Origin of dimensional crossover in quasi-one-dimensional hollandite K$_{2}$Ru$_{8}$O$_{16}$

Asif Ali; B. H. Reddy; Ravi Shankar Singh; Sakshi Bansal

REVIEW 3 major objections 4 minor 82 references

Origin of dimensional crossover in quasi-one-dimensional hollandite K$_{2}$Ru$_{8}$O$_{16}$

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read K2Ru8O16 undergoes a 1D-to-3D electronic crossover at about 150 K, driven by Fermi-surface warping that overtakes thermal broadening as temperature falls.

desk verdict Solid experimental evidence for a TLL-to-3D crossover in K2Ru8O16, but the quantitative warping argument for T* ~ 150 K is a free-electron estimate that shifts to ~100 K with the paper's own mass enhancement. read the letter →

arxiv 2501.07822 v1 pith:ZEPLOQIT submitted 2025-01-14 cond-mat.str-el

Asif Ali , Sakshi Bansal , B. H. Reddy , Ravi Shankar Singh This is my paper · ORCID

classification cond-mat.str-el PACS 71.27.+a71.18.+y79.60.-i71.10.Pm

keywords dimensionalcrossoverTomonaga-Luttingerliquidnon-FermiK2Ru8O16hollanditeFermi-surfacewarpingLDA+DMFTphotoemissionspectroscopy

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 argues that the quasi-one-dimensional hollandite K2Ru8O16 undergoes a dimensional crossover at about 150 K, from a Tomonaga-Luttinger liquid (a state of interacting electrons in one dimension) to a three-dimensional non-Fermi-liquid metal, and that this crossover is driven by Fermi-surface warping. High-resolution photoemission spectra collapse onto a single Tomonaga-Luttinger scaling curve with exponent alpha = 0.45 from 300 K down to 150 K, then deviate at lower temperatures where a clear Fermi cutoff appears. Dynamical mean-field calculations based on a local-density-approximation starting point show the Fermi surface becoming progressively more warped as temperature falls. A simple parabolic-band estimate indicates that below roughly 150 K this warping exceeds the momentum broadening caused by thermal energy, so interchain hopping becomes coherent and the one-dimensional behavior is lost. If this picture is correct, it explains why the crossover temperature appears in transport, spectroscopy, and theory at the same value.

What carries the argument

The argument rests on two pieces of machinery. First, the experimental fingerprint: the Tomonaga-Luttinger liquid spectral intensity I(epsilon) proportional to T^$\alpha$ times an absolute value squared of a Gamma function, whose temperature-collapse with exponent $\alpha$ identifies one-dimensional behavior; here the collapse holds for $\alpha$ = 0.45 down to 150 K and fails below. Second, the theoretical engine: the momentum-resolved spectral function A(k, omega) from LDA+DMFT, from which the Fermi-surface warping $\Delta$ k_z is read off as a function of temperature. The crossover criterion compares this warping to the thermal momentum broadening $\Delta$ k = k_B T / ($hbar^{2}$ k_F / m_e) of a single parabolic band crossing the Fermi level; T* is where the two curves intersect.

What would settle it

Angle-resolved photoemission on single crystals at several temperatures would settle it: if the measured Fermi-surface warping does not grow as temperature is lowered, or if the temperature at which the spectra stop scaling with alpha = 0.45 shifts while the calculated warping curve stays fixed, the proposed mechanism would be falsified.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is a mechanism, not just a crossover observation: the 150 K crossover in K2Ru8O16 is set by the competition between temperature-dependent Fermi-surface warping and thermal energy. The warping, which expresses the transverse (interchain) hopping t_perp, grows almost linearly as temperature is lowered in the LDA+DMFT spectral function, while the thermal momentum broadening of a parabolic band shrinks linearly with temperature. The two curves cross near 150 K, matching the temperature at which the photoemission spectra stop following Tomonaga-Luttinger scaling and instead develop a Fermi cutoff with monotonically decreasing intensity at the Fermi level. The paper also shows that alternative explanations, such as a temperature-dependent chemical potential shift or disorder-induced Altshuler-Aronov behavior, cannot reproduce the observed spectral evolution.

Load-bearing premise

The quantitative match between the calculated and measured crossover temperatures rests on the assumption that single-site LDA+DMFT, with Coulomb parameters U = 5.0 eV and J = 0.5 eV chosen by analogy with other 4d systems, gives a reliable temperature trend for the Fermi-surface warping in this quasi-one-dimensional material, and that the free-electron parabolic-band estimate of thermal momentum broadening is a fair comparison.

Editorial extensions

If this is right

The measured ~150 K crossover in transport and photoemission is reproduced without invoking structural, magnetic, or charge-order transitions, so the phenomenon is electronic in origin.
The Tomonaga-Luttinger exponent alpha = 0.45 obtained from scaling gives a quantitative measure of the Luttinger parameter K_rho in the high-temperature regime.
Below 150 K the appearance of a Fermi cutoff together with monotonically decreasing spectral weight at the Fermi level means the low-temperature state is a non-Fermi liquid, not a conventional Fermi liquid.
The strong temperature dependence of Fermi-surface warping implies that effective dimensionality in quasi-1D systems is temperature-tunable, which should affect resistivity anisotropy and magnetotransport.

Reading between the lines

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

A direct extrapolation of the same mechanism predicts that applying pressure along the transverse direction, which increases interchain hopping, should raise the crossover temperature T*; the paper's slope of warping versus temperature could be used to estimate the shift.
The comparison uses the free-electron mass in the thermal-broadening estimate; using the experimentally inferred enhanced mass would reduce the slope of the thermal line and move the calculated T* downward, so the precise agreement at 150 K may be somewhat fortuitous.
Because the paper itself notes single-site DMFT is insufficient for one-dimensional systems, non-local correlation effects (e.g., cluster DMFT or coupled-chain calculations) could either sharpen or shift the crossover; testing this would clarify whether the warping trend is an artifact.
The observed failure of the Tomonaga-Luttinger collapse below 150 K could also be tested by directly measuring the momentum dependence with angle-resolved photoemission on single crystals, which would provide a point-by-point confirmation of the warping increase.

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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

Here's my take on Ali et al. The experimental core is solid and worth referee time: temperature-dependent PES on K2Ru8O16 showing a clean TLL scaling collapse with alpha = 0.45 from 300 K down to 150 K, and a clear breakdown below, with careful checks against chemical-potential shift and Altshuler-Aronov disorder physics. The LDA+DMFT spectral functions also do real work, reproducing the lower Hubbard band and a mass enhancement ~1.5 that matches specific heat. The authors are admirably candid about single-site DMFT's limits in 1D.

The soft spot is exactly where the stress-test note lands. The whole quantitative origin story—that FS warping overtakes thermal momentum broadening at T* ~ 150 K—is built on converting k_B T to a momentum spread using a single parabolic band and the free-electron mass. Their own DMFT says m*/m_b ~ 1.5. Put that in, and the crossing drops to ~100 K, not 'slightly' reduced as the paper claims. And for a quasi-1D band, the relevant thermal smearing is set by the chain's Fermi velocity, not an isotropic free-electron parabola. So the claimed quantitative match at 150 K is not evidence for the warping mechanism; it's an artifact of the m_e choice. The qualitative trend—warping grows as T falls—is fine, and the experimental crossover itself is independent. But the 'spectacular observation' of matched temperatures is not established.

Minor quibbles: the low-T non-Fermi liquid label rests on a Fermi cutoff plus decreasing EF intensity, without a quantitative line-shape fit; that's a reasonable suggestion, not a proof. And the DMFT uses U = 5 eV, J = 0.5 eV while cRPA gives 3.3 eV; the paper does show insensitivity to U and J in Appendix A, so this is minor.

Who's it for: people working on quasi-1D correlated oxides. I'd bring it to our reading group; the TLL scaling data is a nice data point, and the warping analysis is a good cautionary tale about back-of-the-envelope estimates. I'd send it to review; the experimental part is solid and the theoretical part is worth publishing after the quantitative claim is fixed or properly hedged.

Referee Report

3 major / 4 minor

Summary. The manuscript reports a combined photoemission and LDA+DMFT study of the quasi-one-dimensional hollandite K2Ru8O16, arguing that the system exhibits a Tomonaga-Luttinger liquid (TLL) behavior above approximately 150 K and undergoes a dimensional crossover to a three-dimensional non-Fermi-liquid-like metallic state below that temperature. The experimental evidence includes a scaling collapse of near-EF photoemission spectra with TLL exponent alpha = 0.45 for 300-150 K, the failure of that collapse below 150 K, and the appearance of a Fermi cutoff with monotonically decreasing intensity at EF at low temperature. The theoretical part computes the Fermi-surface warping from LDA+DMFT as a function of temperature and compares it with a simple thermal momentum-broadening estimate, obtaining a crossover temperature near 150 K. The paper concludes that temperature-dependent FS warping, enhanced by correlation, is the origin of the dimensional crossover.

Significance. If the central claim is valid, the paper provides a rare direct spectroscopic observation of a TLL-to-higher-dimensional crossover in a bulk quasi-1D oxide and proposes a concrete microscopic mechanism based on temperature-dependent Fermi-surface warping. The manuscript is commendable for combining high-resolution temperature-dependent photoemission with self-consistent LDA+DMFT calculations, and for explicitly testing alternative explanations such as chemical-potential shifts and Altshuler-Aronov disorder effects. The experimental scaling collapse and its breakdown below 150 K are consistent with earlier transport data, giving internal coherence to the interpretation. However, the quantitative link between the calculated warping and the experimentally determined crossover temperature rests on a simplified free-electron estimate, so the 'origin' claim is not yet established at the same level as the existence of the crossover.

major comments (3)

[§III, Fig. 4(b)] The crossover temperature T* is obtained by comparing the LDA+DMFT warping Δk_z(T) with the thermal momentum broadening Δk = k_B T / (ℏ² k_F / m_e), where m_e is the bare electron mass. This choice of mass is not justified for a quasi-1D band; the relevant scale is the Fermi velocity along the chain. More importantly, the paper's own LDA+DMFT calculation yields m*/m_b ≈ 1.5 and specific heat data give a mass enhancement of 1.7. Replacing m_e by m* = 1.5 m_e in the same formula shifts the crossing from ~150 K to ~100 K, which is not 'slightly reduce T*' as the text claims. The quantitative agreement at 150 K is therefore not robust evidence for the warping mechanism; the claim that warping dominates below T* would need to be reexamined with a proper quasi-1D Fermi velocity or a band-structure-based estimate of the thermal broadening.
[§III, Fig. 3(c) and Conclusion] The assignment of the low-temperature state as 'non-Fermi liquid like behaviour' rests on the appearance of a Fermi cutoff and monotonically decreasing spectral intensity at EF. No quantitative line-shape fit to any non-Fermi-liquid model is provided; the paper only states that no value of the TLL exponent alpha can describe the data. This leaves open alternative interpretations, such as a pseudogap-like suppression of spectral weight or a dimensional crossover into a more conventional three-dimensional metal with reduced density of states near EF. Because the non-Fermi-liquid claim is stated in the abstract and conclusion, it should be either supported by a quantitative fit or explicitly softened to 'Fermi-cutoff behavior with suppressed EF weight'.
[Appendix D and Fig. 4(a)] The temperature dependence of the Fermi-surface warping Δk_z(T) is computed with single-site LDA+DMFT, an approximation that the authors themselves describe as 'insufficient to fully capture the subtleties of one-dimensional systems.' The slope of Δk_z(T) is a load-bearing input for the T* estimate, yet the manuscript does not show how this slope varies with the choice of U and J (the spectral function is shown to be robust, but not the FS-warping slope) or with alternative methods such as cluster DMFT. A sensitivity analysis of Δk_z(T) would help establish whether the near-agreement with the experimental T* is accidental or structurally meaningful.

minor comments (4)

[§II, Fig. 2] The text refers to the Ru 3d5/2 core-level spectra as being shown in Fig. 2(d), but Fig. 2(d) displays LDA+DMFT spectral functions; the core-level spectra appear in a separate panel. The figure/table cross-references should be corrected.
[§III, Fig. 4(a)] The sentence 'the larger FS warping was observed in the full Brillouin zone (Fig. 1(a))' appears to point to the wrong panel; the Fermi surface is shown in Fig. 1(e) or 1(c), not the band structure in Fig. 1(a).
[Appendix B, Fig. 6] The description of the simulated spectra and the comparison with experiment in Fig. 6(b) is somewhat hard to follow; explicitly stating which lines correspond to which temperature and which are the shifted spectra would improve clarity.
[Throughout] The phrase 'monotonously decreasing' should be 'monotonically decreasing' in several places for grammatical correctness.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the LDA+DMFT warping analysis and the TLL scaling collapse are independent; the only same-group citations (parameter choices and disorder checks) are not load-bearing.

full rationale

The paper's central derivation chain is: (1) fit the TLL exponent alpha = 0.45 to the high-temperature photoemission scaling and observe its breakdown below ~150 K; (2) compute the LDA+DMFT Fermi-surface warping Delta k_z(T) from the band structure and self-energy; (3) compare Delta k_z(T) with the free-electron thermal-broadening line Delta k = k_B T / (hbar^2 k_F / m_e), with k_F = 0.08 A^-1 taken from the calculation, and read off T* ~ 150 K as the crossing; (4) conclude that warping dominates below T*. Steps (2) and (3) do not use alpha or the experimental T* as input, so the match with the photoemission-derived crossover is an independent quantitative comparison rather than a fit renamed as a prediction. The alpha fit is a data-analysis step, and the 150 K crossover read from the same spectra is corroborated by transport (Ref. [29]) and by the independent DMFT crossing. The paper explicitly acknowledges that the single-site LDA+DMFT approach is insufficient to capture all 1D subtleties and that the parabolic-band broadening estimate is simplistic; these are robustness limitations, not circularity. The only same-group citations (Ref. [48] for the U = 5 eV, J = 0.5 eV choice, and Refs. [66] in the disorder-lineshape control) are non-load-bearing: the DMFT parameter choice is additionally checked in Appendix A against varying U and J, and the disorder analysis is a negative control. No step reduces to its own input.

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

The paper's experimental crossover observation depends on fitting the TLL exponent alpha; its 'origin' claim depends on a parabolic-band estimate and on DMFT with U, J chosen by analogy with other compounds rather than from the reported cRPA values. These are free parameters and domain assumptions, not invented physical entities.

free parameters (4)

TLL exponent alpha = 0.45 ± 0.05
Fitted to collapse the scaled photoemission intensity for 300-150 K; a free parameter in the TLL lineshape formula used to assert one-dimensional behavior.
Hubbard U in LDA+DMFT = 5.0 eV
Chosen by analogy with other 4d systems (Refs. 48,49), not from the cRPA value of 3.33 eV reported in the SM; affects the magnitude and temperature dependence of the FS warping.
Hund coupling J in LDA+DMFT = 0.5 eV
Set alongside U by analogy with prior 4d studies; Appendix A shows limited sensitivity of spectra, but warping analysis uses this fixed value.
Linear extrapolation of Delta kz(T) = intercept 0.02 Å^-1 at 0 K
Obtained by linear fit to LDA+DMFT warping values at finite T; used to mark the crossover where warping equals thermal momentum broadening.

assumptions (4)

domain assumption A single parabolic band with free-electron mass converts thermal energy kBT into a momentum broadening scale that can be compared with FS warping.
This is the basis of the grey line and the T* estimate in Fig. 4(b); no material-specific effective mass or full band structure is used.
domain assumption Single-site LDA+DMFT with CTQMC and maximum entropy analytic continuation gives quantitatively reliable temperature-dependent FS warping for this quasi-1D system.
The authors themselves state this approach 'is insufficient to fully capture the subtleties of one-dimensional systems', so the calculated warping trend and its extrapolation are uncertain.
domain assumption The TLL lineshape and universal scaling form apply to the momentum-integrated photoemission spectra of the polycrystalline sample.
The analysis fits a single exponent to polycrystalline, momentum-integrated spectra; this is standard practice but not directly justified for this compound.
domain assumption The near-EF photoemission spectra are dominated by bulk electronic structure with negligible surface or matrix-element temperature dependence.
The authors note surfaces were fractured in UHV but do not report a surface-sensitivity check; matrix-element changes with temperature are assumed absent.

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Cite this review

Pith. "Pith review of Origin of dimensional crossover in quasi-one-dimensional hollandite K$_{2}$Ru$_{8}$O$_{16}$." pith.science (2026). https://pith.science/paper/ZEPLOQIT

@misc{pith2026250107822,
  author       = {Pith},
  title        = {Pith review of: Origin of dimensional crossover in quasi-one-dimensional hollandite K$_2$Ru$_8$O$_16$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZEPLOQIT}},
  note         = {Machine review of arXiv:2501.07822}
}

abstract

Intriguing phenomenon of dimensional crossover is comprehensively studied by experimental and theoretical investigation of electronic structure in quasi-one-dimensional hollandite K$_{2}$Ru$_{8}$O$_{16}$. Valence band photoemission spectra in conjunction with density functional theory within local density approximation combined with dynamical mean field theory (LDA+DMFT) reveal moderately correlated electronic structure. Anomalous temperature dependence of high-resolution spectra in the vicinity of Fermi level suggests Tomonaga-Luttinger liquid state down to 150 K, below which it undergoes a dimensional crossover from one-dimensional to three-dimensional electronic behaviour. Monotonously decreasing spectral intensity at the Fermi level along with Fermi cut-off at low temperature suggests non-Fermi liquid like behaviour. Many body effects captured within LDA+DMFT reveal increased warping of the Fermi surface with lowering temperature. A simple analysis suggests that the warping dominates the thermal energy induced momentum broadening at low temperature, leading to the 3D electronic behaviour. Our results offer valuable insight in understanding the interplay of dimensionality, electron correlation and thermal energy governing various exotic phenomena in quasi-one-dimensional systems.

Figures

Figures reproduced from arXiv: 2501.07822 by the authors.

**Figure 2.** FIG. 2. (a) Valence band photoemission spectra of K [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** FIG. 3. (a) Temperature dependent high-resolution photoe [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: FIG. 4. (a) LDA+DMFT calculated FS cut in the Γ-X-P-Z [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

**Figure 5.** Figure 5: FIG. 5. Ru 4 [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

**Figure 7.** Figure 7: FIG. 7. (a) Variation of spectral intensity at [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]

**Figure 8.** Figure 8: FIG. 8. (a-c) Temperature dependence of the imaginary part [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]

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