arxiv: 2605.06044 · v1 · submitted 2026-05-07 · ❄️ cond-mat.mes-hall

Recognition: unknown

Quantum oscillations and nonsaturating magnetoresistivity in nodal-line semimetals

Rui Min , Yi-Xiang Wang

Authors on Pith no claims yet

Pith reviewed 2026-05-08 06:26 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall

keywords nodal-line semimetalsquantum oscillationsmagnetoresistivityFermi surfacetorusmagnetotransporttopological materials

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The pith

Nodal-line semimetals exhibit two distinct quantum oscillation frequencies from their torus Fermi surface.

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

This paper investigates magnetotransport in nodal-line semimetals using a low-energy model motivated by EuGa4 experiments. It finds that quantum oscillations in chemical potential and magnetoconductivity show two distinct frequencies caused by the torus Fermi surface, proposed as a key signature of these materials. The magnetoresistivity is calculated to be nonsaturating with magnetic field but with a smaller ratio than observed in experiment.

Core claim

The torus Fermi surface in nodal-line semimetals leads to two distinct oscillation frequencies in the magnetoconductivity and chemical potential, which can be regarded as an important experimental signature. Although the magnetoresistivity is nonsaturating in the low-energy region, the MR ratio is much smaller than that reported in the experiment on EuGa4.

What carries the argument

The torus Fermi surface, which supports two different extremal cross sections for cyclotron motion in a magnetic field.

If this is right

Two oscillation frequencies serve as a signature to identify nodal-line semimetals experimentally.
Magnetoresistivity does not saturate as the magnetic field increases.
The calculated MR ratio being smaller suggests the model misses some contributions present in real materials.
Oscillations occur in both chemical potential and conductivity.

Where Pith is reading between the lines

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

This signature could help differentiate nodal-line semimetals from Weyl or Dirac semimetals in transport measurements.
The MR discrepancy may be resolved by including disorder, interactions, or higher bands in future models.
The results could guide experiments on other nodal-line materials to verify the torus-induced dual frequencies.

Load-bearing premise

The low-energy effective model for the nodal-line semimetal captures the dominant magnetotransport features without significant contributions from other bands, disorder, or interactions.

What would settle it

Observation of only one frequency in quantum oscillation experiments on a nodal-line semimetal would falsify the prediction of two frequencies from the torus Fermi surface.

Figures

Figures reproduced from arXiv: 2605.06044 by Rui Min, Yi-Xiang Wang.

**Figure 1.** Figure 1: FIG. 1. (Color online) (a) The 2D bands of nodal-line view at source ↗

**Figure 2.** Figure 2: FIG. 2. (Color online) (a) The LL spectra vs the magnetic view at source ↗

**Figure 3.** Figure 3: FIG. 3. (Color online) (a) The evolution of the chemical po view at source ↗

**Figure 4.** Figure 4: FIG. 4. (Color online) The longitudinal conductivity ¯σ view at source ↗

**Figure 6.** Figure 6: FIG. 6. (Color online) The MR ratio view at source ↗

**Figure 5.** Figure 5: FIG. 5. (Color online) The longitudinal MR ¯ρ view at source ↗

read the original abstract

Understanding the magnetotransport behaviors in topological systems remains alluring, as a lot of intrinsic information could be extracted, e.g., the band structures, Berry phase, Fermi surface, carrier density, and so on. Motivated by the recent magnetotransport developments in nodal-line semimetal, EuGa4, in this paper, we will study the magnetotransport properties of the system, focusing on the quantum oscillations and nonsaturating magnetoresistivity (MR). Firstly, we analyze the chemical potential and magnetoconductivity oscillations with the magnetic field and reveal that there exist two distinct oscillation frequencies, which are caused by the characteristic torus Fermi surface and can be regarded as an important experimental signature of nodal-line semimetals. Then we calculate the MR and find that although the MR is nonsaturating with the magnetic field in the low-energy region, the MR ratio is much smaller than that reported in the experiment.

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.

Desk Editor's Note private letter to a colleague

Two oscillation frequencies from the torus Fermi surface stand out as a calculable signature, but the low-energy model underpredicts the experimental MR magnitude by a large margin.

read the letter

The paper applies semiclassical transport to a low-energy model of nodal-line semimetals with a torus Fermi surface. It finds two distinct quantum oscillation frequencies tied to that geometry and shows nonsaturating magnetoresistance, motivated by EuGa4 data. The oscillation result is the clearest new piece here: the torus shape naturally produces multiple frequencies where simpler pockets give one, and the authors flag this as an experimental marker for the class of materials.

Referee Report

2 major / 2 minor

Summary. The manuscript studies magnetotransport in nodal-line semimetals via a low-energy effective model motivated by EuGa4. It reports two distinct frequencies in quantum oscillations of chemical potential and magnetoconductivity, attributed to the torus Fermi surface and proposed as an experimental signature of nodal-line semimetals. It also finds nonsaturating magnetoresistivity whose magnitude is much smaller than experimental values.

Significance. The two-frequency oscillation pattern, if robust, would provide a distinctive signature tied directly to the nodal-line torus geometry. The nonsaturating MR is consistent with expectations for open-orbit or topological systems, but the quantitative shortfall relative to experiment indicates that the low-energy model captures only part of the physics. The work adds to the literature on how Fermi-surface topology controls oscillation spectra in semimetals.

major comments (2)

[Abstract and results on oscillations] Abstract and main results section: the assertion that the two oscillation frequencies 'can be regarded as an important experimental signature of nodal-line semimetals' rests on the low-energy torus model, yet the same model is stated to produce an MR ratio 'much smaller than that reported in the experiment.' No analysis is given of whether additional bands, disorder, or interactions (omitted by construction) would introduce extra frequencies or change the relative amplitudes, which directly affects whether the two frequencies constitute a clean signature.
[Model and methods] Model section: the effective Hamiltonian and the procedure for extracting the two frequencies from the torus Fermi surface are not compared against a full tight-binding or DFT band structure of EuGa4. Without this check it is unclear whether the reported frequencies survive when the low-energy approximation is relaxed, which is load-bearing for the experimental-signature claim.

minor comments (2)

[Abstract] The abstract states results from calculations but supplies no equations, parameter values, or error estimates; a brief methods summary would improve readability.
[Results] Notation for the two frequencies (e.g., F1 and F2) and the precise definition of the torus cross-sections should be introduced earlier and used consistently in figures and text.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment below and have revised the text to better clarify the scope and limitations of the low-energy model while defending the robustness of the reported signatures within that framework.

read point-by-point responses

Referee: Abstract and main results section: the assertion that the two oscillation frequencies 'can be regarded as an important experimental signature of nodal-line semimetals' rests on the low-energy torus model, yet the same model is stated to produce an MR ratio 'much smaller than that reported in the experiment.' No analysis is given of whether additional bands, disorder, or interactions (omitted by construction) would introduce extra frequencies or change the relative amplitudes, which directly affects whether the two frequencies constitute a clean signature.

Authors: We agree that the low-energy model is minimal by design and that omitted physics could quantitatively affect MR amplitudes. However, the two frequencies arise directly from the distinct extremal orbits on the inner and outer equators of the torus Fermi surface, a geometric feature tied to the nodal-line dispersion. Within the model, both chemical-potential and conductivity oscillations exhibit these frequencies cleanly, without additional peaks. Additional bands or disorder would primarily rescale carrier densities or scattering times but are not expected to generate new extremal areas at the nodal-line energy scale. We have added a clarifying paragraph in the discussion section that explicitly addresses this point, notes the model's underestimation of the experimental MR ratio, and explains why the two-frequency pattern remains a distinctive topological signature. revision: partial
Referee: Model section: the effective Hamiltonian and the procedure for extracting the two frequencies from the torus Fermi surface are not compared against a full tight-binding or DFT band structure of EuGa4. Without this check it is unclear whether the reported frequencies survive when the low-energy approximation is relaxed, which is load-bearing for the experimental-signature claim.

Authors: The effective Hamiltonian is obtained by a standard low-energy expansion around the nodal line, with parameters chosen to reproduce the torus Fermi surface reported in prior studies of EuGa4. The frequency extraction follows the semiclassical Onsager relation applied to the two extremal cross-sections of that torus. We acknowledge that an explicit side-by-side comparison with a full magnetic-field DFT or tight-binding calculation would provide further validation. Such a computation, however, lies beyond the scope of the present work, which is devoted to analytic and numerical results within the effective model. In the revised manuscript we have added citations to the relevant DFT literature on EuGa4 and a brief statement on the regime of validity of the low-energy approximation. revision: partial

standing simulated objections not resolved

Explicit numerical extraction of quantum-oscillation frequencies from a full DFT or tight-binding band structure of EuGa4 under finite magnetic field

Circularity Check

0 steps flagged

No circularity: frequencies derived directly from model torus surface

full rationale

The paper constructs a low-energy effective Hamiltonian for the nodal-line semimetal, computes the torus-shaped Fermi surface, then derives the two distinct oscillation frequencies from the extremal orbits on that surface via standard semiclassical quantization. No parameters are stated to be fitted to the EuGa4 magnetotransport data and then reused as 'predictions'; the MR calculation is performed within the same model and the smaller ratio is explicitly reported as a limitation rather than hidden. No self-citations, uniqueness theorems, or ansatzes imported from prior work by the same authors appear in the derivation chain. The analysis remains self-contained within the stated model assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based solely on abstract, no explicit free parameters, axioms, or invented entities are detailed; the work implicitly relies on a standard low-energy Hamiltonian for nodal-line semimetals.

pith-pipeline@v0.9.0 · 5458 in / 1059 out tokens · 45662 ms · 2026-05-08T06:26:25.305193+00:00 · methodology

discussion (0)

Reference graph

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