Charge-density-wave quantum critical point under pressure in 2$H$-TaSe$_2$

Adrian Merritt; Alexei Bosak; Alsu Ivashko; Amir-Abbas Haghighirad; Ayman H. Said; Florian K. Diekmann; Frank Weber; Gaston Garbarino; Kai Rossnagel; Luigi Paolasini

REVIEW 3 major objections 6 minor 2 references

Charge-density-wave quantum critical point under pressure in 2$H$-TaSe$_2$

T0 review · 3 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read High-pressure scattering places 2H-TaSe2's charge-density-wave quantum critical point at pc = 19.9(1) GPa, next to the 8.2 K superconducting maximum.

desk verdict Solid high-pressure XRD/IXS study pins the CDW endpoint at 19.9 GPa with a predictive DFPT calculation, but the claim that the QCP sits exactly at the superconducting dome hangs on a single-point pressure offset. read the letter →

arxiv 2501.12315 v2 pith:QQBXTZ2T submitted 2025-01-21 cond-mat.str-el cond-mat.mtrl-sci

Yuliia Tymoshenko , Amir-Abbas Haghighirad , Rolf Heid , Tom Lacmann , Alsu Ivashko , Adrian Merritt , Xingchen Shen , Michael Merz

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Gaston Garbarino Luigi Paolasini Alexei Bosak Florian K. Diekmann Kai Rossnagel Stephan Rosenkranz Ayman H. Said Frank Weber

This is my paper · ORCID

classification cond-mat.str-elcond-mat.mtrl-sci

keywords chargedensitywavequantumcriticalpointsuperconductivity2H-TaSe2highpressuresoftphononmodeinelasticX-rayscatteringelectron-phononcoupling

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

2H-TaSe2, a layered metal whose electrons condense into a periodic charge-density wave at low temperature, becomes superconducting when pressure suppresses that order. The paper reports high-pressure X-ray diffraction and inelastic X-ray scattering showing that the charge-density-wave transition is driven continuously to zero temperature at a quantum critical point $p_c = 19.9(1)\,\mathrm{GPa}$. That critical pressure sits essentially on top of the published maximum superconducting transition temperature $T_{\mathrm{sc}} = 8.2\,\mathrm{K}$. If the result holds, the same lattice vibration that freezes into the charge-density wave is what pairs electrons into superconductivity, making 2H-TaSe2 a reference case for order-suppressed enhanced superconductivity.

What carries the argument

The load-bearing object is the CDW soft phonon mode: the low-energy lattice vibration, pinned near the commensurate ordering wave vector $q_{\mathrm{CCDW}} = (1/3,0,0)$, whose squared frequency goes to zero at the critical pressure. Inelastic X-ray scattering tracks this mode down to $4\,\mathrm{K}$ and shows the softening persists up to $p_c$, which is what makes the zero-temperature suppression point a genuine quantum critical point rather than a first-order endpoint. The same soft branch carries most of the electron-phonon coupling in the calculations, so the mechanism that freezes the charge-density wave is also the mechanism that produces the superconducting dome. X-ray diffraction of the CDW superlattice peak, through its position and linewidth, supplies the incommensurability $\delta$ and the low-temperature critical pressure.

What would settle it

Measure $T_{\mathrm{sc}}(p)$ and the CDW ordering temperature on the same 2H-TaSe2 crystal in the same helium pressure cell from 15 to 27 GPa. If the superconducting dome's maximum appears more than about 2 GPa away from $p_c = 19.9(1)\,\mathrm{GPa}$, or if the CDW transition shows a discontinuous jump at high pressure, the central claim of a CDW quantum critical point tied to the superconducting dome would be contradicted.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that charge-density-wave order in 2H-TaSe2 is suppressed continuously rather than abruptly: the CDW soft phonon mode softens to zero energy and the incommensurate CDW ordering temperature extrapolates to zero at $p_c = 19.9(1)\,\mathrm{GPa}$. Low-temperature elastic scattering brackets the critical pressure between $19.7$ and $20\,\mathrm{GPa}$, and the measured soft-mode energy goes to zero there, confirming that the transition stays second order. Ab initio lattice-dynamical calculations give a close critical pressure of $18.8\,\mathrm{GPa}$, and a strong-coupling calculation of the superconducting transition temperature from the same electron-phonon coupling produces a dome peaking near that pressure at about $11.9\,\mathrm{K}$, with roughly 73% of the coupling coming from the soft branch. The paper reconciles this with the previously reported experimental maximum of $8.2\,\mathrm{K}$ by adopting a pressure-medium offset of about $4.4\,\mathrm{GPa}$ between its helium pressure scale and the earlier resistivity pressure scale. The full refinement of the low-pressure commensurate CDW superstructure at $q_{\mathrm{CCDW}} = (1/3,0,0)$ resolves a long-standing structural debate and anchors the analysis.

Load-bearing premise

The load-bearing premise is that one matching point, $T_{\mathrm{CDW}} \approx 70\,\mathrm{K}$ at $15.5\,\mathrm{GPa}$ in the present helium pressure cell versus $20\,\mathrm{GPa}$ in the earlier resistivity study, fixes a constant $4.4\,\mathrm{GPa}$ offset between the two pressure scales over the whole range from 15 to 27 GPa; if that offset drifts, the published superconducting maximum may not actually sit at the measured critical pressure.

Editorial extensions

If this is right

The charge-density-wave transition in 2H-TaSe2 remains continuous up to its zero-temperature endpoint, so $p_c = 19.9(1)\,\mathrm{GPa}$ is a genuine quantum critical point.
Because the soft phonon branch supplies about 73% of the electron-phonon coupling, the same lattice instability that forms the CDW also mediates the superconducting pairing.
The reported $8.2\,\mathrm{K}$ superconducting maximum falls in the same pressure window as the CDW quantum critical point once the pressure-medium offset is applied, making 2H-TaSe2 a benchmark for order-fluctuation-enhanced superconductivity.
The refined low-pressure commensurate CDW superstructure settles the earlier structural debate and provides a bulk reference for interpreting single-layer TaSe2 experiments.
Re-examining $T_{\mathrm{sc}}(p)$ across the reentrant commensurate region near $8.6\,\mathrm{GPa}$ may reveal additional structure in the superconducting dome, since the published data skip that pressure window.

Reading between the lines

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

Editorial inference: if a constant pressure offset is the right correction, older non-hydrostatic pressure scales may have shifted CDW critical points and superconducting maxima apart in other transition-metal dichalcogenides; re-measuring those materials in helium could reveal more coincidences of this kind.
Editorial inference: a genuine CDW quantum critical point should leave a measurable quantum-critical fan, for example a $T$-linear resistivity or a diverging specific-heat coefficient just above $p_c$, so transport and thermodynamic measurements near $19.9\,\mathrm{GPa}$ could test whether the soft phonon really controls the pairing.
Editorial inference: the reentrant commensurate state between about 5 and 8.6 GPa is a natural place to look for a kink or a second peak in $T_{\mathrm{sc}}(p)$, because the published resistivity data do not resolve that window.
Editorial inference: the fully refined bulk CDW structure can serve as a benchmark input for first-principles studies of monolayer TaSe2, where enhanced superconductivity and a possibly different CDW pattern have been reported.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Two things to know. First, the experimental core is genuinely good: 120+ pressure-temperature XRD points in helium, a full refinement of the 3×3×1 commensurate CDW superstructure at 0.3 GPa and 40 K, and elastic IXS scans that bracket the CDW critical pressure at 10 K between 19.7 and 20 GPa. The pc=19.9(1) GPa value is about as clean as these measurements get, and the deposited CIFs and raw data are a real plus. Second, the DFPT calculation is a legitimate prediction, not a fit: it uses lattice parameters from the XRD, a standard μ*=0.1, and gets a soft-mode collapse at 18.8 GPa, within 1 GPa of the measured pc. That is meaningful, and it makes the case for a CDW QCP in 2H-TaSe2 reasonably solid.

The soft spot is exactly where the reader puts it: the proximity of the QCP to Tsc,max. The authors shift the Freitas et al. superconducting dome down by 4.4 GPa based on a single comparison—their TCDW≈70 K at 15.5 GPa versus Freitas's at 20 GPa. That offset is then assumed constant between 15 and 27 GPa. A ±2 GPa nonlinearity would pull Tsc,max away from pc, and the central narrative ('QCP in close vicinity to Tsc,max') loses its experimental anchor. The authors are transparent about the pressure-media mismatch, but transparency doesn't add anchor points. Full IXS evidence for the second-order character is also deferred to a later paper; the soft-mode data shown are suggestive but not the full analysis.

What's actually new is the pc determination, the superstructure refinement (which settles a long-standing structural question), and the revised pressure scale linking CDW and superconductivity. If you work on TMDs or CDW-superconductor interplay, you should cite the pc and the refinement. The dome-QCP link should be treated as a proposal, not a settled result, until there is a second pressure anchor or a direct measurement of Tsc on the same scale.

I'd send this to a serious referee—the dataset and the predictive DFPT deserve refereeing even if the dome link needs revision. For a reading group, it's a good case study in how a single calibration anchor can carry a lot of narrative weight.

Referee Report

3 major / 6 minor

Summary. The paper reports high-pressure synchrotron X-ray diffraction and inelastic X-ray scattering on 2H-TaSe2 up to 30 GPa and down to 4 K, together with DFPT lattice-dynamical and Eliashberg calculations. The authors determine a CDW quantum critical point at pc = 19.9(1) GPa, show that the CDW transition remains second order via a soft phonon mode, and propose that this QCP lies in close vicinity to the reported maximum superconducting transition temperature Tsc,max = 8.2 K (Ref. 33) after applying a pressure-scale offset of about 4.4 GPa. The ab-initio calculations predict a CDW soft-mode instability at pc,DFPT = 18.8 GPa and a superconducting dome peaking near that pressure, supporting the scenario of CDW-fluctuation-enhanced superconductivity.

Significance. If the central claim holds, 2H-TaSe2 would be a textbook example of a CDW quantum critical point enhancing superconductivity, useful for understanding other CDW superconductors including kagome metals. The experimental dataset is strong: more than 120 pressure-temperature XRD points, helium pressure medium, a full refinement of the commensurate CDW superstructure, and deposited raw data and CIFs. The DFPT calculations are not fitted to the experimental QCP; they use measured lattice parameters and a standard value of mu* = 0.1, yielding a predicted pc,DFPT = 18.8 GPa close to the observed 19.9 GPa. This independent prediction is a genuine strength. However, the experimental proximity of the QCP to Tsc,max rests on a single-anchor pressure-scale correction, and the full soft-mode evidence for continuous order is deferred to a separate publication, so the most publicized conclusion is not yet fully secured.

major comments (3)

[Results, Fig. 5(a) and the paragraph 'We assign the discrepancy of up to 4-5 GPa...'] The placement of Tsc,max near pc relies on a single-anchor pressure offset inferred from comparing TCDW ≈ 70 K at 20 GPa in Ref. 33 with TCDW ≈ 70 K at 15.5 GPa in this work, and then assuming a constant 4.4 GPa offset over the 15–27 GPa range. Because the comparison involves different observables (resistivity-derived TCDW vs XRD superstructure TCDW) and different pressure media, and because only one anchor is used, a variation of even ±2 GPa across this range would move the shifted Tsc,max window (≈18.6–22.6 GPa) away from pc = 19.9 GPa and undermine the central claim. The authors should provide additional pressure anchors, for example by comparing several (TCDW, p) points or by using a secondary calibration, and give a quantitative uncertainty estimate for the offset.
[Footnote a and Fig. 5(b)] The quantum-critical-point assignment requires that the suppressed CDW transition is continuous, and the only experimental evidence for this is the soft-phonon behavior. However, the manuscript defers the full inelastic scattering report to a separate publication ('A full report of the (ongoing) inelastic scattering experiments will be published elsewhere'). The present paper should include sufficient IXS data—such as the energy scans in Fig. S5 with the DHO fit parameters and the pressure dependence of the soft-mode energy—so that readers can independently assess whether the mode truly softens to zero at pc.
[Discussion, paragraph beginning 'Emergent superconductivity...'] The statement 'For the TMD 2H-TaSe2 we can conclusively say yes' is stronger than the evidence permits, given the pressure-scale offset uncertainty described above and the deferred IXS analysis. The conclusion should be tempered, or the supporting analysis for the offset and the soft mode should be included in the main text.

minor comments (6)

[Methods, IXS paragraph] The text says the IXS experiments were carried out at beamline ID28 at ESRF, but reference 85 describes a spectrometer at beamline 30-ID of the Advanced Photon Source. Please cite the correct instrument reference for ID28 or clarify the relationship.
[Methods, crystallographic software] The names 'SHELLXS97' and 'SHELLXL97 2014/7' should be written as 'SHELXS-97' and 'SHELXL-2014/7'.
[Supporting Information author list] The name 'Paolosini' is a typo for 'Paolasini'.
[Reference 38] The name 'Maartinez' should be 'Martinez'.
[Fig. 5(c) caption vs text] The caption states Tsc,DFPT = 11.8 K, while the main text gives Tsc,max(DFPT) = 11.9 K; please use a single value consistently.
[Fig. 5(a) caption] The open circles showing Tsc from Ref. 33 have been shifted by the pressure offset; this should be explicitly stated in the caption so that the reader is not misled about the raw pressure scale.

Circularity Check

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No significant circularity: the CDW QCP is fixed by direct XRD/IXS data and the DFPT calculations are independent parameter-free comparisons, so the central claim does not reduce to its inputs.

full rationale

The paper's central claim, a CDW quantum critical point at pc = 19.9(1) GPa, is determined experimentally from the disappearance of the CDW superlattice peak: elastic momentum scans at T = 10 K 'define the critical pressure of the CDW order in 2H-TaSe2 at this temperature to be between 19.7 GPa and 20 GPa, i.e. pc = 19.9(1) GPa.' This determination does not use the superconducting data or any fitted parameter. The DFPT lattice-dynamical calculation is similarly independent: pressure is included through experimentally measured lattice parameters ('Pressure dependent properties were calculated by using corresponding lattice parameters deduced from XRD at T = 40 K'), and the Eliashberg estimate uses a standard value of the Coulomb repulsion ('Using a typical value of μ∗ = 0.1'). The resulting pc,DFPT = 18.8 GPa and Tsc,DFPT = 11.9 K are compared with the measured values rather than imposed by them. The proximity of the QCP to the reported superconducting maximum is obtained by a one-point pressure-scale calibration anchored to TCDW ≈ 70 K in both pressure scales, i.e. Freitas et al. at 20 GPa versus the present 15.5 GPa measurement. This is an experimental offset assumption rather than a fitted quantity renamed as a prediction; its fragility is a robustness concern, not a circularity. Self-citations to the authors' prior work (Ref. 47) are used for sample provenance, calculation details, and a previous corroborating soft-mode calculation, but the load-bearing measurements and calculations are presented and re-derived in this paper. No equation is defined in terms of the quantity it is claimed to predict, and no fitted parameter is relabeled as a prediction. The derivation chain is therefore self-contained against the external superconducting data and against the experimental QCP.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claim rests on experimental observations plus a pressure-scale calibration and standard DFT-based theory. No new physical entities are postulated. The main non-experimental inputs are the DFPT approximation, the choice of mu*, and the single-point pressure offset.

free parameters (2)

mu* (effective Coulomb repulsion) = 0.1
Used in the Eliashberg equation to estimate Tsc; a typical value chosen by hand, not fitted to this material's data.
Pressure-scale offset = 4.4 GPa
Derived from a single comparison of TCDW ~70 K at 15.5 GPa (this work) and 20 GPa (Ref. 33); used to shift the published Tsc(p) data onto the helium pressure scale. The uncertainty is not quantified.

assumptions (4)

domain assumption DFPT with LDA and spin-orbit coupling accurately describes lattice dynamics and electron-phonon coupling in 2H-TaSe2 under pressure
Underlies the calculated soft-mode energies and Tsc,DFPT; accuracy is checked by comparison with measured pc, but LDA is an approximation.
domain assumption The pressure offset between this work and Ref. 33 is constant over 15-27 GPa
Load-bearing for placing Tsc,max near pc; based on one comparison point.
domain assumption The soft phonon mode near Q=(2.69,0,1) at 4 K is the CDW soft mode and its softening indicates a continuous transition
Used to infer the 2nd-order character of the suppressed transition; full IXS report deferred.
domain assumption The superlattice peak linewidth broadening above the resolution limit marks the critical pressure at T=40 K
Defines pc,T=40K ~ 18 GPa; assumes broadening is intrinsic to the transition.

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Cite this review

Pith. "Pith review of Charge-density-wave quantum critical point under pressure in 2$H$-TaSe$_2$." pith.science (2026). https://pith.science/paper/QQBXTZ2T

@misc{pith2026250112315,
  author       = {Pith},
  title        = {Pith review of: Charge-density-wave quantum critical point under pressure in 2$H$-TaSe$_2$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QQBXTZ2T}},
  note         = {Machine review of arXiv:2501.12315}
}

abstract

Suppressing of an ordered state that competes with superconductivity is one route to enhance superconducting transition temperatures. Whereas the effect of suppressing magnetic states is still not fully understood, materials featuring charge-density waves and superconductivity offer a clearer scenario as both states can be associated with electron-phonon coupling. Metallic transition-metal dichalcogenides are prime examples for such intertwined electron-phonon-driven phases, yet, various compounds do not show the expected interrelation or feature additional mechanisms which makes an unambiguous interpretation difficult. Here, we report high-pressure X-ray diffraction and inelastic X-ray scattering measurements of the prototypical transition-metal dichalcogenide 2$H$-TaSe$_2$ and determine the evolution of the charge-density-wave state and its lattice dynamics up to and beyond its suppression at the critical pressure $p_c = 19.9(1)\,\rm{GPa}$ and at low temperatures. The high quality of our data allows the full refinement of the commensurate charge-density-wave superstructure at low pressure and we find the quantum critical point of the charge-density-wave to be in close vicinity to the reported maximum superconducting transition temperature $T_{sc} = 8.2\,\rm{K}$. $Ab-initio$ calculations corroborate that 2$H$-TaSe$_2$ is a reference example of order-suppressed enhanced superconductivity and can serve as a textbook case to investigate superconductivity near a charge-density-wave quantum critical point.

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Works this paper leans on

2 extracted references · 1 canonical work pages

[2]

35 Liu, X., Chong, Y

Solid State Communications 18, 1393-1395 (1976). 35 Liu, X., Chong, Y. X., Sharma, R. & Davis, J. C. S. Discovery of a Cooper-pair density wave state in a transition-metal dichalcogenide. Science 372, 1447-1452 (2021). 36 Sanna, A. et al. Real-space anisotropy of the superconducting gap in the charge-density wave material 2H-NbSe2. npj Quantum Materials 7...

work page 1976
[3]

39 Sipos, B

Physical Review Letters 95, 117006 (2005). 39 Sipos, B. et al. From Mott state to superconductivity in 1T- TaS2. Nature materials 7, 960-965 (2008). 40 Kusmartseva, A., Sipos, B., Berger, H., Forró, L. & Tutiš, E. Pressure Induced Superconductivity in Pristine 1T-TiSe2. Physical Review Letters 103, 236401 (2009). 41 Moulding, O., Osmond, I., Flicker, F., ...

arXiv 2005

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Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [2]

35 Liu, X., Chong, Y

Solid State Communications 18, 1393-1395 (1976). 35 Liu, X., Chong, Y. X., Sharma, R. & Davis, J. C. S. Discovery of a Cooper-pair density wave state in a transition-metal dichalcogenide. Science 372, 1447-1452 (2021). 36 Sanna, A. et al. Real-space anisotropy of the superconducting gap in the charge-density wave material 2H-NbSe2. npj Quantum Materials 7...

work page 1976

[2] [3]

39 Sipos, B

Physical Review Letters 95, 117006 (2005). 39 Sipos, B. et al. From Mott state to superconductivity in 1T- TaS2. Nature materials 7, 960-965 (2008). 40 Kusmartseva, A., Sipos, B., Berger, H., Forró, L. & Tutiš, E. Pressure Induced Superconductivity in Pristine 1T-TiSe2. Physical Review Letters 103, 236401 (2009). 41 Moulding, O., Osmond, I., Flicker, F., ...

arXiv 2005