and the topological interpretation of the surface states are not established.","section":"Electronic structure and topology (Fig. 3(d))"},{"comment":"The surface-state interpretation depends on the bulk invariant. In a multi-band metal with open Fermi sheets, surface bands crossing EF can be ordinary surface resonances, and the spin texture alone does not establish a topological origin. The authors should show the projected bulk continuum and demonstrate that the surface crossing is protected (for example, by the bulk invariant or by the number of surface branches at time-reversal invariant momenta). This point is not independent of the first comment, but it should be addressed explicitly if the topological surface-state claim is retained.","section":"Electronic structure and topology, Figs. 3(f)–(g)"}],"minor_comments":[{"comment":"The integrand as typeset ('EdEp') is garbled; it should read E dE / sqrt(E^2 − Δ(T)^2).","section":"μSR results, Eq. (2)"},{"comment":"'Kadowski-Woods ratio' should be 'Kadowaki-Woods ratio'.","section":"Bulk superconductivity"},{"comment":"'decagonal QC approximent' should be 'decagonal QC approximant'.","section":"Summary and discussion"},{"comment":"The Uemura plot places Al13Os4 close to the unconventional regime, while the text concludes weak-coupling conventional BCS; a sentence explaining that the Uemura classification is heuristic and does not by itself signal unconventional pairing would remove an apparent contradiction.","section":"μSR results, Fig. 2(f)"},{"comment":"The band labels are inconsistent between text and figure: the text uses γ1–γ4, while the figure labels include γ0, γ2, and γ4; please harmonize the notation.","section":"Electronic structure and topology, Fig. 3(a)"}],"recommendation":"major_revision","confidential_remarks":"The experimental superconducting study is solid and likely publishable. The requested revision should focus on the topological claim: either provide a well-defined Z2 invariant for this metal or downgrade the topological statements to a prediction and soften the title/abstract accordingly."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. The superconductivity part is real and well documented; Al13Os4 is a bulk weak-coupling BCS superconductor at 5.47 K with consistent evidence from resistivity, magnetization, specific heat, and muSR. The topological part is not yet established: the Z2=1 claim uses Fu-Kane parity on a metal with four bands crossing the Fermi level, and the paper's own text admits the answer depends on which bands you treat as valence. That is a load-bearing flaw in the title and the abstract.\n\nWhat is genuinely new: this is the first decagonal approximant superconductor and the highest Tc in the quasicrystal/approximant family. The DFT work on this specific compound, including van Hove singularities, is new. The experimental methods are solid: four independent probes give Tc about 5.45 K, the gap ratios from specific heat (1.72(1)) and muSR (1.78(6)) agree, and ZF-muSR shows preserved time-reversal symmetry. That is a convincing superconducting-core story.\n\nThe soft spot is exactly the Z2 calculation. The paper says SOC opens a continuous bandgap at each k-point, then computes parity products for bands γ1-3, and finds Z2=1 'when either γ2 or γ3 bands are considered as valence bands.' That phrasing is a red flag. In a metal there is no canonical set of occupied bands; the parity product is cutoff-dependent. The authors do not show the result is stable against including γ4 or shifting the chemical potential. So the nontrivial Z2 and the interpretation of the surface states as topological are unsupported. This is not a minor typo; it is the second half of the central claim.\n\nA secondary concern: the data availability statement says data are in the paper/SM and 'may be requested' from the corresponding author. For a paper this heavy on fitting, a repository link would be better. That is minor.\n\nBottom line: the experimental discovery deserves publication and a serious referee. The topology section needs either a rigorous justification of the Z2 invariant in a metallic band structure or a clear caveat that the invariant is provisional. I would send to peer review, with the expectation of heavy revision on the topological part.","headline":"Solid superconductivity discovery, but the Z2=1 topological claim is not yet justified for a metal with multiple Fermi crossings.","tokens_in":12030,"tokens_out":3027,"would_cite":true,"duration_ms":29498,"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":"Al13Os4 is claimed to be a bulk superconductor at 5.47 K and a predicted Z2 topological metal, the first quasicrystal approximant to combine both.","keywords":["quasicrystal approximant","superconductivity","Z2 topological metal","van Hove singularity","muon spin rotation","first-principles calculations","Al13Os4","BCS superconductor"],"falsifier":"Spin-resolved ARPES on the (001) surface should reveal the predicted spin-momentum-locked surface states crossing the Fermi level; their absence would falsify the Z2 = 1 claim. A simpler calculation check: verify that spin-orbit coupling opens a finite gap at every k-point in the Brillouin zone, since the parity product is only defined when such a gap exists.","tokens_in":10921,"feed_emoji":"⚛️","tokens_out":8787,"duration_ms":69237,"temperature":0.7,"pith_summary":"The paper reports that Al13Os4, a monoclinic approximant of the decagonal quasicrystal, becomes a bulk superconductor at 5.47 K and, according to first-principles calculations, is simultaneously a Z2 nontrivial topological metal. If correct, this makes Al13Os4 the first quasicrystal or approximant to show both bulk superconductivity and a predicted nontrivial topological electronic structure, and the highest superconducting transition temperature reported in this class of materials. The authors support the superconducting claim with resistivity, magnetization, specific heat, and muon spin rotation measurements, which point to weak-coupling BCS pairing with preserved time-reversal symmetry. They also identify three-dimensional saddle-point van Hove singularities with substantial flat dispersion near the Fermi level, which they argue can enhance the superconducting instability.","feed_headline":"Al13Os4: a 5.47 K superconductor with nontrivial Z2 topology","feed_subtitle":"Bulk BCS superconductor and predicted topological metal make it a platform for topological superconductivity in quasicrystals.","key_machinery":"The central machinery has three parts: (1) the monoclinic C2/m approximant structure made of two quasiperiodic layers, which gives a periodic unit cell on which ordinary band theory can be used; (2) the parity-based Z2 invariant, applied after spin-orbit coupling opens a local gap at every k-point, which yields Z2 = 1 and predicts topological surface states; (3) the three-dimensional saddle-point van Hove singularity at the Fermi level, whose flat dispersion raises the density of states and is argued to enhance superconductivity. The surface states and spin texture are computed from a Wannier-based tight-binding model, while the experimental characterization pins down the superconducting parameters.","core_discovery":"Al13Os4 is a bulk, type-II, weak-coupling BCS superconductor with Tc = 5.47(2) K, established by resistivity, magnetization, specific heat, and muon spin rotation measurements; the same compound is, by symmetry and electronic structure analysis, a Z2 nontrivial topological metal with spin-momentum-locked surface states crossing the Fermi level. The paper further identifies three-dimensional saddle-point van Hove singularities with large flat energy dispersion near the Fermi level, which it argues can enhance the superconducting transition temperature, and it reports preserved time-reversal symmetry in the superconducting ground state.","pith_inferences":["If the parity-based topological invariant is accepted for this gapless metal, similar approximants of decagonal quasicrystals containing heavy elements may systematically combine superconductivity and nontrivial topology; scanning other Al–TM approximants would test this prediction.","The authors note that the calculated Sommerfeld coefficient is only 60% of the measured value, which could signal stronger mass renormalization than phonons alone; treating the van Hove flat bands with correlated-electron methods may reveal whether the pairing is purely phononic.","The topological claim itself is not independently verified by experiment; spin-resolved ARPES on the (001) surface, or an explicit calculation of the invariant that does not rely on a gapped-insulator criterion, would settle whether Al13Os4 is truly Z2 nontrivial."],"forward_implications":["Al13Os4 becomes the highest-transition-temperature superconductor reported among quasicrystals and approximants, at 5.47 K with weak-coupling BCS pairing.","If the Z2 = 1 assignment holds, the (001) surface should host spin-polarized conducting states that are proximitized by the bulk superconductivity, giving a concrete route to topological superconductivity and possibly Majorana modes in vortex cores.","The presence of saddle-point van Hove singularities near the Fermi level implies that shifting the chemical potential by doping or pressure could tune the superconducting transition temperature, making this compound a tunable platform.","The fully gapped, clean-limit s-wave gap and preserved time-reversal symmetry measured by muon spin rotation rule out several unconventional pairing scenarios and support phonon-mediated superconductivity in a quasicrystalline approximant."],"supporting_citations":[{"why":"Supplies the parity criterion for computing the Z2 invariant in inversion-symmetric insulators, applied here to the local SOC gap of Al13Os4.","marker":"[28]"},{"why":"Reports the discovery of superconductivity in an icosahedral quasicrystal, providing the low-Tc baseline this paper compares against.","marker":"[15]"},{"why":"Reports superconductivity in a van der Waals layered quasicrystal, the other 2D quasicrystal superconductor used for comparison.","marker":"[16]"},{"why":"Establishes the monoclinic approximant crystal structure of Al13Co4-type, which Al13Os4 isostructurally adopts.","marker":"[22]"},{"why":"Generates the material-specific Wannier tight-binding model from the DFT wavefunctions, used for surface-state calculations.","marker":"[38]"},{"why":"Provides the iterative Green's function method used to compute the (001) surface states and spin texture.","marker":"[39]"},{"why":"Theoretical work on superconductivity on a quasiperiodic lattice, cited as the framework for possible non-BCS pairing that the paper argues against.","marker":"[12]"},{"why":"Specific-heat study of an icosahedral approximant superconductor, used as a reference for thermodynamic parameters.","marker":"[13]"}],"fun_headline_variants":["Al13Os4: topological superconductor in quasicrystal form","Quasicrystal Al13Os4 superconducts at 5.47 K with Z2 topology","5.47 K superconductor in Al13Os4 with Z2=1 topology","Z2 nontrivial superconductor in Al13Os4 quasicrystal","Al13Os4: superconducting topological quasicrystal"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The topological claim depends on treating a metal with several bands crossing the Fermi level as though it were a fully gapped insulator when computing the parity-based Z2 invariant, and on choosing which bands count as valence bands.","fun_headline_variants_meta":{"raw":{"variants":["Al13Os4: topological superconductor in quasicrystal form","Quasicrystal Al13Os4 superconducts at 5.47 K with Z2 topology","5.47 K superconductor in Al13Os4 with Z2=1 topology","Z2 nontrivial superconductor in Al13Os4 quasicrystal","Al13Os4: superconducting topological quasicrystal"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.003041,"raw_usage":{"total_tokens":11495,"prompt_tokens":891,"completion_tokens":10604,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":507,"completion_tokens_details":{"reasoning_tokens":10501}},"tokens_in":507,"tokens_out":10604,"duration_ms":67439,"temperature":1.0,"reasoning_tokens":10501,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T22:48:36.011028+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Spin-resolved ARPES on the (001) surface should reveal the predicted spin-momentum-locked surface states crossing the Fermi level; their absence would falsify the Z2 = 1 claim. A simpler calculation check: verify that spin-orbit coupling opens a finite gap at every k-point in the Brillouin zone, since the parity product is only defined when such a gap exists.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Reports the discovery of superconductivity in an icosahedral quasicrystal, providing the low-Tc baseline this paper compares against."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Reports superconductivity in a van der Waals layered quasicrystal, the other 2D quasicrystal superconductor used for comparison."},{"cited_title":"& Steurer, W","cited_arxiv_id":null,"evidence_quote":"Establishes the monoclinic approximant crystal structure of Al13Co4-type, which Al13Os4 isostructurally adopts."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Generates the material-specific Wannier tight-binding model from the DFT wavefunctions, used for surface-state calculations."},{"cited_title":"& Soluyanov, A","cited_arxiv_id":null,"evidence_quote":"Provides the iterative Green's function method used to compute the (001) surface states and spin texture."},{"cited_title":"& Arita, R","cited_arxiv_id":null,"evidence_quote":"Theoretical work on superconductivity on a quasiperiodic lattice, cited as the framework for possible non-BCS pairing that the paper argues against."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Specific-heat study of an icosahedral approximant superconductor, used as a reference for thermodynamic parameters."}],"review_version":1}