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Interaction-Driven Topological Transitions in Monolayer TaIrTe$_4$

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Pith's one-line read Monolayer TaIrTe4, a single-layer quantum spin Hall insulator whose van Hove singularities sit near its topological gap, is claimed to be a natural non-moiré platform where electron interactions and strain select among quantum spin Hall…

desk verdict A solid, conditional paper: the Hartree-Fock phase diagram is internally coherent and the device statistics are real, but the ordering vector is imposed rather than self-consistently selected, and the experiment's 'dual insulator' category cannot distinguish the predicted HOTI from a trivial insulator. read the letter →

arxiv 2506.18412 v1 pith:KCCKW2II submitted 2025-06-23 cond-mat.str-el cond-mat.mes-hall

Jiangxu Li , Jian Tang , Louis Primeau , Thomas Siyuan Ding , Rahul Soni , Tiema Qian , Kenji Watanabe , Takashi Taniguchi
show 4 more authors
Ni Ni Adrian Del Maestro Qiong Ma Yang Zhang
This is my paper · ORCID
classification cond-mat.str-elcond-mat.mes-hall PACS 71.10.Fd71.45.Lr73.20.At
keywords monolayerTaIrTe4vanHovesingularityHartree-FockmeanfieldquantumspinHallinsulatorhigher-ordertopologicalchargedensitywaveuniaxialstrainnonlocaltransport
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

Monolayer TaIrTe4 is a single-layer quantum spin Hall insulator whose band structure has van Hove singularities sitting just above the topological gap, so electrostatic doping can push the material into a strongly correlated regime. This paper claims that at van Hove filling — two added electrons per $15\times1$ charge-density-wave supercell — electron interactions generate a set of distinct ground states: a correlated quantum spin Hall insulator, a higher-order topological insulator with corner states, a trivial insulator, and a metal. The phase that wins is controlled by two experimentally accessible knobs, dielectric screening and uniaxial strain, and the paper argues that tensile strain drives a transition from the quantum spin Hall phase into the higher-order topological insulator. Transport data across 105 monolayer devices, where fabrication-induced strain varies randomly, show exactly the kinds of coexisting behavior the phase diagram predicts: dual quantum spin Hall, quantum spin Hall plus metal, and dual insulator states with no protected edge conduction. If the picture holds, TaIrTe4 is one of the first natural non-moiré monolayers where correlated topology can be designed by gating, screening, and strain.

What carries the argument

The load-bearing construction is a minimal eight-band tight-binding model — two Ta $5d$ orbitals ($d_{x^2-y^2}$, $d_{yz}$) on two sublattices plus spin, with symmetry-constrained spin-orbit coupling — fitted to DFT, whose Lindhard charge susceptibility peaks at $Q_a = 0.067 \cdot 2\pi/a$ and thereby fixes a $15\times1$ charge-density-wave supercell. Into this supercell the paper places an extended Hubbard interaction (on-site $U$ plus density-density $V$ up to third nearest neighbours) and solves it in Hartree-Fock mean field, using a matrix-product form of the correlation function with batched GPU eigensolves and quasi-Newton acceleration to converge the 120-orbital fixed-point problem. Topological character is diagnosed by parity products at the four time-reversal invariant momenta, Wilson-loop winding, the Fu-Kane $Z_2$ invariant, the $Z_4$ symmetry indicator $\kappa_1$, and real-space corner-state densities in open-boundary supercells.

What would settle it

Measure the density-wave periodicity directly at the van Hove filling ($n \approx 6.5 \times 10^{12}\,\text{cm}^{-2}$) in gated monolayer TaIrTe4 using scanning tunneling microscopy or grazing-incidence diffraction: if the dominant wavevector is not $Q_a \approx 0.067 \cdot 2\pi/a$ (a $15a$ period), the superlattice the Hartree-Fock calculation assumes is the wrong one and the predicted phase boundaries do not apply. A second decisive test is to re-run the Hartree-Fock calculation with the ordering vector as a free variational parameter and check whether the $\kappa_1 = 2$ higher-order topological insulator survives at any $\mathbf{q}$.

Watch

Extended reading notes

Core claim

The paper's central claim is that electron-electron interactions at the van Hove filling of monolayer TaIrTe4 do not merely renormalize the known quantum spin Hall state — they select among several topologically distinct correlated ground states. In the Hartree-Fock phase diagrams, the relative strength of the onsite Hubbard term to the intersite Coulomb term, together with the dielectric constant, separates a dual quantum spin Hall insulator ($Z_2 = 1$ in both the charge-neutral and doped gaps), a dual higher-order topological insulator ($Z_4$ indicator $\kappa_1 = 2$ with two degenerate corner states obeying $C_{2z}$ symmetry), a dual trivial insulator, and metallic phases, including mixed cases such as QSHI plus metal in which the two gaps carry different characters. Uniaxial strain enters through an exponential hopping renormalization fitted to DFT gap evolution, and produces the same phase sequence: tensile strain past about 1% inverts additional bands, turning the $Z_2$ QSHI into a $\kappa_1 = 2$ higher-order topological insulator. The authors support the calculation with transport on 105 monolayer devices, finding that roughly 35% show dual QSHI behavior with quantized $2e^2/h$ edge conductance, about 7% show QSHI plus metal, and the majority show an insulating response without edge conduction — consistent with the theoretical phases once random fabrication strain and screening variations are taken into account.

Load-bearing premise

The entire interacting phase diagram rests on the choice of the $15\times1$ charge-density-wave supercell: its period is fixed by the noninteracting Lindhard susceptibility and the Hartree-Fock calculation never allows the ordering vector to change, so if interactions prefer a different period the predicted phases, including the higher-order topological insulator, could shift or disappear.

Editorial extensions

If this is right

  • If the Hartree-Fock phase diagram is correct, monolayer TaIrTe4 is a non-moiré platform in which correlated topological phases — QSHI, HOTI, trivial insulator, metal — can be selected by dielectric environment and uniaxial strain rather than by twist angle.
  • Tensile strain of a few percent converts the quantum spin Hall phase into a higher-order topological insulator with a $Z_4$ invariant $\kappa_1 = 2$, whose hallmark is two degenerate corner states rather than helical edge states; compressive strain strengthens the QSHI and enlarges its gap.
  • The correlated state at the van Hove filling and the charge-neutral state can carry different topological characters at once (e.g., QSHI plus metal, HOTI plus QSHI), so the same material can show gap-selective topology.
  • The experimental statistics — about 35% dual QSHI, 7% QSHI plus metal, 58% dual insulator across 105 devices — are consistent with the predicted phase diagram once sample-to-sample variations in strain and screening are folded in, implying that device fabrication already samples multiple phases.
  • The authors argue the vHS-driven superlattice potential could host time-reversal-invariant fractional topological insulators, and that suppressing the CDW by strain, pressure, or screening could give way to superconductivity — a route toward topological superconductivity.

Reading between the lines

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

  • My reading: the most fragile step is the fixed superlattice. The $15\times1$ period is taken from the noninteracting Lindhard susceptibility, and since the Hartree-Fock calculation never re-optimizes the ordering vector, a self-consistent CDW that prefers a different or incommensurate $\mathbf{q}$ would shift every phase boundary in the figures; re-solving with a variational $\mathbf{q}$ is the ch
  • My reading: the same construction — Hubbard interactions on top of a $Z_2$ band-inverted monolayer with vHSs near the gap — may be generic. The specific $15\times1$ period is TaIrTe4-specific, but the qualitative sequence trivial $\rightarrow$ QSHI $\rightarrow$ HOTI under decreasing screening, and QSHI $\rightarrow$ HOTI under tensile strain, should recur in other 1T$'$-like monolayers with simil
  • My reading: the 'dual insulator' majority (58%) is very likely a mixture of trivial insulators and HOTIs that transport cannot distinguish; corner-state-sensitive local probes (scanning tunneling microscopy or SQUID-on-tip on a finite flake) would separate the two sub-populations and test the strain-driven HOTI prediction directly.
  • My reading: whether fractionalised phases are realistic depends on how deep the Hartree-Fock-generated CDW potential is compared with the renormalised bandwidth; extracting that ratio from the converged Hartree-Fock solutions would give a quantitative estimate of how close this non-moiré platform is to the fractional regime.
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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 / 5 minor

Summary. This manuscript combines density functional theory, an eight-band tight-binding model, and Hartree-Fock mean-field calculations in a fixed 15×1 supercell to map the interaction-driven phase diagram of monolayer TaIrTe4 at a filling of 0.13, corresponding to two additional electrons per supercell above charge neutrality. The authors report four correlated phases—quantum spin Hall insulator, higher-order topological insulator, trivial insulator, and metal—as functions of dielectric screening and interaction ratio U/V1, and they use a strain-dependent hopping model to predict strain-induced QSHI-to-HOTI transitions. The theoretical part is complemented by transport measurements on 105 monolayer devices, which are classified into dual QSHI (35%), QSHI+metal (7%), and dual insulator (58%), with quantized h/2e2 conductance observed in short-channel devices. The paper positions monolayer TaIrTe4 as a non-moiré platform for engineering correlated topological phases.

Significance. The internal consistency of the paper is a genuine strength: parity products, Wilson loops, edge spectra, and corner-state density distributions mutually agree for the assigned phases, and the reproduction of the previously reported dual QSHI gives some confidence in the mean-field machinery. The large device statistics with quantized conductance in short channels are also valuable, as is the concrete, falsifiable prediction of a strain-driven QSHI-to-HOTI transition. However, the significance of the central claims is conditional. The predicted HOTI and the phase boundaries are computed in a supercell whose period is imposed from the noninteracting Lindhard response rather than determined self-consistently, and the experimental 'dual insulator' category deliberately conflates the predicted HOTI with a trivial insulator. Until these two gaps are addressed, the paper establishes a plausible and internally consistent mean-field scenario, not a demonstrated material realization.

major comments (3)
  1. [Sec. III A; Supplemental Eq. (S8)] The mean-field calculation is performed in a 15×1 supercell whose period is fixed by the noninteracting Lindhard susceptibility peak at Q_a = 0.067·2π/a (Sec. II C, Fig. 2(d)), and the ordering vector is not a variational degree of freedom. Consequently, the HF loop cannot select a different CDW wavevector, a homogeneous state, or no CDW at all, so the HOTI phase in Fig. 4(d–f) and the strain phase boundaries in Fig. 6(b–c) are conditional on the assumed period. In addition, the translational-invariance constraint stated in Supplemental Eq. (S8) is ambiguous: if it is enforced at the single-Ta-site level, a spontaneous 15a density modulation cannot appear by construction, whereas if it is enforced only at the supercell level, the 15a order is imposed rather than self-consistently established. The authors should clarify this point and, ideally, perform a self-consistent ordering-vector search or compare competing supercell periods before the phase diagram can be accepted as a property of the interacting system.
  2. [Sec. IV C; Table II] The 'dual insulator' category in Table II is explicitly defined to include both the predicted HOTI and a trivial insulator, because neither exhibits gapless edge transport; no corner-state measurement or other discriminating signature is presented. Since 58% of the 105 devices fall into this category, the experimental data cannot independently confirm the existence of the HOTI phase. The phrasing in the abstract that the devices 'realize several phases consistent with theoretical predictions' should be qualified accordingly, or the paper should present a measurement capable of distinguishing the HOTI from a trivial insulator.
  3. [Sec. III C, Eq. (4)] The strain exponent β = 1.5 is obtained by fitting the tight-binding gap evolution to DFT under uniaxial strain (Fig. 6(a)), and no device in the experimental section has a quantified strain value. The predicted tensile-strain QSHI-to-HOTI transition at δ ≈ 3% in Fig. 6(b–c) is therefore not calibrated against the correlated phase it is meant to predict, and the attribution of the observed device-to-device variation to 'unavoidable strain variations' remains a hypothesis rather than a demonstrated mechanism.
minor comments (5)
  1. [Fig. 3 caption] The caption labels the second panel as '(a) Phase diagram for CNP states' again; it should be '(b)' for the electron-doped states.
  2. [Sec. III A] The 'commensurate filling of 0.13' should be defined more explicitly: the text gives 'two additional electrons per supercell', but the numerical value 0.13 should be reconciled with a per-site or per-unit-cell definition.
  3. [Eq. (2)] The notation '3rdNN' for the interaction range is not defined in the main text; a brief definition or a reference to the Supplemental derivation would improve readability.
  4. [Sec. III B] The values of U and V1 for the representative points (e.g., ϵ = 13, U/V1 = 2.25) are not given in the main text; including the actual energy scales would help readers connect the model to experiment.
  5. [Sec. II C] The phrase 'particle swarm optimization' for the tight-binding fit should be accompanied by a quantitative measure of the fit error or a plot of the residuals.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the Hartree-Fock phase diagram is a forward parameter scan and the strain model is fit to DFT gaps, not to the claimed target phases.

full rationale

The claimed derivation chain is: DFT bands -> fitted eight-band tight-binding model -> Lindhard susceptibility -> fixed 15x1 CDW supercell -> Hartree-Fock mean-field phase diagram as a function of epsilon and U/V1 -> strain model with beta fitted to DFT gap closure -> comparison with transport data. None of the central predictions reduces to its own input by construction. The HFMF phase diagram is a forward scan over interaction parameters, and the topological labels (Z2, Z4, parity products, Wilson loops) are computed from self-consistent solutions rather than fitted to the experimental data. The representative dual QSHI point (epsilon=13, U/V1=2.25) is calibrated to the prior experimental observation in Ref. [4], but that calibration anchors a consistency check and does not force the new HOTI, trivial-insulator, or metallic regions of the phase diagram. The strain exponent beta=1.5 is fitted to reproduce the DFT single-particle gap closure, while the ne-gap QSHI-to-HOTI transition is a different quantity computed from the same strain-tuned model, so the predicted transition is not the fit itself. The 15x1 supercell period is taken from the noninteracting Lindhard susceptibility and is not re-evaluated inside Hartree-Fock; this is a genuine correctness/robustness limitation (the ordering vector is not variational), but it is not circularity because the predicted phases are explicitly conditional on that CDW period. The experimental 'dual insulator' category is openly described as consistent with either HOTI or trivial insulator, so the experiment is not being used to force the HOTI claim. Self-citations to Ref. [4] provide external experimental evidence and are not load-bearing for the new predictions.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central claim rests on a chain of modeling choices: PBE DFT, a two-orbital tight-binding fit, a density-density truncated interaction, Hartree-Fock mean field, and a fixed 15x1 CDW supercell. Each is standard but introduces uncertainty; the most consequential is the fixed supercell. The strain knob enters through beta fitted to DFT. No invented particles or forces are introduced.

free parameters (4)
  • Tight-binding hopping parameters = Table S1 values, e.g., mu1=1610 meV, t1=-700 meV
    Obtained by particle swarm optimization fitting to DFT bands; these define the single-particle starting point for the Hartree-Fock phase diagram.
  • U/V1 interaction ratio and on-site U cutoff = U/V1 scanned; representative 2.25; U from r in 0.8-2.0 Å
    Chosen model inputs; the representative value is anchored to the previously observed dual QSHI experiment [4].
  • Dielectric constant epsilon = scanned, representative 13
    Background dielectric in the double-gate screening formula; not measured in the devices.
  • Strain deformation parameter beta = 1.5
    Fitted so the tight-binding gap closure under strain matches DFT (Eq. 4, Fig. 6a), then used unchanged in the Hartree-Fock strain phase diagram.
assumptions (6)
  • domain assumption Hartree-Fock decoupling captures the correlated ground states at van Hove filling
    The phase diagram is computed from self-consistent Hartree-Fock; quantum fluctuations and competing orders beyond mean field are not assessed (Sec III A).
  • domain assumption Only on-site U and density-density V up to third nearest neighbors are retained
    The bare interaction is truncated to density-density terms in the extended Hubbard model (Eq. 2 and SI D).
  • domain assumption Two Ta d orbitals per site and eight bands suffice for low-energy physics
    DFT orbital decomposition shows dx2-y2 and dyz dominate near the Fermi level; other orbitals are neglected (Sec II C and SI C).
  • domain assumption The CDW ordering vector is fixed to Qa=0.067*2pi/a (15x1) from the noninteracting Lindhard susceptibility
    Hartree-Fock is solved only for this period; self-consistent determination of the ordering vector is not performed (Sec II C, Fig. 2d, and Sec III A).
  • domain assumption Coulomb interactions are screened by perfect metallic gates at distance d=100 Å
    Controls the U and V values used in Hartree-Fock; the authors check d=200 Å gives a similar diagram but do not compare to measured device dielectric environments (SI D1).
  • domain assumption PBE-GGA with SOC gives reliable single-particle bands and topology
    Used for tight-binding fitting, parity analysis, and strain gap evolution; no hybrid or GW corrections are applied (SI A).

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Cite this review

Pith. "Pith review of Interaction-Driven Topological Transitions in Monolayer TaIrTe$_4$." pith.science (2026). https://pith.science/paper/KCCKW2II

@misc{pith2026250618412,
  author       = {Pith},
  title        = {Pith review of: Interaction-Driven Topological Transitions in Monolayer TaIrTe$_4$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KCCKW2II}},
  note         = {Machine review of arXiv:2506.18412}
}
abstract

Discovering materials that combine topological phenomena with correlated electron behavior is a central pursuit in quantum materials research. Monolayer TaIrTe$_4$ has recently emerged as a promising platform in this context, hosting robust quantum spin Hall insulator (QSHI) phases both within a single-particle gap and within a correlation-induced gap arising from van Hove singularities (vHSs), accessed via electrostatic doping. Its intrinsic monolayer nature offers exceptional tunability and the potential to realize a versatile array of interaction-driven topological phases. In this work, we combine theory and experiment to map the phase landscape of monolayer TaIrTe$_4$. Using Hartree-Fock calculations, we investigate the interaction-driven phase diagram near the vHSs under commensurate filling conditions. By systematically tuning the dielectric screening and strain, we uncover a rich set of ground states--including QSHI, trivial insulator, higher-order topological insulator, and metallic phase--among which are interaction-driven topological phase transitions. Experimentally, we perform both local and nonlocal transport measurements across a broad set of devices, which--due to unavoidable strain variations during fabrication-realize several phases consistent with theoretical predictions. Together, our results lay the groundwork for understanding correlation-driven topological phenomena in TaIrTe$_4$ and open new directions for engineering exotic quantum phases in low-dimensional materials beyond the limitations of moir\'e superlattices.

Figures

Figures reproduced from arXiv: 2506.18412 by the authors.

Figure 1
Figure 1. FIG. 1. Band structures and topological properties of mono [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Band structures and topological properties of monolayer TaIrTe [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The Hartree-Fock mean-field phase diagram and associated band topology at filling of 0.13. (a) Phase diagram for [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Topological characterization of the dual QSHI and dual HOTI phases. (a-c) Band structure, Wilson loop evolution [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Topological band features of the dual trivial insulator and QSHI+metal phases. (a-c) Band structure along high [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. The phase transitions under strain. (a) The energy gap at different strains. The red lines represent the data from DFT [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Three representative transport behaviors of monolayer TaIrTe [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Temperature-dependent resistance of the CNP and [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]

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    Band Structure -0.5 1 -1 0.5E-Ef (eV) 0 -0.5 1 -1 0.5 E-Ef (eV) 0 -0.04 0.04 0.08 -0.08 E-Ef (eV) 0 R Y XΓ R Y XΓ Y YΓ -0.08 0.08E-Ef (eV) 0 X XΓ 1 6 2 3 4 5 1 6 2 3 4 5 (a) (b) (c) (d) w/ SOC w/o SOC DFT Wannier ξ=−1 ξ=+1 ξ=−1 ξ=+1 FIG. S1. DFT band structures and topological...

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    directions calculated from the Wannier-based tight-binding model, clearly showing the gapless helical edge states features of QSHI. Based on the relaxed structure, we compute the electronic band structures with and without spin-orbit coupling (SOC) to understand the role of SO...

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    As shown in Fig

    crystallographic directions. As shown in Fig. S1(c,d), well-defined helical edge states emerge in both directions, traversing the bulk gap and confirming the nontrivial topology and bulk-edge correspondence of TaIrTe 4

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    Methods Here, we consider general Coulomb interactions in TaIrTe 4, ˆV = 1 2 x drdr′X s,s′ ˆc† s(r)ˆc† s′(r′)Vint(|r− r′|)ˆcs′(r′)ˆcs(r) where ˆcs(r) is electron annihilation operator at continuous coordinate r with spin s. It can be projected to the Wannier lattice basis as: ...

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    S6, we further characterize the topological properties of the dual HOTI phase

    Topological Properties of the Dual HOTI Phase In Fig. S6, we further characterize the topological properties of the dual HOTI phase. At both the ne gap and CNP gap, the parity product distributions of the occupied bands are identical, as shown in Fig. S6. Specifically, the par...

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    Topological Characterization of the QSHI+Metal Phase In the regime of weak electron-electron interactions, particularly at large dielectric constants (e.g., ϵ = 20), our Hartree-Fock mean-field calculations reveal a distinct phase in which the system exhibits a metallic state ...

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    As shown in Fig

    Topological Properties of QSHI under Compressive Strain To confirm the strain-induced topological response in monolayer TaIrTe 4, we perform first-principles calculations under−1% uniaxial compressive strain. As shown in Fig. S8(a), the DFT-calculated band structure (blue) and...

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    direction, also showing helical edge modes protected by time-reversal symmetry. FIG. S9. Topological properties of TaIrTe4 under +5% tensile strain. (a) DFT band structure (blue) and Wannier interpolation (red dashed) under strain, showing a new band inversion at the Γ point. ...

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    As shown in Fig

    Topological Properties under Tensile Strain To illustrate the strain-driven topological phase transition from a QSHI to a HOTI phase, we perform first-principles calculations at +5% tensile strain. As shown in Fig. S9(a), the DFT and Wannier-interpolated bands reveal a clear b...

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    Dual HOTI phase under 4% tensile strain By further increasing the tensile strain to 4%, while keeping the interaction parameters fixed at U/V1 = 2.25 and dielectric constantϵ = 13, we observe a clear transition from the QSHI + HOTI coexistence at 2% strain into a robust dual H...

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    The elements were placed in an alumina crucible, sealed in a vacuum quartz tube, and gradually heated to 1373 K, where they were held for 10 hours

    TaIrTe 4 Crystal Growth Process: TaIrTe4 crystals were synthesized using the Te-flux method with a molar ratio of Ta:Ir:Te ( > 99.99% purity) of 3:3:94. The elements were placed in an alumina crucible, sealed in a vacuum quartz tube, and gradually heated to 1373 K, where they ...

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    The layer thickness was determined through optical microscopy (Fig

    TaIrTe 4 Exfoliation and Device Fabrication: TaIrTe4 flakes were exfoliated onto oxygen plasma-cleaned SiO 2 chips using the scotch-tape method inside an Ar-filled glovebox to solve the air sensitivity nature of thin flakes. The layer thickness was determined through optical m...

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    The electrical transport properties of TaIrTe 4 devices were characterized using standard lock-in techniques, and gate voltages were applied via Keithley source meters

    Electrical measurements of TaIrTe 4 devices: Electrical measurements were performed using Montana and Cryomagnetics cryostats. The electrical transport properties of TaIrTe 4 devices were characterized using standard lock-in techniques, and gate voltages were applied via Keith...

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    As shown in Fig

    Thermal Activation Gap Analysis To quantitatively evaluate the insulating behavior observed at the charge neutrality point and on the electron- doped side, we perform thermal activation analysis on the longitudinal conductance Gxx(T ) for three representative monolayer TaIrTe4...

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    A total of 105 high-quality devices were investigated, allowing robust statistical analysis of the observed transport behaviors

    Statistical significance and experimental reproducibility To systematically assess the reproducibility and universality of the observed correlated topological phases, we performed transport measurements across a large number of monolayer TaIrTe 4 devices. A total of 105 high-q...

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    Type-I ( dual QSHI ): Comprising about 35% of measured devices, these samples exhibit quantized edge conductance at both the CNP and an electron-doped correlated insulating state, consistent with the theoretically predicted dual QSHI phase arising from significant electron-ele...

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    Type-II ( QSHI + Metal ): Representing approximately 7% of the devices, these samples exhibit well- quantized edge conductance only at the CNP and metallic behavior at finite doping, indicative of relatively weak electron correlations insufficient to stabilize correlated insul...

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    This category likely encompasses trivial insulating or higher-order topological insulating phases, both characterized by the absence of gapless helical edge modes

    Type-III ( dual insulator ): The majority (58%) of measured devices demonstrate insulating transport throughout the doping range, without clear edge conductance quantization. This category likely encompasses trivial insulating or higher-order topological insulating phases, bot...

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Reviewed August 15, 2026 · model on record in the stance chip above.