{"id":"ad73dfea-d759-4d2e-917a-2c2a1b00a0dc","arxiv_id":"2508.03427","paper_version":2,"verdict":"REJECT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":3,"one_line_summary":"Bulk FeSe becomes a predicted strong topological insulator when C4 symmetry is broken by uniaxial strain or by the low-temperature orthorhombic distortion.","lead":"This paper predicts that breaking the fourfold rotation symmetry of bulk FeSe, by squeezing it or by cooling through its structural transition, turns it into a strong topological insulator. If right, strain becomes a practical switch for topological physics in a famous superconductor family.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The strong-TI claim depends on an unproven global gap: the shown ≈0.1 meV gap is below the 0.05 eV DFT smearing and no full-BZ check is given, so the symmetry indicators may label a semimetal rather than an insulator.","rationale":"We read the paper in good faith: the authors ask whether lowering the crystal symmetry from C4 to D2h can gap out the FeSe bands and produce a strong TI. If a global gap existed, the TQC/SI analysis would be a legitimate route. The paper is careful in some respects: it uses fully relativistic VASP, Wannier interpolation, and cscDMFT, and it explicitly flags that non-local correlations could destroy the topology. However, the entire strong-TI claim hinges on a gap at the Fermi level, and the evidence for that gap is thinner than any other step. The 0.1 meV quoted for the orthorhombic case is more than 500 times smaller than the 0.05 eV broadening used in the DFT runs and is at the limit of numerical reliability; even if real, it is far below the energy scale of correlations, which the paper's own DMFT analysis cannot resolve. The absence of a full-BZ gap map is decisive: symmetry indicators are global invariants and require an isolated band manifold. A semimetal with a small avoided crossing along Γ–Z would give the same parity products without being a TI. The reader's REJECT verdict is therefore supported; if the authors can demonstrate a robust global gap (and a Wilson-loop Z2 of 1), the conclusion could be resurrected, so a conditional acceptance after such a check would be a reasonable alternative. We agree with the reader's weakest assumption and see no additional independent support that would overturn it.","tokens_in":14054,"tokens_out":10898,"duration_ms":129626,"concrete_test":"Recompute the strained (SG 59) and orthorhombic (SG 67) cases from the provided structures (or Wannier models) and evaluate min_k [E29(k) − E28(k)] on a dense uniform k-mesh (e.g., 40×40×40 in the full BZ, or Wannier-interpolated). Also compute the Z2 invariant via Wilson loop on a 2D plane. If the minimum direct gap is negative (band overlap) or below ~1 meV and changes sign/order under k-mesh refinement or smearing, the global-gap premise fails and the strong-TI claim is unsupported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—that breaking C4 turns bulk FeSe into a strong TI at 28-electron filling—requires a direct gap between bands 28 and 29 throughout the entire Brillouin zone. The paper does not establish this. Figs. 2 and 3 display only high-symmetry paths; the only quantitative gap quoted is ≈0.1 meV (Fig. 3c inset), two orders of magnitude below the 0.05 eV Gaussian broadening used in the VASP runs (Methods) and below typical DFT/pseudopotential accuracy. No Fermi surface or full-BZ gap map is provided. The paper itself states that in the tetragonal phase no gap exists and a topological classification is not well-defined; for the strained (SG 59) and orthorhombic (SG 67) phases the same classification is applied on the strength of a sub-meV gap along Γ–Z. Since symmetry indicators z2w,3 and z4 are only meaningful for an isolated set of occupied bands, a gap closure at generic k would invalidate the strong-TI label. The DMFT section further concedes that non-local correlations, known to be important in FeSe, could destroy the topology; with a 0.1 meV DFT gap, even moderate correlation-induced shifts could close it. Thus the load-bearing premise is an unverified global insulating gap.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper predicts that breaking the C4 rotational symmetry in FeSe—either by in-plane uniaxial strain (SG 59) or by the tetragonal-to-orthorhombic structural transition (SG 67)—drives the 28-electron filling into a strong Z2 topological insulator. The authors support this with DFT+SOGGA band structures, topological quantum chemistry and symmetry indicators, Wannier-based surface spectral functions, and charge-self-consistent DMFT calculations. They report z2w,3=1 and z4=1 for both C4-broken structures, interpret this as a strong TI phase, and argue that correlations do not destroy the topology.","tokens_in":14347,"tokens_out":7524,"duration_ms":91391,"significance":"If the central claim holds, the paper identifies a simple experimental knob—uniaxial strain or temperature—for turning bulk FeSe into a strong topological insulator, a result that would be valuable in the iron-based superconductor and topological-matter communities. The manuscript uses a standard and appropriate toolbox (TQC, symmetry indicators, WannierTools, cscDMFT) and provides a NOMAD dataset, which are strengths. However, the entire strong-TI claim rests on the existence of a bulk gap at 28-electron filling that is not established globally: the only quantitative gap quoted is about 0.1 meV in the orthorhombic case, which is two orders of magnitude below the 0.05 eV Gaussian broadening used in the VASP calculations and below typical DFT accuracy. Without a full-Brillouin-zone gap verification, the symmetry indicators may label a semimetal rather than an insulator.","major_comments":[{"comment":"The strong-TI classification at 28-electron filling requires a global direct gap between bands 28 and 29 throughout the entire Brillouin zone. The paper shows band structure only along the Γ–Z path (Figs. 2 and 3) and quotes a gap of ≈0.1 meV only in the orthorhombic inset (Fig. 3c). The VASP calculations use a Gaussian broadening of 0.05 eV (Methods), which is five hundred times larger than the reported gap; no full-BZ direct-gap map or Fermi-surface plot is provided. If the bands touch at any generic k point, the symmetry indicators z2w,3=1 and z4=1 label a semimetal rather than an insulator, and the strong-TI interpretation collapses. Please provide a dense-k direct-gap calculation and a Fermi-surface view for both C4-broken structures, and report the gap size for the strained case as well.","section":"Electronic structure at ambient pressure and low temperature; Fig. 3c; Methods"},{"comment":"The DMFT analysis does not compute a topological invariant; it argues from spectral functions that no new crossings appear and that the bands remain identifiable with the DFT bands. Given that the DFT gap is ≈0.1 meV, even moderate correlation-driven shifts—from double counting, orbital-selective renormalization, or non-local self-energy effects—could close it. The manuscript itself concedes that non-local correlations, known to be important in FeSe, could destroy the topology. This is not a peripheral caveat: the robustness claim in the abstract requires a quantitative demonstration that the gap survives correlations, for example by computing the DMFT spectral gap or the renormalized direct gap over the full Brillouin zone.","section":"DFT+DMFT calculations"},{"comment":"The low-temperature orthorhombic phase is the experimentally realized phase of FeSe, which is a superconductor with hole and electron Fermi pockets. The paper does not reconcile its predicted gapped strong-TI state at 28 electrons with the well-established metallic/superconducting character of bulk FeSe in this phase. This is a load-bearing tension: if the real material has Fermi surfaces, the symmetry indicators are not a valid strong-TI label. The authors need to address this explicitly, for example by showing that the calculated DFT bands are consistent with ARPES Fermi surfaces and by explaining how a sub-meV gap can coexist with the measured metallicity.","section":"Electronic structure at ambient pressure and low temperature"},{"comment":"The paper correctly states that in the tetragonal phase the topological classification is not well-defined because no gap exists near the Fermi level. The same criterion must be applied to the C4-broken phases: the occupied 28-band subspace must be isolated from band 29 over the entire Brillouin zone, not just along Γ–Z. In addition, a 0.1 meV gap is below the numerical precision of the DFT setup (functional, pseudopotential, vdW correction, smearing); the authors should test sensitivity of the gap to these choices and verify that the Wannier-interpolated tight-binding model reproduces the direct gap before using it for surface-state calculations.","section":"Symmetry indicators; Table I"}],"minor_comments":[{"comment":"The caption says that surface Dirac cones are present in all three structures 'due to the strong Z2-odd topology,' while the main text states that the unstrained tetragonal phase is not a strong TI and its Dirac cone is not topologically protected. Please revise the caption to distinguish protected and unprotected surface states.","section":"Fig. 4 caption"},{"comment":"The sentence 'All simulation data is provided in a NOMAD dataset [ ? ]' contains an unresolved reference; please supply the dataset identifier.","section":"Methods"},{"comment":"The abstract and text claim that both uniaxial compression and expansion induce topology, but Table I and the band-structure figures report only a 1% compressive strain. Please show results for expansion (or state that expansion has the same effect with evidence) and, ideally, map the topological phase as a function of strain magnitude.","section":"Compression along the a1 axis; Table I"},{"comment":"The sentence 'z2w,3=1 ... although the weak index is odd, indicates a strong TI phase because the z4 index is odd' would benefit from a brief reminder of the SI convention used (e.g., how z4 alone gives the strong index), since the weak index alone would suggest a weak TI.","section":"Symmetry indicators"},{"comment":"The phrase 'The band coloring are a guide to the eye' should be corrected to 'The band coloring is a guide to the eye,' and the caption of Fig. 2 should state explicitly which path is shown and why only that path is displayed.","section":"Figs. 2 and 3 captions"}],"recommendation":"major_revision","confidential_remarks":"The stress-test concern is valid and central: the strong-TI claim depends on a global gap that is not demonstrated. I recommend major revision rather than rejection because the missing full-BZ gap calculation and Fermi-surface check are within the scope of the manuscript's methods and could settle the issue. Please ask the authors to provide these calculations and to address the experimental metallicity of the orthorhombic phase before resubmission."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper proposes something genuinely new: that breaking the C4 axis, either by uniaxial strain or by the existing orthorhombic transition, turns bulk FeSe into a strong topological insulator at 28-electron filling. To my knowledge this is the first TQC/symmetry-indicator classification of exactly those two structures, and the mechanism—symmetry lowering forces hybridizations that open a gap along Γ–Z—is clean and physically motivated. The DFT+DMFT section is a real effort to address correlations, and the authors are honest about its limits, explicitly conceding that non-local correlations could destroy the topology. That honesty is worth crediting.\n\nBut the load-bearing assertion is a global bulk gap between bands 28 and 29, and the paper never shows one. The band structures in Figs. 2 and 3 are along high-symmetry paths only. The only quantitative gap quoted is ≈0.1 meV in the orthorhombic inset of Fig. 3c, which is two orders of magnitude below the 0.05 eV Gaussian broadening used in the VASP runs and below any reasonable DFT accuracy. There is no Fermi surface, no full-BZ gap map, and no direct-gap minimum from the Wannier model. Since the tetragonal parent is a semimetal, the plausible default is that the strained and orthorhombic phases remain semimetallic with a tiny gap or a small band overlap somewhere generic, which would make the z2w,3=z4=1 indicators meaningless. The authors do note that in the tetragonal case the classification is ill-defined, but they never apply the same scrutiny to the C4-broken cases.\n\nThe paper also has a reproducibility leak: the NOMAD dataset is referenced only as a placeholder “[ ? ]” in the Methods. That should be fixed before anything else.\n\nSo where does this leave us? The idea is worth taking seriously, and the authors have done the standard TQC analysis correctly as far as it goes. The missing global-gap check is fixable—compute the direct gap over the full BZ from the Wannier interpolation, plot the Fermi surface, and, if the gap survives, the prediction becomes significant. As it stands, I would not cite the strong-TI claim. I would send it to peer review, because a good referee can force that check, and the question—can strain make bulk FeSe a strong TI—is interesting enough to deserve a careful answer.","headline":"Interesting prediction, but the strong-TI claim hinges on a global gap that the paper never actually demonstrates; the only quoted gap is ~0.1 meV along Γ–Z, below the 0.05 eV smearing, so the symmetry indicators may be labeling a semimetal.","tokens_in":14923,"tokens_out":1514,"would_cite":false,"duration_ms":18078,"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":"Strain turns FeSe into a strong topological insulator.","keywords":["FeSe","iron-based superconductor","strong topological insulator","symmetry indicators","uniaxial strain","orthorhombic phase","DFT+DMFT","surface Dirac cone"],"falsifier":"Compute the full-Brillouin-zone band structure of the relaxed strained (SG 59) and orthorhombic (SG 67) structures and check whether a direct gap separates the 28th and 29th bands at every k-point; if those two bands overlap in energy anywhere in the zone, the symmetry indicators no longer certify a strong insulator, and the predicted protected surface cone should be absent. The experimental counterpart is angle-resolved photoemission on orthorhombic FeSe below the roughly 90 K transition, which should show a surface Dirac cone near the Fermi level at the zone center if the claim is right.","tokens_in":2140,"feed_emoji":"⚛️","tokens_out":2521,"duration_ms":153310,"temperature":0.7,"pith_summary":"The paper claims that breaking the fourfold rotational symmetry of bulk FeSe — by in-plane uniaxial strain or by the natural transition to the low-temperature orthorhombic phase — drives the material into a strong topological insulator, a phase with a protected Dirac cone on every surface. The evidence is a symmetry-indicator analysis of density-functional band structures: the strained (space group 59) and orthorhombic (space group 67) structures both yield nonzero indicators at the 28-electron filling, while the high-temperature tetragonal structure (space group 129) cannot even be classified because no gap opens there. Dynamical mean-field calculations with $U = 4.6$ eV show that correlations renormalize the relevant bands by about a factor of 2.4 but introduce no new crossings, so the authors conclude the topological labels survive strong correlations. A sympathetic reader would care because strain is a practical, already-available knob, and because the same calculation says bulk FeSe below its roughly 90 K structural transition is already in the predicted phase at ambient pressure.","feed_headline":"Strain flips FeSe into a strong topological insulator","feed_subtitle":"A 1% in-plane squeeze, or crossing the 90 K structural transition, puts bulk FeSe in a strong-TI phase.","key_machinery":"The load-bearing object is the symmetry-indicator classification of the occupied bands, computed from the irreducible representations of the electronic states at time-reversal-invariant momenta. Concretely, the mechanism is the subduction of the two-dimensional little-group irreps at $\\Gamma$ and $Z$ ($\\bar{\\Gamma}_6/\\bar{\\Gamma}_7$ and $\\bar{\\Gamma}_8/\\bar{\\Gamma}_9$ in the tetragonal phase) into one-dimensional irreps once the $C_4$ axis is lost; with only one irrep available along $\\Gamma$–$Z$, the previously non-hybridizing bands can mix, a gap can open, and the symmetry indicators — here the weak index $z_{2w,3}$ and the strong index $z_4$ — become well-defined and nonzero, certifying that the 28 occupied bands cannot be decomposed into atomic-limit bands. Slab Green's function calculations then turn this algebraic statement into a concrete observable: a two-dimensional Dirac cone on the $(001)$ surface.","core_discovery":"The central claim is that the fourfold rotation axis in FeSe's tetragonal structure is what prevents a topological phase: its little-group irreps at the $\\Gamma$ and $Z$ points cannot hybridize, no gap can open at the Fermi filling, and the symmetry indicators are trivial. Once $C_4$ is broken, those two-dimensional irreps subduce to one-dimensional irreps that hybridize, the band structure along $\\Gamma$–$Z$ gaps out, and the occupied bands at filling 28 can no longer be expressed as a positive sum of atomic-limit (elementary) band representations. The authors compute symmetry indicators from inversion eigenvalues and find $z_{2w,3} = 1$ and $z_4 = 1$ for both the strained tetragonal (SG 59) and the orthorhombic (SG 67) structures, which they read as a strong topological insulator with a protected surface Dirac cone, in contrast to zero indicators in the unstrained tetragonal structure. They add evidence from a slab calculation showing a Dirac cone at the top surface for all three structures, protected only in the $C_4$-broken ones, and from charge-self-consistent DFT+DMFT calculations indicating that the near-Fermi bands are renormalized but keep their order, so correlations do not close the classifying gap. The unstrained ambient tetragonal phase, by contrast, has no gap at the Fermi level and no well-defined topological classification.","pith_inferences":["The practical corollary the authors leave implicit: if bulk FeSe is a strong topological insulator below roughly 90 K and also superconducts, the protected surface Dirac cone coexists with the superconducting gap, which would make $C_4$-broken FeSe a candidate platform for topological superconductivity and Majorana bound states in the spirit of the Fe(Se,Te) proposals the paper cites.","The orthorhombic classification rests on a quoted gap of about 0.1 meV along a single symmetry line; thermal energies near the roughly 90 K transition are orders of magnitude larger, so the phase realized in experiments is more likely a nearly gapless topological semimetal whose surface states appear as weak spectral features.","The same symmetry argument should transfer to other iron pnictide and chalcogenide superconductors with orthorhombic (nematic) low-temperature phases: any member at the equivalent filling whose symmetry-broken structure opens a gap should acquire the same nonzero indicators.","Because the indicators derive from inversion eigenvalues at a handful of momenta, a computationally cheap next check is a strain and anion-height scan, tuning the Se height (a known lever on the $\\Gamma$–$Z$ dispersion) to map the topological phase boundary and the size of the gap that carries it."],"forward_implications":["Applying roughly 1% in-plane uniaxial compression or expansion along an Fe–Fe axis should take bulk FeSe from a metal with trivial indicators to a strong topological insulator at the same 28-electron filling.","Because the low-temperature orthorhombic structure yields the same nonzero indicators, bulk FeSe below its roughly 90 K structural transition is predicted to already be a strong topological insulator at ambient pressure.","The $(001)$ surface of the strained or orthorhombic crystals should host a Dirac cone near the Fermi level, whereas the similar cone found in the high-temperature tetragonal structure is not topologically protected.","Charge-self-consistent dynamical mean-field calculations renormalize the Fermi-level bands by a factor of about 2.4 without introducing new crossings, so the topological labels are not a one-electron artifact.","Strain is thereby established, alongside chemical substitution, as a tunable mechanism for inducing topological phases in the FeSe family."],"supporting_citations":[{"why":"Establishes the topological-quantum-chemistry criterion used to decide whether the occupied bands can be expressed as atomic-limit combinations.","marker":"[57]"},{"why":"Supplies the symmetry-indicator formalism and database used to assign the strong-TI label from the computed irreps.","marker":"[58]"},{"why":"Defines the $Z_2$ weak index $z_{2w,3}$ and the $z_4$ indicator, with the odd-$z_4$ condition identifying a strong topological insulator.","marker":"[59]"},{"why":"Provides the experimental basis for in-plane uniaxial strain on FeSe as the symmetry-breaking knob.","marker":"[56]"},{"why":"Supplies the experimental tetragonal structure used to generate strained geometries and the Fe(Se,Te) band-inversion precedent this work extends to $C_4$-broken bulk FeSe.","marker":"[39]"},{"why":"Introduces the split elementary band representation, the concept used to show that the 16-to-20-electron block is an atomic-limit block while the 20-to-24-electron block is not.","marker":"[88]"},{"why":"Documents the ~90 K tetragonal-to-orthorhombic structural transition that motivates the ambient-pressure topological prediction.","marker":"[89]"},{"why":"Provides the angle-resolved photoemission benchmark against which DFT+DMFT is checked when the paper argues correlations preserve the near-Fermi band order.","marker":"[19]"},{"why":"Gives the monolayer FeSe surface-state reference used to assess the DMFT-renormalized Dirac cone position against experiment.","marker":"[49]"}],"fun_headline_variants":["Breaking C4 symmetry turns FeSe into a strong TI","Squeeze FeSe, and it becomes a topological insulator","FeSe's strong topology appears when C4 symmetry is broken","Strain or structural transition gives FeSe strong topology","Breaking FeSe's C4 symmetry yields a topological insulator"],"cache_read_input_tokens":16896,"weakest_assumption_plain":"A genuine energy gap separates the 28th and 29th bands across the whole Brillouin zone in the strained and orthorhombic structures, making the symmetry indicators physically meaningful; the paper shows this gap only along the $\\Gamma$–$Z$ line (about 0.1 meV in the orthorhombic case) and does not display the Fermi surface, while FeSe is experimentally a semimetal with Fermi pockets.","fun_headline_variants_meta":{"raw":{"variants":["Breaking C4 symmetry turns FeSe into a strong TI","Squeeze FeSe, and it becomes a topological insulator","FeSe's strong topology appears when C4 symmetry is broken","Strain or structural transition gives FeSe strong topology","Breaking FeSe's C4 symmetry yields a topological insulator"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000801,"raw_usage":{"total_tokens":3576,"prompt_tokens":1052,"completion_tokens":2524,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":668,"completion_tokens_details":{"reasoning_tokens":2442}},"tokens_in":668,"tokens_out":2524,"duration_ms":20220,"temperature":1.0,"reasoning_tokens":2442,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T04:27:49.688087+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the full-Brillouin-zone band structure of the relaxed strained (SG 59) and orthorhombic (SG 67) structures and check whether a direct gap separates the 28th and 29th bands at every k-point; if those two bands overlap in energy anywhere in the zone, the symmetry indicators no longer certify a strong insulator, and the predicted protected surface cone should be absent. The experimental counterpart is angle-resolved photoemission on orthorhombic FeSe below the roughly 90 K transition, which should show a surface Dirac cone near the Fermi level at the zone center if the claim is right.","supporting_citations":[{"cited_title":"Bradlyn, L","cited_arxiv_id":null,"evidence_quote":"Establishes the topological-quantum-chemistry criterion used to decide whether the occupied bands can be expressed as atomic-limit combinations."},{"cited_title":"Elcoro, B","cited_arxiv_id":null,"evidence_quote":"Supplies the symmetry-indicator formalism and database used to assign the strong-TI label from the computed irreps."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the $Z_2$ weak index $z_{2w,3}$ and the $z_4$ indicator, with the odd-$z_4$ condition identifying a strong topological insulator."},{"cited_title":"Nakajima, Y","cited_arxiv_id":null,"evidence_quote":"Provides the experimental basis for in-plane uniaxial strain on FeSe as the symmetry-breaking knob."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the experimental tetragonal structure used to generate strained geometries and the Fe(Se,Te) band-inversion precedent this work extends to $C_4$-broken bulk FeSe."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Documents the ~90 K tetragonal-to-orthorhombic structural transition that motivates the ambient-pressure topological prediction."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the angle-resolved photoemission benchmark against which DFT+DMFT is checked when the paper argues correlations preserve the near-Fermi band order."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the monolayer FeSe surface-state reference used to assess the DMFT-renormalized Dirac cone position against experiment."}],"review_version":1}