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arxiv: 2509.21303 · v1 · pith:TXW4DOA2new · submitted 2025-09-25 · ❄️ cond-mat.mtrl-sci · cond-mat.str-el

Topological nontrivial berry phase in altermagnet CrSb

Jianhua Du , Xin Peng , Yuzhi Wang , Shengnan Zhang , Yuran Sun , Chunxiang Wu , Tingyu Zhou , Le Liu
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Hangdong Wang Jinhu Yang Bin Chen Chuanying Xi Zhiwei Jiao Quansheng Wu Minghu Fang
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Pith reviewed 2026-05-18 13:44 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci cond-mat.str-el
keywords altermagnetCrSbBerry phasetopological semimetalShubnikov-de Haas oscillationsmagnetotransportfirst-principles calculations
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The pith

CrSb altermagnet shows a nontrivial Berry phase approaching π through quantum oscillations and band calculations.

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

The paper examines CrSb as a prototypical altermagnet to probe how its magnetic order connects to topological electronic states. High-field transport data reveal unsaturated magnetoresistance, nonlinear Hall response, and clear Shubnikov-de Haas oscillations that display Zeeman splitting. First-principles Fermi-surface calculations combined with Berry-phase extraction from these oscillations establish a phase value near π, confirming nontrivial topology. A reader would care because this supplies concrete evidence that altermagnets can host protected band features without conventional net magnetization, opening routes to study their interplay in quantum transport.

Core claim

Systematic Fermi surface and band calculations combined with Berry phase analysis confirm the nontrivial topological character of this material (with a Berry phase approaching π). High-field magneto-transport measurements show magnetoresistance with no saturation up to 35 T and a power-law exponent of 1.48, while nonlinear Hall resistivity points to multiband transport and SdH oscillations exhibit Zeeman splitting at 1.6 K.

What carries the argument

Berry phase extracted from Shubnikov-de Haas quantum oscillations, cross-checked against first-principles Fermi-surface and band calculations.

If this is right

  • CrSb exhibits unsaturated magnetoresistance up to 35 T that follows a power law with exponent 1.48.
  • Nonlinear Hall resistivity signals multiband charge transport.
  • Zeeman-induced band splitting appears in the quantum oscillations at 1.6 K.
  • The combination of transport and calculations positions CrSb as a platform for topological states inside altermagnetic order.

Where Pith is reading between the lines

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

  • Similar Berry-phase signatures may appear in other altermagnetic compounds once comparable high-field oscillation data are obtained.
  • Surface-sensitive probes could test whether the bulk nontrivial phase produces protected boundary states.
  • Magnetic-field tuning of the altermagnetic order might offer a route to switch topological features on and off.

Load-bearing premise

The measured Shubnikov-de Haas oscillations come from well-defined Fermi-surface pockets whose phase can be cleanly isolated by standard Lifshitz-Kosevich fitting without major interference from other bands or scattering.

What would settle it

An independent angle-resolved photoemission measurement that finds no band crossings near the Fermi level, or a Berry-phase value extracted from oscillations that deviates substantially from π, would contradict the reported nontrivial topology.

Figures

Figures reproduced from arXiv: 2509.21303 by Bin Chen, Chuanying Xi, Chunxiang Wu, Hangdong Wang, Jianhua Du, Jinhu Yang, Le Liu, Minghu Fang, Quansheng Wu, Shengnan Zhang, Tingyu Zhou, Xin Peng, Yuran Sun, Yuzhi Wang, Zhiwei Jiao.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Single-crystal XRD pattern. The inset on the upper left: a schematic diagram of the magnetic moment configuration. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) SdH oscillatory components at various temperatures plotted as a function of the inverse magnetic field (1/ [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) The [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Band structure of CrSb without spin-orbit coupling (SOC) along the high-symmetry path Γ-M-K-Γ-A-L-H-A. [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Evolution of the selected fermi surface from weak SOC to SOC. (a) Selected fermi surface in the weak SOC limit, [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
read the original abstract

The study of topological properties in magnetic materials has long been one of the forefront research areas in condensed matter physics. CrSb, as a prototypical candidate material for altermagnetism, has attracted significant attention due to its unique magnetic properties. This system provides a novel platform for exploring the intrinsic relationship between altermagnetic order and exotic topological states. In this study, we combine systematic electrical transport experiments with first-principles calculations to investigate the possible realization mechanisms of topological semimetal states in CrSb and their manifestations in quantum transport phenomena. Our high field magneto-transport measurements reveal that the magnetoresistance of CrSb exhibits no sign of saturation up to 35 T, following a distinct power-law dependence with an exponent of 1.48. The nonlinear Hall resistivity further indicates a multiband charge transport mechanism. Under high magnetic fields, we observe pronounced Shubnikov-de Haas (SdH) quantum oscillations and discernible Zeeman-effect-induced band splitting at 1.6 K. Systematic Fermi surface and band calculations combined with Berry phase analysis confirm the nontrivial topological character of this material (with a Berry phase approaching {\pi}). These findings not only provide crucial experimental evidence for understanding the electronic structure of CrSb, but also establish an important foundation for investigating topological quantum states in altermagnets.

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 manuscript reports high-field magnetotransport measurements on the altermagnet CrSb, including nonsaturating magnetoresistance with a power-law exponent of 1.48 up to 35 T, nonlinear Hall resistivity indicating multiband transport, and Shubnikov-de Haas (SdH) oscillations with Zeeman splitting at 1.6 K. These are combined with first-principles DFT calculations of the Fermi surface and bands to extract a Berry phase approaching π via Lifshitz-Kosevich analysis of the oscillations, supporting the claim of nontrivial topological character in this material.

Significance. If the Berry phase extraction proves reliable despite the multiband and Zeeman effects, the work would provide valuable experimental evidence linking altermagnetic order to topological semimetal states, strengthening the case for CrSb as a platform for studying such phenomena and contributing to the broader understanding of topological properties in magnetic materials.

major comments (2)
  1. [SdH oscillations and Berry phase analysis] SdH oscillations and Berry phase section: The extraction of a Berry phase approaching π relies on standard Lifshitz-Kosevich phase analysis (Landau fan diagram intercept) of the observed oscillations. However, the abstract explicitly notes multiband transport (nonlinear Hall) and 'discernible Zeeman-effect-induced band splitting', which can introduce superposition or phase shifts of order π/2 in the apparent intercept without explicit multi-frequency decomposition, temperature/field-dependent damping analysis, or accounting for spin-split contributions; this directly affects the reliability of the central topological claim.
  2. [Fermi surface and band calculations] Fermi surface assignment and DFT comparison: The assignment of specific oscillation frequencies to Fermi surface pockets and the identification of Zeeman splitting appear to depend on the same first-principles band calculations used to confirm the nontrivial topology. This creates a risk of circularity, as the experimental phase extraction is interpreted through the lens of the calculated surface without independent verification of pocket contributions or splitting effects.
minor comments (2)
  1. [Abstract] Abstract: Specific experimental values (exponent 1.48, T=1.6 K, B=35 T) are given without error bars, raw data references, or explicit description of the Berry phase fitting procedure, which reduces clarity for the central result.
  2. [Figures and data analysis] Presentation of data: Landau fan diagrams and SdH traces should include explicit fits, error estimates on the phase intercept, and checks for damping factors to strengthen the analysis section.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. The comments highlight important considerations for the robustness of our Berry phase analysis and the interpretation of the Fermi surface. We address each point below and indicate the revisions planned for the resubmitted version.

read point-by-point responses

  1. Referee: [SdH oscillations and Berry phase analysis] SdH oscillations and Berry phase section: The extraction of a Berry phase approaching π relies on standard Lifshitz-Kosevich phase analysis (Landau fan diagram intercept) of the observed oscillations. However, the abstract explicitly notes multiband transport (nonlinear Hall) and 'discernible Zeeman-effect-induced band splitting', which can introduce superposition or phase shifts of order π/2 in the apparent intercept without explicit multi-frequency decomposition, temperature/field-dependent damping analysis, or accounting for spin-split contributions; this directly affects the reliability of the central topological claim.

    Authors: We agree that multiband transport and Zeeman splitting require careful handling in the phase analysis. The dominant SdH frequency was isolated via FFT of the high-field oscillatory component, and the Landau fan diagram was constructed using the positions of the main oscillation maxima for that frequency, giving an intercept near 1/2. The observed splitting is consistent with the Zeeman energy scale estimated from the DFT g-factor, and amplitude damping with temperature follows the expected Lifshitz-Kosevich form for the primary pocket. Nevertheless, we acknowledge that an explicit multi-frequency decomposition and additional field-dependent damping analysis would strengthen the claim. We will add these analyses and a revised discussion of possible phase shifts in the updated manuscript. revision: yes

  2. Referee: [Fermi surface and band calculations] Fermi surface assignment and DFT comparison: The assignment of specific oscillation frequencies to Fermi surface pockets and the identification of Zeeman splitting appear to depend on the same first-principles band calculations used to confirm the nontrivial topology. This creates a risk of circularity, as the experimental phase extraction is interpreted through the lens of the calculated surface without independent verification of pocket contributions or splitting effects.

    Authors: The SdH frequencies themselves are obtained directly from the experimental FFT spectrum of the magnetoresistance, independent of any calculation. DFT is used only afterward to assign the observed frequencies to specific Fermi-surface orbits and to corroborate the magnitude of the Zeeman splitting seen in the data. The Berry phase value is determined solely from the experimental Landau-level fan diagram intercept and does not incorporate the DFT results. We will revise the relevant sections to state this separation of experimental extraction and theoretical assignment more explicitly, thereby removing any appearance of circular reasoning. revision: partial

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper's central claim rests on independent first-principles DFT calculations of the band structure and Fermi surface combined with separate experimental extraction of Berry phase from SdH oscillations via standard Lifshitz-Kosevich analysis of Landau fan diagrams. The calculations are parameter-free in the sense of ab initio methods and provide predicted pocket areas and topology; the experiment supplies measured frequencies, damping, and phase intercept as external data. Although frequency-to-pocket assignment and Zeeman splitting identification draw on the calculated Fermi surface for interpretation, this constitutes standard cross-validation rather than a reduction of the result to its inputs by construction. No self-definitional steps, fitted parameters renamed as predictions, or load-bearing self-citations appear in the load-bearing chain. The nontrivial topology confirmation therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard condensed-matter analysis tools and a small number of fitted transport parameters; no new particles or forces are introduced.

free parameters (1)
  • magnetoresistance power-law exponent = 1.48
    Fitted value of 1.48 extracted from high-field MR data up to 35 T.
axioms (2)
  • standard math Berry phase can be extracted from the phase shift of Shubnikov-de Haas oscillations using the Lifshitz-Kosevich formula.
    Invoked when converting observed oscillation phase to topological character.
  • domain assumption First-principles DFT calculations accurately reproduce the Fermi surface pockets responsible for the observed quantum oscillations.
    Used to assign frequencies and confirm nontrivial topology.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Band splitting in altermagnet CrSb

    cond-mat.str-el 2026-02 unverdicted novelty 5.0

    Magnetic groups formalism applied to CrSb reveals additional momentum-dependent spin splitting in electron bands beyond the exchange approximation of spin groups theory.

Reference graph

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