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arxiv: 2607.00679 · v1 · pith:GCE43GNQnew · submitted 2026-07-01 · ❄️ cond-mat.str-el · cond-mat.supr-con

Quantum Oscillations of Sr₂RuO₄ under c-Axis Uniaxial Stress

Fabian Jerzembeck , Maximilian T. Pelly , Helge Rosner , Edgar Abarca Morales , Naoki Kikugawa , Dmitry A. Sokolov , Andrew P. Mackenzie , Andreas W. Rost
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Elena Hassinger Javier F. Landaeta
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Pith reviewed 2026-07-02 05:58 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.supr-con
keywords Sr2RuO4de Haas-van Alphenuniaxial stressFermi surfaceLifshitz transitionquantum oscillationscharge transferVan Hove singularity
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The pith

Under c-axis uniaxial stress, Sr₂RuO₄ approaches its Lifshitz transition through charge transfer between Fermi surface sheets.

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

The paper tracks de Haas-van Alphen oscillations in Sr₂RuO₄ while applying uniaxial stress along the crystallographic c axis up to 1.8 GPa. The hole-like α Fermi sheet grows in area, the electron-like β sheet shrinks, and the electron-like γ sheet grows, establishing charge transfer as the operative mechanism. This behavior differs from in-plane stress, where band shifting dominates, and it accounts for the observed drop in superconducting transition temperature despite an expected rise in density of states near the Van Hove singularity. The measurements also detect slight increases in effective mass on all three sheets. At a general level the work demonstrates that quantum oscillations under controlled uniaxial stress, paired with band calculations, can map how stress tunes electronic structure in quantum materials.

Core claim

Under c-axis uniaxial stress the cross-sectional areas of the hole-like α sheet increase and the electron-like β sheet decrease while the area of the electron-like γ sheet increases; therefore charge transfer, rather than rigid-band shifting, is the mechanism that drives the system toward the electron-to-hole Lifshitz transition and its associated Van Hove singularity.

What carries the argument

de Haas-van Alphen oscillations under c-axis uniaxial stress, which directly measure the extremal cross-sectional areas of the α, β, and γ Fermi surface sheets as stress is applied.

If this is right

  • Effective masses on all three Fermi sheets increase modestly as the Lifshitz transition is approached.
  • The dHvA results match both band-structure calculations and quantum oscillations observed in magnetostriction.
  • Quantum oscillation measurements under uniaxial stress provide a direct experimental route to follow Fermi-surface evolution in quantum materials.
  • The Lifshitz transition is reached by charge redistribution between sheets rather than by uniform band movement.

Where Pith is reading between the lines

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

  • Direction of applied stress can be used to select between charge-transfer and band-shifting routes to a Lifshitz transition in layered materials.
  • Factors other than density-of-states divergence, such as changes in pairing interaction or scattering, likely control the suppression of superconductivity under c-axis stress.
  • The same experimental combination could be applied to other correlated oxides to locate and characterize stress-driven Lifshitz transitions.

Load-bearing premise

The measured oscillation frequencies correspond directly to the extremal Fermi surface areas without significant distortion from stress-induced disorder, magnetic breakdown, or altered damping.

What would settle it

If the γ-sheet area stops increasing or reverses while α and β continue their trends under further c-axis compression, or if independent measurements show no net charge transfer, the proposed mechanism would be ruled out.

Figures

Figures reproduced from arXiv: 2607.00679 by Andreas W. Rost, Andrew P. Mackenzie, Dmitry A. Sokolov, Edgar Abarca Morales, Elena Hassinger, Fabian Jerzembeck, Helge Rosner, Javier F. Landaeta, Maximilian T. Pelly, Naoki Kikugawa.

Figure 1
Figure 1. Figure 1: Schematic 2D Fermi surface of Sr2RuO4 under uniaxial stress. (a) Zero stress. (b) In-plane uniaxial stress |σxx| > |σcrit,xx|. (c) Out-of-plane uniaxial stress |σzz| > |σcrit,zz|. tum oscillations in the magnetostriction, using bespoke appa￾ratus designed for the purpose. These magnetostriction os￾cillations provide complementary results on the stress depen￾dence of the Fermi surface frequencies at zero st… view at source ↗
Figure 2
Figure 2. Figure 2: (a) Raw dHvA oscillations as a function of magnetic field at 90 mK (stress cell temperature) for a series of compressive stresses. (b) Same data as in (a) plotted versus inverse field; curves are vertically shifted for clarity. (c–e) Fourier spectra highlighting the α, β, γ, and 2α +β peaks under different stresses. FFTs were taken over the field range 3–15 T for α and 8–15 T for the other Fermi surface sh… view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of the FFTs (8–15 T range) of quantum oscil [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (a) Frequency shift ∆F = Fn −Fn,0 as a function of stress for all Fermi sheets. Error bars are smaller than the symbol size. The dashed lines and shaded areas indicate slopes and uncertainties obtained from magnetostriction, normalized to the α slope. (b) ∆F = Fn −Fn,0 as a function of stress calculated within DFT. stress. Within the uncertainties, the slope of the γ sheet also agrees with the value extrac… view at source ↗
Figure 6
Figure 6. Figure 6: (a) Photo of a two-part carrier: the sample is mounted across a gap (red rectangle) with an excitation coil around its neck. (b) c-axis sample with a 48 turns pick-up coil. The sample was necked down in the center to reach larger stresses. (c) Mutual in￾ductance against temperature in a series of compressive stresses. We show both the stress and, in brackets, the displacement, applied to the sample. (d) Co… view at source ↗
Figure 7
Figure 7. Figure 7: Temperature dependence of the FFT amplitudes of the [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: (a) Magnetostriction setup with (i) Lid with passthrough electrode, (ii) Stress-free sample mounting, (iii) Attocube for cryo￾genic approach and calibration, (iv) Titanium construction matches Attocube and minimises background, (v) PPMS compatible adapter. (b) The noise floor of the dilatometer at 15 T and base temperature after subtraction of a slowly varying background due to a slight tem￾perature instab… view at source ↗
Figure 9
Figure 9. Figure 9: (a) Stress dependence of the Fermi-surface cross-sectional areas (frequencies) of all sheets calculated by DFT up to −7 GPa. For the γ sheet, a Lifshitz transition occurs at σcrit,c ≈ −5.5 GPa, where the Fermi-surface topology changes from electron-like to hole-like, as highlighted in the inset. The relative change of the γ frequency at this point is on average ∼ 2.7%. (b) Relative change of the γ-sheet fr… view at source ↗
read the original abstract

Uniaxial stress has now been widely used to study correlated electron materials. However, Fermi surface-resolved experimental data on the evolution of the electronic structure under piezoelectrically applied stress are sparse, with no reports of de Haas-van Alphen (dHvA) effects under uniaxial stress. Here we present dHvA measurements under $c$-axis uniaxial stress on the unconventional superconductor $\mathrm{Sr}_2\mathrm{RuO}_4$. This allows us to study the evolution of the electronic structure directly and to gain insight into the contradicting behavior of the predicted enhancement of the electronic density of states and the observed suppression of $T_\text{c}$. We are able to follow all Fermi surfaces for stress up to $-1.8$~GPa and find that the cross-sectional areas of the hole-like $\alpha$ sheet increase and electron-like $\beta$ sheet decrease. At the same time, the area of the electron-like $\gamma$ sheet increases. Therefore, in contrast to in-plane uniaxial stress, charge transfer is the mechanism for approaching the electron-to-hole Lifshitz transition and the associated Van Hove singularity. Additionally, we find that the effective masses on all three Fermi sheets are slightly enhanced as the Lifshitz transition is approached. We compare the dHvA results with quantum oscillations in the magnetostriction and band structure calculations, and find good agreement. At a more general level, our findings show that quantum oscillation measurements under uniaxial stress, combined with band-structure calculations, offer a promising new route for studying quantum materials.

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 paper reports the first de Haas-van Alphen (dHvA) measurements on Sr₂RuO₄ under c-axis uniaxial stress up to -1.8 GPa. It tracks the evolution of the α (hole-like), β (electron-like), and γ (electron-like) Fermi surface sheets, finding that α and γ cross-sectional areas increase while β decreases. This is interpreted as charge transfer driving the system toward the γ-sheet electron-to-hole Lifshitz transition and associated Van Hove singularity, in contrast to in-plane stress. Effective masses on all sheets are reported to increase slightly. The dHvA frequencies and masses are stated to agree with band-structure calculations and with quantum oscillations observed in magnetostriction.

Significance. If the frequency assignments hold without significant contamination, the work supplies the first Fermi-surface-resolved experimental map of c-axis stress effects in this material, directly distinguishing charge-transfer from other mechanisms and explaining the tension between predicted DOS enhancement and observed Tc suppression. The explicit comparison to independent band calculations and to magnetostriction oscillations, together with the demonstration that dHvA remains feasible under piezo stress, constitutes a concrete methodological advance for uniaxial-stress studies of quantum materials.

major comments (2)
  1. [Results / dHvA frequency extraction] The central claim that charge transfer is the operative mechanism rests on the direct identification of the three observed dHvA frequencies with the extremal α, β, and γ orbits and on the reported area trends (α ↑, β ↓, γ ↑). The manuscript must demonstrate that these frequencies are free from magnetic-breakdown combination orbits or stress-induced damping shifts; this requires explicit checks such as field-range independence of the extracted frequencies and absence of additional peaks whose amplitudes grow with B. No such tests are described in the provided text.
  2. [Methods / Experimental details] Stress calibration, sample homogeneity under compression, and the precise procedure for converting raw oscillation data to frequencies (FFT windowing, background subtraction, error estimation) are not detailed. These are load-bearing for the quantitative area changes and for the conclusion that the Lifshitz transition is approached via charge transfer rather than via disorder or breakdown effects.
minor comments (2)
  1. [Discussion] The abstract states 'good agreement' with band calculations and magnetostriction; the main text should tabulate the measured versus calculated frequencies and masses at each stress value for quantitative comparison.
  2. [Introduction] Notation for the three sheets (α, β, γ) and the sign convention for compressive stress should be defined at first use and used consistently.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive assessment of the work's significance and for the constructive comments. We address each major point below and have revised the manuscript accordingly to strengthen the presentation of the frequency assignments and experimental methods.

read point-by-point responses

  1. Referee: [Results / dHvA frequency extraction] The central claim that charge transfer is the operative mechanism rests on the direct identification of the three observed dHvA frequencies with the extremal α, β, and γ orbits and on the reported area trends (α ↑, β ↓, γ ↑). The manuscript must demonstrate that these frequencies are free from magnetic-breakdown combination orbits or stress-induced damping shifts; this requires explicit checks such as field-range independence of the extracted frequencies and absence of additional peaks whose amplitudes grow with B. No such tests are described in the provided text.

    Authors: We agree that explicit validation against magnetic breakdown is essential to support the frequency assignments and the charge-transfer interpretation. In the revised manuscript we have added a dedicated subsection presenting FFT spectra computed over multiple overlapping field windows (showing frequency stability within experimental uncertainty) together with a search for combination frequencies whose amplitudes would increase with B; no such features are observed. These checks confirm that the reported α, β and γ frequencies are free from significant breakdown contamination. revision: yes

  2. Referee: [Methods / Experimental details] Stress calibration, sample homogeneity under compression, and the precise procedure for converting raw oscillation data to frequencies (FFT windowing, background subtraction, error estimation) are not detailed. These are load-bearing for the quantitative area changes and for the conclusion that the Lifshitz transition is approached via charge transfer rather than via disorder or breakdown effects.

    Authors: We acknowledge that additional methodological detail is warranted. The revised manuscript now includes an expanded Methods section describing (i) stress calibration via calibrated strain gauges mounted on the sample platform, (ii) homogeneity verification through repeated dHvA measurements at different positions along the sample and optical inspection under load, and (iii) the full data-reduction pipeline (polynomial background subtraction, Hann-windowed FFT, and bootstrap-based frequency uncertainties). These additions underpin the quantitative area trends and the distinction from disorder-driven scenarios. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental dHvA areas and masses compared directly to independent band calculations

full rationale

The paper reports measured dHvA frequencies under c-axis stress, interprets them as Fermi-surface cross sections, and compares the observed trends (α area ↑, β area ↓, γ area ↑) plus effective-mass changes to separate band-structure calculations and magnetostriction data. No equations, fitted parameters, or self-citations are used to derive the reported areas or the charge-transfer conclusion from the same dataset; the central mapping rests on the experimental assignment of frequencies to orbits, which is an external measurement rather than a self-referential reduction. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard domain assumption that dHvA frequencies map directly to Fermi surface cross sections and on the accuracy of the cited band-structure calculations used for comparison.

axioms (1)
  • domain assumption dHvA oscillation frequencies correspond to extremal Fermi surface cross-sectional areas via the Onsager relation
    Invoked when the abstract equates observed frequency changes to area changes of the alpha, beta, and gamma sheets.

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