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REVIEW 3 major objections 8 minor 48 references

Non-Trivial Topological Phase in the Sn_{1-x}In_xTe Superconductor

T0 review · 3 major / 8 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Indium-doped SnTe keeps its non-trivial topological phase up to $x = 0.25$, with a mirror Chern number of $-2$.

desk verdict A useful first-principles look at In-doped SnTe with a solid low-doping result, but the metallic-phase mirror Chern numbers are asserted without the required gap check. read the letter →

arxiv 1908.05967 v1 pith:3J4O3BAX submitted 2019-08-16 cond-mat.mtrl-sci

Tome M. Schmidt , G. P. Srivastava This is my paper · ORCID
classification cond-mat.mtrl-sci
keywords topologicalcrystallineinsulatormirrorChernnumberSn1-xInxTeindium-dopedtintelluridesuperconductorsurfacestatesbandinversionWannierchargecenter
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 aims to establish that the superconductor Sn$_{1-x}$In$_x$Te remains topologically non-trivial when indium substitutes for tin. It reports that the inverted band ordering at the fcc L point survives for indium fractions $x = 0.03125$, $0.125$, and $0.25$, and that the mirror Chern number is $n_M = -2$ for all three concentrations. The authors also identify pairs of (001) surface states carrying opposite mirror eigenvalues $\pm i$, and find that their Dirac crossing shifts away from the L point and their Fermi velocity grows as $x$ increases. If these results are right, Sn$_{1-x}$In$_x$Te is a concrete material in which superconductivity coexists with a non-trivial topological phase.

What carries the argument

The load-bearing method is the mirror Chern number $n_M$ computed with hybrid Wannier charge centers: the Wannier functions are built from first-principles band structures, and their charge-center winding on a mirror-invariant plane counts the net number of protected surface-state branches in each mirror subspace. The physical mechanism is band inversion at the fcc L point, where spin-orbit coupling swaps the p-anion and s-cation characters of the valence and conduction edges. The In-5s-derived state sits in or near the band gap, keeps the same [111]-oriented p character as the valence band maximum, and is used to explain why the inversion and the $n_M = -2$ invariant persist despite doping.

What would settle it

Repeat the Wannier-center calculation separately for the two mirror eigenvalue classes at $x = 0.125$ and $x = 0.25$. If either class of Wannier bands closes or cannot be followed continuously across the Brillouin zone, the winding that gives $n_M = -2$ is undefined, and those concentrations would be band-inverted metals rather than topological phases.

Watch

Extended reading notes

Core claim

On its own terms, the paper's central discovery is that the topological character of SnTe survives indium substitution. Spin-orbit coupling keeps the valence and conduction bands inverted at the L point for $x = 0.03125$, $0.125$, and $0.25$, even though the alloy becomes metallic for $x > 0.1$. The computed mirror Chern number is $n_M = -2$ for all three concentrations, and slab calculations show pairs of topological surface states on the (001) surface with mirror eigenvalues $+i$ and $-i$. The paper further finds that the In-5s impurity state sits near the Fermi level, its depopulation explains the experimentally observed transition from hole-like to electron-like carriers, and the near-Fermi density of states is dominated by In-5s, which the authors read as support for s-wave superconductivity.

Load-bearing premise

The results assume that the topological invariant used here remains well defined for the concentrations at which the alloy becomes a metal, even though no gap in the states the invariant counts is demonstrated for those concentrations.

Editorial extensions

If this is right

  • For $x = 0.03125$ the alloy remains a gapped p-type semiconductor with an In state inside the gap, so its $n_M = -2$ mirrors pristine SnTe and the surface Dirac states should be observable in the (001) gap.
  • For $x = 0.125$ and $x = 0.25$ the bulk is gapless, yet the paper still reports $n_M = -2$, implying that the non-trivial invariant is claimed to survive into the metallic regime.
  • As $x$ increases, the surface Dirac crossing moves farther from the projected L point and the hole Fermi velocity rises substantially, matching the trend seen in ARPES experiments on heavily doped samples.
  • The dominance of In-5s states at the Fermi level supports s-wave BCS pairing and explains the experimentally observed hole-to-electron crossover as the In-5s level depopulates.

Reading between the lines

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

  • If $n_M = -2$ truly survives in the metallic regime, the paper's Wannier-center calculation implicitly assumes the mirror subspaces stay gapped even when the total bulk is gapless; checking that subspace gap directly for $x = 0.125$ and $x = 0.25$ would separate a protected topological metal from a merely band-inverted one.
  • The monotonic increase in Fermi velocity with $x$ gives a quantitative prediction: ARPES on (001) surfaces at intermediate concentrations should find the Dirac crossing shifted away from the L point by roughly the paper's computed $k_D$ values.
  • The paper argues for s-wave pairing, but its own topological invariant suggests a natural next question the authors do not ask: whether the mirror symmetry protecting the surface states also protects a topological superconducting phase once the bulk becomes superconducting.
  • Because the In-5s state is both the main source of Fermi-level density of states and the cause of the carrier-sign change, doping that tunes the In-5s occupation should move $T_c$ in step with the density of states; correlating those two quantities experimentally would test the pairing picture.
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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

3 major / 8 minor

Summary. The manuscript reports first-principles DFT calculations of the topological phase in Sn_{1-x}In_xTe for x=0, 0.03125, 0.125, and 0.25. The authors find that band inversion at the L point is preserved for all doped concentrations, and they compute a mirror Chern number n_M=-2 for x=0.03125, 0.125, and 0.25, despite the system becoming metallic for x>0.1. Slab calculations reveal surface states with +/- i mirror eigenvalues for x=0.03125 and x=0.125, with the Dirac point shifting away from L and the Fermi velocity increasing with x. The paper further argues, from the density of states at the Fermi level being dominated by In-5s states, that the superconductivity is s-wave.

Significance. If correct, the central claim would establish that the superconducting alloy Sn_{1-x}In_xTe retains non-trivial mirror-protected topology across the experimentally relevant doping range, strengthening the case for topological superconductivity in this material. The work combines ab initio band structure with Wannier-based topological invariants and makes quantitative contact with ARPES Fermi velocities. Strengths are the use of standard first-principles methods with no free parameters tuned to force the topological result, and explicit comparisons with experiment. However, the claim for the metallic concentrations requires additional justification, as detailed below.

major comments (3)
  1. [Sec. 3.1 (and Sec. 2)] The mirror Chern number is reported as n_M=-2 for x=0.125 and x=0.25, but the text states that the system 'becomes a metal for x>0.1' and shows gapless band structures (Fig. 2(g),(h)). The hybrid Wannier charge center method [34,35] defines the mirror Chern number through the evolution of Wannier centers in each mirror eigensector, which requires a spectral gap on the mirror-invariant plane to quantize the integer. The manuscript does not provide a mirror-resolved gap check on any {110}-type plane for these concentrations, nor does it show the WCC evolution curves. Without this, the values n_M=-2 for the metallic phases are not established. The authors should either demonstrate that the mirror subspaces are gapped at E_F and provide the WCC evolution, or clearly define and justify an alternative invariant for metallic systems.
  2. [Sec. 3.1, last paragraph] The sentence 'Using the same procedure as described above the computed mirror Chern number for each of x = 0.03125 and 0.25 is n_M = -2' omits x=0.125, whereas the abstract and conclusion claim n_M = -2 for x=0.03125, x=0.125, and x=0.25. This is a direct inconsistency between the central claim and the reported computation. The computation for x=0.125 must either be shown or the claim must be revised.
  3. [Sec. 3.2, Fig. 4] For x=0.125, the slab calculation is performed in a metallic regime, and the displayed surface bands cross the Fermi level together with bulk states. The paper does not demonstrate that the surface states are still topologically protected when the bulk is metallic. The argument for protection of the surface states relies on a bulk gap on the mirror plane, which is not established. To support the claim of topological surface states at x=0.125, the authors should present the mirror-resolved surface spectral function and discuss the role of metallic bulk states.
minor comments (8)
  1. [Sec. 1 and throughout] Typos include 'asbence' (Sec. 2), 'compunds' (Sec. 2), 'wheather' (Sec. 3.1), and 'Supressed' in Ref. [47]. These should be corrected.
  2. [Fig. 2 caption] The third panel label 'Sn0.175In0.875Te' appears to be a typo for 'Sn0.875In0.125Te' (i.e., x=0.125).
  3. [Sec. 3.3] The text refers to 'Sn xIn1−xTe'; the intended formula is Sn1−xInxTe.
  4. [Sec. 3.1] The statement that x=0.03125 is 'a gapped p-type doped semiconductor' while the Fermi level 'lies slightly below the valence band maximum' is confusing: a Fermi level below the VBM usually indicates a degenerate (metallic) state. Please clarify the position of the Fermi level and the meaning of 'gapped' in this context.
  5. [Sec. 2] The lattice parameters used for each In concentration are not listed. Since the paper states a linear reduction based on Refs. [22,26], the actual values should be provided for reproducibility.
  6. [Sec. 2] The k-point sampling is reported as 10x10x10 for all bulk calculations, but for metallic concentrations a denser mesh or at least a convergence test against a finer k-point grid should be reported.
  7. [Table 1] The units of kD(L) are given in Å^{-1}, but the shift from the L point should be a momentum difference; please specify the reciprocal lattice direction and define the reference clearly.
  8. [Sec. 3.3] The conclusion that 'This confirms the s-wave nature of the superconducting state' is an overstatement, since the normal-state DOS alone does not determine the pairing symmetry. Rephrase to 'consistent with s-wave pairing' or provide additional justification.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: topological invariants and surface states are computed from first-principles DFT/Wannier calculations with no fit to the target result.

full rationale

The central claim — mirror Chern number nM=-2 for Sn1-xInxTe at x=0.03125, 0.125, and 0.25 — is obtained from hybrid Wannier charge centers constructed from first-principles DFT wavefunctions (Sec. 2). No parameter is fitted to the target invariant; experimental lattice constants and standard GGA/PBE functionals are the only external inputs, and the reported Fermi velocities and DOS values are compared with ARPES/magnetization data only after the fact. The band-inversion analysis (orbital characters Φ±) is an independent characterization, not an input to the invariant calculation. The paper does cite prior work by the authors (Refs. [46,47]) for monolayer topology and slab-thickness behavior, but those citations are not load-bearing for the alloy's nM or surface-state existence, which are computed here from first principles and checked against independent experimental ARPES results [21,33]. A reported gap in support — the WCC invariant for the metallic x=0.125 case is claimed in the abstract but the text only explicitly reports computed values for x=0.03125 and x=0.25 — is an omission/consistency issue, not a circular reduction; the required mirror-plane gap is not shown, but neither is the claim derived from an input. No equation or definition equates the predicted invariant to an assumed input, so no circular step can be exhibited.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The computation rests on standard DFT approximations and on ordered-supercell modeling of a random alloy, plus the assumption that the Wannier-based mirror Chern number remains meaningful for the metallic concentrations. No numerical parameter is fitted to the target results.

assumptions (4)
  • domain assumption PBE-GGA DFT with fully relativistic PAW pseudopotentials correctly captures the band inversion and topological properties of SnTe and its alloys.
    Invoked in Section 2 (Method); no benchmarking beyond the pristine SnTe gap of 0.17 eV is provided.
  • domain assumption The hybrid Wannier charge center scheme yields a well-defined mirror Chern number for the doped systems, including metallic ones.
    Used in Section 3.1 to compute nM for x=0.25 where the alloy is gapless; the applicability to a metal is not justified.
  • domain assumption A single ordered In distribution in a 64-atom supercell is representative of the random alloy Sn1-xInxTe.
    Each concentration is modeled with one configuration (Section 2); configurational disorder is not sampled.
  • domain assumption The linear reduction of the experimental lattice parameter for In content follows Vegard's law and does not affect the topological invariant.
    Stated in Section 2; no test of lattice parameter sensitivity is presented.

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Cite this review

Pith. "Pith review of Non-Trivial Topological Phase in the Sn_{1-x}In_xTe Superconductor." pith.science (2026). https://pith.science/paper/3J4O3BAX

@misc{pith2026190805967,
  author       = {Pith},
  title        = {Pith review of: Non-Trivial Topological Phase in the Sn_1-xIn_xTe Superconductor},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3J4O3BAX}},
  note         = {Machine review of arXiv:1908.05967}
}
read the original abstract

Whereas SnTe is a inverted band gap topological crystalline insulator, the topological phase of the alloy Sn_{1-x}In_xTe, a topological superconductor candidate, has not been clearly studied so far. Our calculations show that the Sn_{1-x}In_xTe band gap reduces by increasing the In content, becoming a metal for x>0.1. However, the band inversion at the fcc L point for both gapped and gapless phases has been maintained. Furthermore, the computed topological invariant shows a non-trivial phase with a mirror Chern number n_M = -2 for In concentrations of x=0.03125, x=0.125, and x=0.25. We also identify pairs of topologically protected states on the (001) surface of Sn_{1-x}In_xTe with +/- i mirror eigenvalues. The character of these topological states is affected by In dopant. As the In content x increases, the Dirac crossing point moves further away from the L point, and the Fermi velocity of the topological states increases significantly. Our results demonstrate a non-trivial topological phase for the superconductor Sn_{1-x}In_xTe, and provide a detailed description of the topological state properties.

Figures

Figures reproduced from arXiv: 1908.05967 by the authors.

Figure 1
Figure 1. The rock-salt structures of SnTe modelled in this work. The panel on the left shows a sample cubic cell of [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Band structure without SO coupling (top row (a)-(d)) and with SO (middle row (e)-(h)) showing the band [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Schematic illustration of the computed orbital components of states in and around the band gap region for [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Topological surface states for Sn1−xInxTe: (a) x = 0 (pristine SnTe); (b) x = 0.03125; (c) x = 0.125. Blue and red symbols represent the mirror eigenvalues +i and −i projected in half of the slab cell for bands around the valence and conduction band edges. The pink are…
Figure 5
Figure 5. Figure 5: Total density of states (black) and local density of states projected on In (maroon) and on In-5s orbital (pink). [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

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Reviewed August 14, 2026 · model on record in the stance chip above.