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REVIEW 4 major objections 5 minor 97 references

Symmetry-breaking-induced topology in FeSe

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Strain turns FeSe into a strong topological insulator.

desk verdict 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. read the letter →

arxiv 2508.03427 v2 pith:TM6IZVEE submitted 2025-08-05 cond-mat.mtrl-sci cond-mat.str-elcond-mat.supr-con

Mikel García-Díez , Jonas B. Profe , Augustin Davignon , Steffen Backes , Roser Valentí , Maia G. Vergniory This is my paper · ORCID
classification cond-mat.mtrl-scicond-mat.str-elcond-mat.supr-con
keywords FeSeiron-basedsuperconductorstrongtopologicalinsulatorsymmetryindicatorsuniaxialstrainorthorhombicphaseDFT+DMFTsurfaceDiraccone
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

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.

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 (4)
  1. [Electronic structure at ambient pressure and low temperature; Fig. 3c; Methods] 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.
  2. [DFT+DMFT calculations] 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.
  3. [Electronic structure at ambient pressure and low temperature] 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.
  4. [Symmetry indicators; Table I] 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.
minor comments (5)
  1. [Fig. 4 caption] 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.
  2. [Methods] The sentence 'All simulation data is provided in a NOMAD dataset [ ? ]' contains an unresolved reference; please supply the dataset identifier.
  3. [Compression along the a1 axis; Table I] 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.
  4. [Symmetry indicators] 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.
  5. [Figs. 2 and 3 captions] 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.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the topological indicators are computed by applying standard TQC/SI algorithms to independently computed DFT bands, with no target quantity fitted to define z4.

full rationale

The derivation chain is DFT band structure -> irrep data (IrRep) -> EBR decomposition and symmetry indicators (z2w,3, z4) -> strong-TI label. None of the inputs are chosen to force the output: the interaction parameters (U = 4.6 eV, J = 0.7 eV) are taken from prior literature and are not fitted to the topological claim; the symmetry indicators are direct functions of inversion eigenvalues at TRIMs; and no quantity defined in terms of z4 is used as an input. The closest self-referential element is that the classification relies on the same band calculation that defines the gap, which is normal in ab initio topology and does not reduce to a fit. The paper's own caveat that non-local correlations 'cannot fully rule out the possibility that these missing effect destroys the topology' is a limitation, not a circular step. The main vulnerability - that only a roughly 0.1 meV gap along Gamma-Z is shown and no full-Brillouin-zone gap map is provided - concerns the validity of applying symmetry-indicator labels to a possibly semimetallic DFT spectrum, which is a correctness risk rather than a circularity.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

No new particles or forces are introduced. The central claim rests on standard topological classification methods applied to DFT bands, plus two fragile modeling assumptions: the existence of a global gap at the Fermi level and the neglect of non-local correlations. The DMFT interaction parameters are imported from prior literature rather than fitted to the target result.

free parameters (3)
  • Uniaxial strain magnitude epsilon_xx = -1% (and -3% in Appendix)
    Chosen values of compressive strain along a1; the central claim that strain drives topology depends on this perturbation, and no critical strain is established beyond showing 1% and 3%.
  • Hubbard U (DMFT) = 4.6 eV
    Interaction parameter for Fe 3d orbitals taken from prior literature [80], not fitted here; the robustness conclusion depends on it.
  • Hund's J (DMFT) = 0.7 eV
    Same as U; together they parameterize the impurity problem in the DFT+DMFT calculations.
assumptions (5)
  • domain assumption DFT-GGA (PBESOL) plus SOC and vdW corrections accurately describes the low-energy band structure and gap of FeSe.
    The entire topological classification is performed on DFT band structures; FeSe is a strongly correlated metal where DFT is known to give wrong crystal structure and electronic properties (stated in Methods), yet the central TI claim uses DFT bands.
  • ad hoc to paper A global band gap exists at 28-electron filling in the strained and orthorhombic structures, making symmetry indicators z4=1 physically meaningful.
    The paper only shows bands along Gamma-Z and reports a ~0.1 meV gap in the orthorhombic inset; no full-BZ gap or Fermi surface is shown, and FeSe is experimentally metallic. This is the load-bearing premise for the strong-TI label.
  • standard math Topological Quantum Chemistry and the symmetry-indicator framework (z2w,3, z4) classify the topology correctly for the DFT band manifold.
    TQC and SIs are established methods [57-59]; no formal proof is needed, but their validity requires the gapped condition in the previous axiom.
  • ad hoc to paper Non-local correlations beyond DMFT do not close the topological gap or change the band ordering.
    The paper admits 'we cannot fully rule out the possibility that these missing effect destroys the topology' in the DMFT section; the robustness statement is an assumption, not a computed result.
  • domain assumption The DFT-derived strain tensor can be applied to the experimental structure to model realistic strained FeSe.
    Appendix A rescales the experimental structure using DFT relaxation ratios and does not relax the Se position because DFT gives a zSe significantly too small; internal coordinates are therefore approximated.

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Pith. "Pith review of Symmetry-breaking-induced topology in FeSe." pith.science (2026). https://pith.science/paper/TM6IZVEE

@misc{pith2026250803427,
  author       = {Pith},
  title        = {Pith review of: Symmetry-breaking-induced topology in FeSe},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TM6IZVEE}},
  note         = {Machine review of arXiv:2508.03427}
}
abstract

FeSe has been one of the most intensively studied iron-based superconductors over the past two decades, exhibiting a wide range of phenomena such as unconventional superconductivity, nematic order, magnetism, orbital-selective correlations, and structural phase transitions. While topologically non-trivial phases have been identified in certain cases -- such as Te-doped FeSe and monolayer FeSe -- topology in bulk FeSe has largely remained unexplored. In this work, we propose a new route to realize topological phases directly in bulk FeSe. We demonstrate that breaking the tetragonal $C_4$ rotational symmetry, thereby lowering the crystal symmetry, can drive FeSe into a strong topological insulating phase. To support this, we perform density functional theory calculations and analyze the band structure using Topological Quantum Chemistry and symmetry-based indicators. Our results show that both uniaxial strain and temperature-induced structural changes lead to non-trivial band topology. Moreover, incorporating electronic correlations through dynamical mean field theory reveals that the topological characteristics near the Fermi level remain robust, as the relevant bands experience only moderate renormalization. These findings highlight strain as a promising mechanism to induce topological phases in FeSe

Figures

Figures reproduced from arXiv: 2508.03427 by the authors.

Figure 1
Figure 1. FIG. 1. Atomic structure of FeSe. Strain is applied along the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Electronic band structure of FeSe under a) ambient conditions in the high temperature tetragonal phase, b) compressive [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Zoom in on the Γ [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Momentum resolved density of states for a semi-infinite slab in the [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Spectral functions of FeSe under ambient conditions in a) the high temperature tetragonal phase, b) compressive strain [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

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