Effect of mechanical strain on the optical properties of nodal-line semimetal ZrSiS

A. N. Rudenko; Shengjun Yuan; Weiqing Zhou

REVIEW 3 major objections 5 minor 81 references

Effect of mechanical strain on the optical properties of nodal-line semimetal ZrSiS

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read ZrSiS, a layered nodal-line semimetal, keeps its flat infrared conductivity under compression up to 10 GPa, undergoes a Lifshitz transition near 2 GPa tension that lowers infrared spectral weight, and hosts low-loss ~20 eV plasmons whose…

desk verdict A solid, well-calibrated DFT+RPA study with interesting strain predictions, but the headline Lifshitz-transition stress is internally inconsistent and rests on meV-scale band physics the method doesn't anchor. read the letter →

arxiv 1908.08789 v2 pith:DPVFIEIP submitted 2019-08-23 physics.comp-ph cond-mat.mtrl-sci

Weiqing Zhou , A. N. Rudenko , Shengjun Yuan This is my paper · ORCID

classification physics.comp-phcond-mat.mtrl-sci

keywords nodal-linesemimetalZrSiSopticalconductivityplasmonhyperbolicmaterialstrainengineeringLifshitztransitionfirst-principlescalculation

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

This paper uses first-principles calculations to ask how external strain changes the optical response of the nodal-line semimetal ZrSiS. It predicts that the material's signature flat infrared conductivity survives uniaxial compression up to 10 GPa, but the flat region narrows as the load increases. Under tensile stress near 2 GPa, a Lifshitz transition reshapes the Fermi surface and weakens interband screening, cutting the infrared spectral weight. At high energy the same calculations predict low-loss plasmons near 20 eV with anisotropic dispersion, and the strongly anisotropic dielectric response implies a type-I hyperbolic regime for deep-ultraviolet plasmons. The practical payoff is a single air-stable layered material whose infrared and ultraviolet optical properties could be tuned mechanically.

What carries the argument

The argument is carried by the wave-vector- and frequency-dependent dielectric function computed in the random phase approximation from first-principles band structures, with interband transitions treated from dipole matrix elements in the long-wavelength limit and intraband transitions added as a standard Drude term. Plasma excitations are identified with the zeros of the real part of the dielectric function, and the energy loss function $\operatorname{Im}[-1/\epsilon(q,\omega)]$ locates which of these modes are low-loss. The hyperbolic regime is diagnosed from the product $\epsilon_{xx}(\omega)\,\epsilon_{zz}(\omega) < 0$, which makes the constant-frequency surface in Eq. (11) a hyperboloid rather than a sphere. The same dielectric function, evaluated at $q \to 0$ with a finite damping parameter, produces the infrared conductivity and the screened plasma frequency that calibrate the calculation against experiment.

What would settle it

Measure the electron energy loss spectrum of a ZrSiS crystal under uniaxial strain: the paper predicts a sharp low-loss peak near 20 eV with anisotropic quadratic dispersion, and a separate check is that the in-plane and out-of-plane permittivities obtained from optical ellipsometry should have opposite signs in a ~0.6 eV window near 20 eV; if the 20 eV loss peak is absent or the permittivity signs are the same, the high-energy plasmon and hyperbolic claims fail. For the Lifshitz transition, quantum oscillation or ARPES measurements on a crystal under ~2 GPa tensile stress should show the hole pockets merging near $k_z=\pi/c$ and the quadratic band crossing the Fermi level along Z-R.

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Extended reading notes

Core claim

The central claim is that ZrSiS combines a strain-tolerant low-energy optical fingerprint with strain-tunable high-energy plasmonics. The frequency-independent in-plane optical conductivity, a known fingerprint of this nodal-line semimetal, remains flat under uniaxial compression up to 10 GPa, although the flat window shrinks and the spectral weight grows by roughly 50% at 5% compression. Tensile strain acts differently: near 1.3-3.4 GPa the Fermi surface changes topology through two Lifshitz transitions, and the resulting drop in interband screening reduces the infrared spectral weight and raises the screened plasma frequency from about 1.0 eV to about 1.3 eV at 4% tension. In the high-energy region, the calculations show a weakly damped plasmon near 20 eV whose quadratic dispersion is strongly anisotropic, and where the product of the in-plane and out-of-plane permittivities is negative over a ~0.6 eV window, the defining condition for type-I hyperbolic plasmons. The strain response of this high-energy mode is small in frequency but large in dispersion, so strain acts as a tuning knob rather than a switch.

Load-bearing premise

The load-bearing premise is that the calculated band structure and scalar dielectric function are accurate enough that the quadratic band sits at the right energy near the Fermi level and the permittivity signs near 20 eV are correct; a shift of a few tens of meV would move or erase the tensile Lifshitz transition, and wrong signs would make the hyperbolic regime an artifact of the calculation.

Editorial extensions

If this is right

Uniaxial compression up to 10 GPa leaves the flat infrared conductivity intact, so ZrSiS-based infrared elements could tolerate large mechanical loads without losing their broadband response.
Tensile stress near 2 GPa acts as a mechanical switch: the Lifshitz transition weakens interband screening and lowers the infrared spectral weight, with the effect saturating after the Fermi-surface reconstruction around 3.4 GPa.
Electron energy loss measurements should find a sharp, low-loss peak near 20 eV whose dispersion is quadratic and markedly different in-plane and out-of-plane.
The negative product of permittivities near 5 and 20 eV implies type-I hyperbolic plasmon propagation in windows of about 0.6 eV; the 20 eV window is the practically relevant one because the 5 eV mode is strongly damped.
Strain of up to 5% changes the 20 eV plasmon frequency by only a few percent, but can change its out-of-plane dispersion coefficient by roughly 30%, giving a quantitative strain-tuning handle.

Reading between the lines

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

Beyond the paper's own claims, the predicted tensile Lifshitz transition offers a clean test of the chemical-pressure picture: stretched ZrSiS should optically resemble ZrSiSe or ZrSiTe, and the ~2 GPa transition stress could be measured by quantum oscillations or ARPES under a four-point bending setup.
Beyond the paper's own claims, the 20 eV hyperbolic window, if verified by EELS, would make ZrSiS one of the few natural (unstructured) hyperbolic materials in the deep ultraviolet; applications like subwavelength imaging and thermal emission engineering would follow without nanofabrication.
Beyond the paper's own claims, since the scalar RPA neglects local-field effects and spin-orbit coupling, the most decisive numerical check is a full dielectric-matrix or Bethe-Salpeter calculation at 15-25 eV; if the sign of either permittivity changes there, the hyperbolic regime would move or disappear.

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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

Colleague,

Quick take: this is a careful first-principles study that reproduces the measured zero-strain optics of ZrSiS and then pushes two new claims — a strain-driven Lifshitz transition that weakens interband screening, and a ~20 eV hyperbolic plasmon regime. The low-energy calibration is genuinely good: unscreened plasma frequency 3.15 vs 2.88 eV, flat conductivity ~7000 vs 6600, ε∞≈9 vs 7.8. That anchors the method where it matters for the infrared claim. And the results are computed, not fitted; the only tuned parameter is broadening η, and they test its effect. No circularity.

What's actually new: the strain dependence of the flat conductivity region, the tensile Lifshitz transition, and the deep-UV hyperbolic plasmons. Prior work measured zero-strain optics and connected the ZrSiX family via chemical pressure; this adds the strain axis.

The soft spots are where the paper makes its loudest claims. The hyperbolic regime at ~20 eV rests on scalar RPA without local field effects, computed from GGA-PBE bands without SOC, and there is no independent check in that energy range. That doesn't kill it, but it means the UV prediction is a plausibility argument, not a settled result.

The bigger problem is the Lifshitz transition. The abstract and conclusions say '2 GPa', but Sec. IV and Fig. 8 report P1=1.3 GPa and P2=3.4 GPa. Those are two distinct topology changes; the text does not say which one causes the screening reduction. This is not a typo-level issue, because the whole tensile-strain story hangs on the quadratic band crossing the Fermi level at a specific stress, and that crossing is exactly the kind of meV-scale feature that GGA-PBE with no SOC can misplace. The authors justify neglecting SOC as a low-temperature/low-frequency effect, but a Lifshitz transition is a zero-energy Fermi-surface property, so that justification doesn't hold. A tens-of-meV error could shift the critical stress by more than 1% or remove the transition. They calibrate aggregate low-energy quantities, but none of those is sensitive to the quadratic band's position within tens of meV.

Who should read this: anyone working on ZrSiX optics, topological semimetal plasmons, or natural hyperbolic materials. The infrared part is solid enough to cite; the UV and Lifshitz parts should be treated as predictions needing follow-up.

Recommendation: send it to peer review. A serious referee should ask for (a) a consistent statement of the critical stress, (b) a band-structure check of the quadratic band position at the relevant energy scale (e.g., hybrid functional or GW, and an estimate of SOC-induced shifts), and (c) a caveat on the scalar-RPA/no-LFE approximation in the UV. With those addressed, it would be a useful paper.

Referee Report

3 major / 5 minor

Summary. The manuscript reports first-principles calculations of the optical conductivity, dielectric function, and plasmonic response of the nodal-line semimetal ZrSiS, focusing on the effect of uniaxial strain. Using GGA-PBE band structures and a scalar RPA dielectric function with a Drude correction (Sec. II), the authors reproduce several low-energy experimental quantities for the pristine compound: the in-plane unscreened plasma frequency (3.15 vs 2.88 eV), the flat infrared conductivity (~7000 vs 6600 Ohm^-1 cm^-1), and epsilon_inf ~ 9 vs the experimental ~7.8. The main claims are that the frequency-independent infrared conductivity is robust under uniaxial compression up to 10 GPa but its flat region narrows with increasing compression; that tensile stress around 2 GPa induces a Lifshitz transition that weakens interband screening and reduces infrared spectral weight; and that the high-energy response hosts low-loss ~20 eV plasmons with strongly anisotropic dispersion, including a possible hyperbolic regime in the deep ultraviolet. The strain dependence of the high-energy plasmon dispersion is also discussed.

Significance. If the predictions hold, the paper identifies ZrSiS as a mechanically tunable natural hyperbolic material for ultraviolet plasmonics and connects the strain response to the chemical-pressure trend across the ZrSiX family (X=S, Se, Te). The manuscript has clear strengths: the zero-strain calculations are calibrated against measured optical quantities, the Drude contribution is handled explicitly, and the central predictions are concrete and falsifiable by EELS and infrared spectroscopy under uniaxial stress. The high-energy and tensile-strain predictions, however, rest on approximations that are not validated at the relevant energy scale, which is the main source of uncertainty in the paper.

major comments (3)

[Abstract; Sec. IV, Fig. 8] The abstract and Conclusions state that 'Upon uniaxial tensile stress of 2 GPa, the Fermi surface undergoes a Lifshitz transition,' but Sec. IV identifies two Lifshitz transitions at P1 ≈ 1.3 GPa and P2 ≈ 3.4 GPa (with tension as negative stress in Fig. 8). The manuscript should reconcile this discrepancy: if the headline claim refers to the P1 transition, the abstract should say so and mention the second transition; if it refers to a single transition near 2 GPa, that conflicts with the two computed critical stresses. As written, the central quantitative claim is internally inconsistent.
[Sec. IV, Figs. 7-8] The prediction that tensile strain of order 2 GPa triggers a Lifshitz transition and weakens interband screening depends on the energy position of the quadratic electron band along Z–R relative to the Fermi level. This band is obtained from GGA-PBE without spin-orbit coupling, and the calibration quantities in Sec. III A—unscreened plasma frequency, flat optical conductivity, and epsilon_inf—are aggregate low-energy properties that are insensitive to the band position at the meV scale. Because the stated SOC-induced gaps are up to ~20–30 meV, an error of that size could shift the critical strain substantially or remove the transition altogether. The authors should provide a direct check of this band's position (e.g., ARPES comparison, SOC-included band structure, or a hybrid-functional calculation) or explicitly qualify the predicted critical stress as an estimate with large uncertainty.
[Sec. III B, Fig. 5] The claims of low-loss ~20 eV plasmons and a hyperbolic regime are based on the signs of epsilon_xx(omega) and epsilon_zz(omega) computed in the scalar RPA with local field effects neglected and using GGA-PBE band structures. The experimental calibration in Sec. III A covers only the low-energy (<= 2 eV) response; no independent check is presented for the ~20 eV region, where the permittivity signs are the load-bearing input for the hyperbolic dispersion. The authors should discuss the expected influence of local field effects, self-energy corrections, and SOC on the 20 eV permittivity, or compare with existing EELS or vacuum-UV optical data. Alternatively, the hyperbolic-regime claim should be explicitly labeled as a prediction that remains to be confirmed.

minor comments (5)

[Sec. IV; Figs. 7 and 8] The strain sign convention is confusing: the text defines uzz as positive for compression and negative for tension, while the critical stresses are printed as P1 = -1.3 GPa and P2 = -3.4 GPa. Please adopt a single, clearly stated convention and apply it consistently in the text and figure captions.
[Sec. II B, Eq. (8)] The expression for sigma_{2,intra}(omega) appears to be missing a factor of omega; the standard relation is sigma_2(omega) = omega [1 - epsilon_1(omega)]/(4 pi). Please check and correct the formula.
[Sec. III B] There are several typographical errors in this section: 'Simliar' should be 'Similar', 'hyprobolic' should be 'hyperbolic' (twice), and 'electronmagnetic' should be 'electromagnetic'.
[Sec. IV] In the discussion of the nonsymmorphic Dirac node, 'Andreas et al.' should be 'Topp et al.' (Ref. [13]) for accuracy.
[Sec. IV, Eq. (10) and Fig. 10] The values of the dispersion coefficient A in Eq. (10) are not reported; given the paper's emphasis on strain tuning of the plasmon dispersion, providing A and its strain dependence would make the claim quantitative.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central predictions are computed from first-principles DFT band structures and RPA response functions, with no target-derived fitting or load-bearing self-citation.

full rationale

The paper's central results — the flat infrared conductivity, its robustness and narrowing under compression, the tensile Lifshitz transition, the ~20 eV low-loss plasmons, and the hyperbolic UV regime — are all outputs of a DFT+RPA calculation, not quantities fed into the calculation. The only adjustable parameter is the damping η, which is set to 40 meV from the experimentally estimated electron linewidth (~30 meV at 300 K), and the resulting flat conductivity value (~7000 Ω−1cm−1) emerges from the computed band structure and matrix elements rather than being imposed by the choice of η. The Lifshitz transition at P1 ≈ 1.3 GPa and P2 ≈ 3.4 GPa is a band-structure consequence of the strain-dependent position of the quadratic electron band along Z–R relative to the Fermi level; no fitting to the claimed transition stress is performed. The high-energy plasmon and hyperbolic-regime claims follow directly from the momentum-resolved RPA dielectric function and the sign condition εxx(ω)·εzz(ω) < 0, with no parameter tuned to produce those signs. Comparisons to experiment (unscreened plasma frequency, flat conductivity, ε∞ ≈ 9 vs ~7.8) are validations rather than inputs. The chemical-pressure comparison to Ref. [45] is an independent external trend used for consistency, not a premise on which the strain calculations depend. Self-citations in Refs. [34,35,66] concern correlation effects or similar EELS behavior and are not load-bearing for the optical predictions. No uniqueness theorem, ansatz, or renamed empirical pattern is invoked as a substitute for computation. The paper therefore shows no circularity; any concern about GGA-PBE accuracy at the meV scale for the quadratic band is a correctness or robustness issue, not a circularity issue.

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

The central predictions depend on standard DFT+RPA modeling assumptions (GGA-PBE bands, scalar head-only RPA, no SOC, separate Drude intraband term) and on two broadening parameters, eta and delta; no new entities are introduced. The free parameters are physical broadenings, but their values affect the shape of the low-energy spectra.

free parameters (2)

damping parameter eta = 40 meV
Introduced in Eq. (2) as the electron linewidth and treated as a free parameter in Sec. II B. The paper chooses eta=40 meV for all low-energy conductivity calculations, motivated by the experimental linewidth ~30 meV at 300 K; the flatness of the conductivity is robust for eta=30-60 meV, so this is a physical broadening, but it also smooths numerical oscillations for eta<20 meV.
Drude damping delta = not stated
Appears in Eq. (6) for the intraband Drude contribution; the paper says it has similar physical meaning as eta but never gives its value, so the low-energy intraband response has an unspecified broadening parameter.

assumptions (4)

domain assumption The independent-particle RPA with only the G=G'=0 head of the dielectric matrix is adequate; local field effects are negligible.
Sec. II B states this explicitly and justifies it by weak charge density inhomogeneity in 3D systems [59]. The hyperbolic regime near 20 eV depends on the signs and magnitudes of the q=0 permittivities, so this assumption directly supports the most novel claim.
domain assumption Spin-orbit coupling is negligible for the energy ranges considered (above 20 meV and above 100 K).
Sec. II A states SOC is not included because it is relevant only below 100 K and below 20 meV [33]. The Lifshitz transition under tensile strain occurs in the low-energy band structure, so SOC could in principle shift the quadratic band or nodal line, though the expected gap is small.
domain assumption GGA-PBE exchange-correlation functional gives a quantitatively reliable band structure near the Fermi level and in the 0-20 eV range.
All results inherit the GGA band structure. The paper validates zero-strain plasma frequencies and conductivity against experiment, but no strained or high-energy validation is provided.
domain assumption The intraband response can be described by a Drude term added separately to the interband RPA response.
Sec. II B adds Drude corrections because the q to 0 limit of Eq. (2) does not explicitly contain intraband transitions. This is standard practice [62] but is an assumption about how to combine the two contributions.

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Cite this review

Pith. "Pith review of Effect of mechanical strain on the optical properties of nodal-line semimetal ZrSiS." pith.science (2026). https://pith.science/paper/DPVFIEIP

@misc{pith2026190808789,
  author       = {Pith},
  title        = {Pith review of: Effect of mechanical strain on the optical properties of nodal-line semimetal ZrSiS},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DPVFIEIP}},
  note         = {Machine review of arXiv:1908.08789}
}

abstract

Optical properties of nodal-line semimetal ZrSiS are studied using first-principles calculations. Frequency-independent optical conductivity is a fingerprint of the infrared optical response in ZrSiS. We find that this characteristic feature is robust with respect to uniaxial compressive strain of up to 10 GPa, yet with the flat region being narrowed with increasing strain. Upon uniaxial tensile stress of 2 GPa, the Fermi surface undergoes a Lifshitz transition accompanied by a weakening of the interband screening, which reduces the spectral weight of infrared excitations. We also show that the high-energy region is characterized by low-loss plasma excitations at $\sim$20 eV with essentially anisotropic dispersion. Strongly anisotropic dielectric properties suggest the existence of a hyperbolic regime for plasmons in the deep ultraviolet range. Although the frequencies of high-energy plasmons are virtually unaffected by external uniaxial deformation, their dispersion can be effectively tuned by strain.

Figures

Figures reproduced from arXiv: 1908.08789 by the authors.

**Figure 1.** FIG. 1. (a) Schematic representation of the ZrSiS crystal structure; (b) Calculated band structure and orbital-resolved density of [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗

**Figure 2.** FIG. 2. (a) Real part of the optical conductivity shown as a [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** FIG. 3. Imaginary (upper panels) and real (lower panels) parts of the dielectric function of pristine ZrSiS calculated as a [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (6 more)

**Figure 4.** Figure 4: FIG. 4. Upper panels: Electron energy loss spectrum [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

**Figure 6.** Figure 6: FIG. 6. Black curve: The [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

**Figure 5.** Figure 5: FIG. 5. (a) Product of the in-plane and out-plane real dielec [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

**Figure 7.** Figure 7: FIG. 7. (a) Band structures calculated in the vicinity of the Fermi energy for different values of the uniaxial strain [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]

**Figure 8.** Figure 8: FIG. 8. Strain-dependent low-energy plasma frequency [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]

**Figure 9.** Figure 9: FIG. 9. Real part of the optical conductivity [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]

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can clearly see the prominent ﬂat conductivity from 0.1 to 0.4 eV

and out-of-plane [001] crystallographic directions; (b) Real part of the in-plane optical conductivity calculated for diﬀerent damping parametersη; (c) Imaginary part of the op- tical conductivity calculated along [100] and [001] directions; (d) Real part of the in-plane diele...

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

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The value obtained for the [100] directions is in good agreement with the exper- imental estimate of 2.88 eV [33]

components, respectively. The value obtained for the [100] directions is in good agreement with the exper- imental estimate of 2.88 eV [33]. In Figures 2(a) and 2(c), we show the real and imaginary parts of the optical conductivity calculated in the region up to 2 eV for [100] and [001] directions of photon propagation. The spectral weight obtained for th...

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