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arxiv: 2605.28259 · v1 · pith:NM356XZL · submitted 2026-05-27 · cond-mat.str-el

Change in charge density wave order beyond the Lifshitz transition in 2H-Tatextsubscript{1pmδ}Stextsubscript{2}

Mihir Date , Jan Berges , Enrico Da Como , Marcin Mucha-Kruczy\'nski , Alex Louat , Gabriele Domaine , Niels B. M. Schr\"oter , Malte R\"osner
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Matthew D. Watson
This is my paper

Reviewed by Pith2026-06-29 10:09 UTCgrok-4.3pith:NM356XZLopen to challenge →

classification cond-mat.str-el
keywords charge density wave2H-TaS2Lifshitz transitionphonon instabilityself-intercalationband fillinginterlayer spacing
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0 comments X

The pith

Band filling and interlayer spacing control the charge density wave ordering vector in 2H-TaS₂.

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

In slightly hole-doped 2H-TaS₂, fingerprints of a 3×3 charge density wave appear, with backfolded features emerging only below about 65 K, pointing to a lock-in transition. Self-intercalated samples, which are electron-doped, instead display signatures of a novel 2√3 CDW. Ab initio phonon calculations show the 3×3 instability at q=2/3 ΓM is highly sensitive to band filling, while increased interlayer spacing produces a competing soft mode near q=1/2 ΓK that matches the observed superstructure in the intercalated phase. The work identifies band filling and interlayer spacing as the primary parameters that select which CDW ordering vector is realized.

Core claim

The 3×3 CDW instability is highly sensitive to band filling, and with increased interlayer spacing a competing soft phonon mode emerges near q=1/2 ΓK corresponding to the 2√3 superstructure observed in the electron-doped self-intercalated phase.

What carries the argument

Ab initio phonon spectrum calculations that track how soft modes at specific wavevectors respond to changes in band filling and interlayer spacing.

If this is right

  • The 3×3 CDW requires a narrow range of hole doping to remain stable.
  • Electron doping combined with expanded interlayer spacing stabilizes a distinct 2√3 CDW phase.
  • The incommensurate-to-commensurate lock-in occurs at a lower temperature than the initial CDW onset.
  • Self-intercalation offers a practical route to access different CDW orders by altering both doping and structure.

Where Pith is reading between the lines

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

  • The same parameters of band filling and spacing may govern CDW selection in related transition-metal dichalcogenides.
  • Independent tuning of interlayer spacing could stabilize the q=1/2 ΓK mode under the experimentally observed doping sign.
  • The sign mismatch between calculated and measured doping for the new mode indicates that intercalation introduces effects beyond simple rigid-band filling.

Load-bearing premise

The experimentally observed 2√3 superstructure in the self-intercalated sample arises from the calculated soft phonon mode near q=1/2 ΓK, even though the calculations produce this instability under hole doping while the experiment infers electron doping.

What would settle it

Measuring the CDW wavevector in samples where doping is varied independently of interlayer spacing to test whether the ordering vector follows the doping dependence seen in the phonon calculations.

Figures

Figures reproduced from arXiv: 2605.28259 by Alex Louat, Enrico Da Como, Gabriele Domaine, Jan Berges, Malte R\"osner, Marcin Mucha-Kruczy\'nski, Matthew D. Watson, Mihir Date, Niels B. M. Schr\"oter.

Figure 1
Figure 1. Figure 1: (a) shows the crystal structure of 2H-TaS2 consisting of two trigonal prismatically stacked layers which are alter￾nately rotated by 180◦ , with the Ta atoms directly on top of each other, following the 2Ha stacking [27]. The Fermi sur￾face measured in the high temperature undistorted phase at 102 K (left half of [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (g-i). We chose this cut, indicated by the yellow dashed lines, to intersect the dogbone pocket in two distinct places, revealing both spectral backfolding and the CDW gap. From the energy distribution curves (EDCs) shown in Fig.2(j), we estimated the CDW gap of the dogbone section to be approx￾imately ∆ ≈ 35 meV at 25 K, whereas we found no such gap for the spectrum at 65 K. Moreover, the momentum dis￾tri… view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
read the original abstract

We investigate electronic instabilities in 2H-TaS\textsubscript{2} and a self-intercalated variant, 2H$^\dagger$-Ta\textsubscript{1+$\delta$}S\textsubscript{2}. In conventional samples, which we determine to be slightly hole-doped, spectral gaps and backfolded features are found as fingerprints of the $3\times3$ charge density wave (CDW). Notably, the backfolded features emerge only at a temperatures below $T\approx$~65~K, substantially lower than the established CDW temperature of 78~K, suggesting an incommensurate-commensurate lock-in transition analogous to the phenomenology of the 2H-TaSe\textsubscript{2}. In contrast, the self-intercalated 2H$^\dagger$ sample exhibits substantial electron doping and signatures of a novel \tworootthree CDW. Using \textit{ab initio} calculations of the phonon spectrum, we demonstrate that the \threebythree instability ($\mathbf{q}=\sfrac{2}{3}\mathbf{\Gamma M}$) is highly sensitive to band filling. Furthermore, with increased interlayer spacing, a competing soft phonon mode emerges near $\mathbf{q}=\sfrac{1}{2}\mathbf{\Gamma K}$, corresponding to the superstructure observed in the 2H$^\dagger$ phase, although in our calculations this instability arises under hole doping rather than the electron doping inferred experimentally. These results establish band filling and interlayer spacing as key control parameters for CDW ordering vectors in 2H-TaS\textsubscript{2}, and highlight a route to engineering electronic instabilities in a prototypical layered material.

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

2 major / 2 minor

Summary. The manuscript presents ARPES data on conventional 2H-TaS₂ (slightly hole-doped) showing 3×3 CDW signatures with backfolded features below ~65 K, interpreted as an incommensurate-commensurate lock-in, and on self-intercalated 2H†-Ta_{1+δ}S₂ (electron-doped) showing a novel 2×√3 CDW. Ab initio phonon calculations demonstrate that the 3×3 instability (q=2/3 ΓM) is sensitive to band filling, while increased interlayer spacing induces a competing soft mode near q=1/2 ΓK that the authors link to the observed 2×√3 superstructure, despite noting that this mode appears under hole doping in calculations rather than the experimental electron doping. The central claim is that band filling and interlayer spacing are key control parameters for CDW ordering vectors in 2H-TaS₂.

Significance. If the correspondence between the calculated soft mode and observed superstructure can be reconciled, the results would identify concrete tuning knobs for CDW vectors in a prototypical TMD, with potential implications for engineering electronic instabilities. The combination of temperature-dependent ARPES and doping/interlayer-dependent phonon calculations is a strength, though the doping-sign discrepancy limits the direct mapping to microscopic mechanism.

major comments (2)
  1. [Abstract / phonon calculations] Abstract and phonon-calculation section: the soft mode near q=1/2 ΓK is reported to emerge under hole doping in the calculations, yet the 2H† sample is inferred to be electron-doped from ARPES; this sign reversal means the ab initio instability does not reproduce the experimental ordering vector under the stated conditions, leaving the claimed correspondence between the calculated mode and the 2×√3 CDW unsupported and weakening the assertion that interlayer spacing controls the vector in the manner described.
  2. [Abstract / discussion] The central claim that the results 'establish band filling and interlayer spacing as key control parameters' rests on the q=1/2 ΓK mode matching the observed 2×√3 superstructure; given the doping mismatch, an explicit reconciliation (e.g., via additional calculations at the experimental doping level or discussion of possible intercalation effects on effective filling) is required before the claim can be considered load-bearing.
minor comments (2)
  1. [Experimental methods / figures] ARPES figures lack explicit error bars on doping estimates and temperature-dependent intensity; adding these would strengthen the lock-in transition interpretation.
  2. [Results] Notation for the 2×√3 superstructure and its relation to the calculated q vector should be clarified with a reciprocal-space diagram.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for identifying the doping-sign discrepancy between the phonon calculations and the experimental inference for the 2H† phase. We address each major comment below and indicate where revisions will be made.

read point-by-point responses

  1. Referee: [Abstract / phonon calculations] Abstract and phonon-calculation section: the soft mode near q=1/2 ΓK is reported to emerge under hole doping in the calculations, yet the 2H† sample is inferred to be electron-doped from ARPES; this sign reversal means the ab initio instability does not reproduce the experimental ordering vector under the stated conditions, leaving the claimed correspondence between the calculated mode and the 2×√3 CDW unsupported and weakening the assertion that interlayer spacing controls the vector in the manner described.

    Authors: We acknowledge the doping-sign mismatch. The manuscript already states in the abstract that the q=1/2 ΓK instability appears under hole doping in the calculations. The central observation remains that increasing the interlayer spacing (as occurs with self-intercalation) stabilizes a competing soft mode at this wavevector whose real-space periodicity matches the observed 2×√3 superstructure. We will expand the discussion section to explicitly address possible origins of the sign discrepancy, including non-rigid-band effects from intercalated Ta atoms and the sensitivity of the mode to small changes in filling near the Lifshitz transition. No additional calculations are feasible within the current computational setup, but the qualitative demonstration that interlayer spacing can switch the dominant instability vector is retained. revision: partial

  2. Referee: [Abstract / discussion] The central claim that the results 'establish band filling and interlayer spacing as key control parameters' rests on the q=1/2 ΓK mode matching the observed 2×√3 superstructure; given the doping mismatch, an explicit reconciliation (e.g., via additional calculations at the experimental doping level or discussion of possible intercalation effects on effective filling) is required before the claim can be considered load-bearing.

    Authors: The claim is supported by two independent results: (i) the 3×3 instability is shown to be highly sensitive to band filling, consistent with the conventional sample, and (ii) the new soft mode at q≈1/2 ΓK emerges specifically when interlayer spacing is increased, independent of the precise doping sign. We will revise the abstract and discussion to qualify the claim by noting the doping-sign limitation and by adding a paragraph discussing how intercalation may alter the effective filling or screening beyond a simple rigid-band picture. This makes the control-parameter statement more precise without overclaiming a direct microscopic mapping. revision: partial

Circularity Check

0 steps flagged

No circularity: independent experiment and ab initio calculations

full rationale

The paper reports ARPES measurements on doping and CDW signatures in two samples, then performs separate DFT phonon calculations showing sensitivity of instabilities to band filling and interlayer spacing. No equation reduces an observed ordering vector to a fitted parameter from the same dataset, and no load-bearing claim rests on self-citation. The acknowledged doping-sign mismatch between calculation and experiment is a correctness issue, not a circularity reduction. The central claim that band filling and interlayer spacing are control parameters follows directly from the two independent data sources without self-definition or renaming.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work relies on standard density-functional-theory phonon calculations and experimental ARPES without introducing new fitted parameters or postulated entities beyond the conventional framework for CDW studies.

axioms (1)
  • standard math Standard approximations of density functional theory suffice to identify phonon instabilities in 2H-TaS2
    Invoked when computing the phonon spectrum to locate the 3x3 and competing soft modes.

pith-pipeline@v0.9.1-grok · 5898 in / 1279 out tokens · 27185 ms · 2026-06-29T10:09:29.782396+00:00 · methodology

discussion (0)

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Reference graph

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