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arxiv: 2605.25906 · v1 · pith:HVKBRO4Unew · submitted 2026-05-25 · ❄️ cond-mat.supr-con · cond-mat.mtrl-sci

Substitution modulated transition from semimetal to superconductor in ZrTe_(2-x)Se_x with coexistence of nontrivial electronic topology

V. M. Fim , C. F. Schuch , L. R. de Faria , F. A. Santos , M. S. da Luz , S. S. Tsirkin , L. T. F. Eleno , A. J. S. Machado This is my paper

Pith reviewed 2026-06-29 19:19 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con cond-mat.mtrl-sci
keywords ZrTe2-xSextopological superconductivityDirac semimetalphase diagramcharge density waveselenium substitutionsuperconductivity
0
0 comments X

The pith

Substituting selenium for tellurium turns ZrTe2 into a superconductor at x=0.15 while preserving a nontrivial Z2 invariant and surface states.

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

The paper shows that adding small amounts of selenium to zirconium ditelluride crystals creates a superconducting state at low temperatures, with the transition temperature reaching a maximum of 4.8 kelvin when 15 percent of the tellurium is replaced. Measurements and calculations map out how the material changes from a charge density wave state through a region where Dirac semimetal behavior coexists with superconductivity, and finally to a semiconductor as more selenium is added. A sympathetic reader would care because this points to a specific composition where superconductivity appears alongside a nontrivial Z2 topological invariant and surface states on certain crystal faces.

Core claim

The central claim is that in the ZrTe_{2-x}Se_x series, selenium substitution drives a transition from semimetal to superconductor, with an extensive phase diagram showing coexistence between the Dirac semimetal and superconductivity up to the semiconductor phase. At x=0.15, the compound ZrTe1.85Se0.15 exhibits superconductivity with Tc=4.8 K and hosts a nontrivial Z2 invariant with nonvanishing surface states in its (001) planes, establishing it as a candidate platform for topological superconductivity.

What carries the argument

The phase diagram constructed from resistive, structural, and thermal measurements combined with ab initio calculations and Wannier Hamiltonian interpolation between ZrTe2 and ZrSe2, which tracks the evolution of the electronic topology and its persistence into the superconducting regime.

If this is right

  • Superconductivity emerges upon Se substitution in the ZrTe2 matrix with a clear dependence of Tc on selenium concentration.
  • The critical temperature peaks at x=0.15 with Tc of 4.8 K.
  • Calorimetric data indicates modification of both electronic contribution and vibrational modes at low Se substitution.
  • The system transitions from charge density wave to Dirac semimetal plus superconductivity coexistence and then to semiconductor phase.
  • ZrTe1.85Se0.15 is identified as hosting a nontrivial Z2 invariant with nonvanishing surface states in (001) planes.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If surface states remain gapless when the bulk becomes superconducting, the material offers a concrete setting in which to test whether topology and pairing can be combined without external fields or proximity effects.
  • The interpolation approach between the two end compounds supplies a practical route to scan topology across other isostructural alloy series without recomputing every intermediate composition from scratch.
  • Transport or tunneling measurements focused on the (001) face could directly test whether the predicted nonvanishing states survive into the superconducting regime.
  • The same substitution window may be worth checking in chemically related transition-metal dichalcogenides to see whether similar coexistence regions appear.

Load-bearing premise

The ab initio calculations combined with Wannier Hamiltonian interpolation between ZrTe2 and ZrSe2 correctly capture the electronic topology and its persistence into the superconducting regime.

What would settle it

An experimental determination that the Z2 invariant becomes trivial or that surface states on the (001) planes vanish once superconductivity sets in at x=0.15 would falsify the claim of a candidate platform for topological superconductivity.

Figures

Figures reproduced from arXiv: 2605.25906 by A. J. S. Machado, C. F. Schuch, F. A. Santos, L. R. de Faria, L. T. F. Eleno, M. S. da Luz, S. S. Tsirkin, V. M. Fim.

Figure 1
Figure 1. Figure 1: FIG. 1: (a) Crystal structure of ZrTe [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: (a) X-ray diffraction pattern of ZrTe [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Proposed phase diagram of the ZrTe [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Evolution of the electronic density of states of [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Electronic structure of ZrTe [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Interpolated band structures of ZrTe [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: ZrTe [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Calculated surface states on the (001) planes along the high-symmetry path [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: The calculated electronic localization function [PITH_FULL_IMAGE:figures/full_fig_p010_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: (a) Bogoliubov-de Gennes (BdG) Hamiltonian spectrum for the 14 slab of ZrTe [PITH_FULL_IMAGE:figures/full_fig_p012_12.png] view at source ↗
read the original abstract

This study explores the emergence of superconductivity in high-quality ZrTe$_{2-x}$Se$_x$ crystals, grown via the isothermal chemical vapor transport (ICVT) technique. Resistive, structural, and thermal measurements reveal that substituting Te with Se in the ZrTe$_2$ matrix induces a superconducting state at low temperatures. The critical temperature ($T_c$) exhibits a clear dependence on the selenium concentration, peaking at $x=0.15$ with a $T_c$ of $4.8$ K. Calorimetric data indicates that even a low Se substitution range is capable of modifying both the electronic contribution and the vibrational modes of the crystal lattice. Combined with ab initio calculations and Wannier Hamiltonian interpolation between ZrTe$_2$/ZrSe$_2$, we established an extensive phase diagram mapping the transition from charge density wave (CDW) to the state with coexistence between the Dirac semimetal and superconductivity (SC), up to the semiconductor phase. This coexistence suggests that ZrTe$_{1.85}$Se$_{0.15}$ could be a candidate platform for topological superconductivity, as it hosts a nontrivial $\mathbb Z_2$ invariant, with nonvanishing surface states in its $(001)$ planes.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript reports the growth of ZrTe_{2-x}Se_x single crystals via isothermal chemical vapor transport and the emergence of superconductivity upon Se substitution, with Tc reaching a maximum of 4.8 K at x=0.15. Resistive, structural, and calorimetric data are combined with ab initio calculations and Wannier Hamiltonian interpolation between ZrTe2 and ZrSe2 to construct a doping-dependent phase diagram spanning CDW, Dirac semimetal plus superconductivity, and semiconducting regimes. The central claim is that ZrTe1.85Se0.15 lies in a region of nontrivial Z2 topology with nonvanishing (001) surface states, making it a candidate platform for topological superconductivity.

Significance. If the topological classification is robust, the work would identify an experimentally accessible doped Dirac semimetal in which superconductivity coexists with protected surface states, offering a platform to test theoretical predictions for topological superconductivity. The integration of crystal growth, multiple experimental probes, and first-principles modeling is a positive feature; however, the significance hinges on whether the interpolated Hamiltonian reliably captures the Z2 invariant inside the superconducting dome.

major comments (1)
  1. [Abstract / ab initio calculations section] Abstract (phase diagram construction paragraph): the nontrivial Z2 invariant and protected (001) surface states at x=0.15 are obtained from linear/virtual-crystal Wannier interpolation between the ZrTe2 and ZrSe2 end points. Because the Z2 index is fixed by parity eigenvalues at the eight TRIM points, any nonlinear shift in band ordering or gap closing caused by actual atomic substitution or local Se placement can flip the invariant without being reproduced by the interpolation; no direct parity or Wilson-loop calculation at the interpolated composition is shown to confirm the result.
minor comments (2)
  1. [Theory section] The manuscript should specify the precise method used to extract the Z2 invariant from the interpolated Hamiltonian (e.g., parity eigenvalues versus Wilson loop) and report the parity eigenvalues at each TRIM point for the x=0.15 composition.
  2. [Experimental results] Figure captions and text should explicitly state whether error bars on Tc, resistivity, and specific-heat data are included and how the superconducting volume fraction was estimated from calorimetry.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for identifying a key methodological point regarding the topological classification. We respond to the major comment below and indicate the planned revision.

read point-by-point responses

  1. Referee: [Abstract / ab initio calculations section] Abstract (phase diagram construction paragraph): the nontrivial Z2 invariant and protected (001) surface states at x=0.15 are obtained from linear/virtual-crystal Wannier interpolation between the ZrTe2 and ZrSe2 end points. Because the Z2 index is fixed by parity eigenvalues at the eight TRIM points, any nonlinear shift in band ordering or gap closing caused by actual atomic substitution or local Se placement can flip the invariant without being reproduced by the interpolation; no direct parity or Wilson-loop calculation at the interpolated composition is shown to confirm the result.

    Authors: We agree that the virtual-crystal Wannier interpolation constitutes an approximation and that, in principle, nonlinear band shifts or local Se disorder could alter parity eigenvalues at the TRIM points. In the calculations presented, the interpolated Hamiltonian is used to obtain the bands at x=0.15, from which the Z2 invariant is evaluated via parity eigenvalues; the interpolation shows continuous evolution without gap closure at the TRIM points, preserving the invariant of the end members. Nevertheless, to directly address the concern, the revised manuscript will include an explicit tabulation (in the supplementary information) of the parity eigenvalues at the eight TRIM points for the interpolated x=0.15 Hamiltonian, together with a short discussion of the limitations of the virtual-crystal approximation at this doping level. This addition provides the requested direct confirmation while clarifying the scope of the result. revision: yes

Circularity Check

0 steps flagged

No circularity; topology and phase diagram derived from independent ab initio + Wannier interpolation

full rationale

The paper measures superconductivity experimentally (resistive, calorimetric data) and separately computes the electronic structure and Z2 invariant via ab initio calculations plus Wannier Hamiltonian interpolation between the ZrTe2 and ZrSe2 endpoints. No equation or claim reduces the computed topology or phase diagram to a fit of the measured Tc, nor does any load-bearing step invoke a self-citation whose content is itself unverified or defined by the present result. The interpolation is an external computational technique whose validity is not established by reference to the target superconducting composition inside the paper. This is the normal case of a self-contained derivation against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that the Wannier-interpolated band structure accurately predicts the Z2 invariant in the doped superconducting state; no free parameters are explicitly named in the abstract, but the Se concentration dependence of Tc is empirically mapped.

axioms (1)
  • domain assumption Ab initio calculations plus Wannier interpolation between ZrTe2 and ZrSe2 correctly determine the topological invariant and its survival into the SC regime.
    Invoked in the abstract to establish the phase diagram and candidate status.

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