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arxiv: 2602.21643 · v2 · pith:HP5CKGSSnew · submitted 2026-02-25 · ❄️ cond-mat.mes-hall

Skyrmion Phase and Non-Fermi Liquid Behavior in Nonsymmorphic Magnetic Weyl Semimetals

Xi Luo , Yue Yu This is my paper

Pith reviewed 2026-05-21 12:26 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords Skyrmion latticenon-Fermi liquidWeyl semimetalsKondo interactionHall conductivitymagnetic Brillouin zone foldingtopological semimetals
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The pith

A Skyrmion lattice in nonsymmorphic magnetic Weyl semimetals drives non-Fermi liquid behavior with resistivity scaling as T to a power between 3 and 5.

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

The paper examines how complex magnetic orders interact with topological states in materials like ReAlX. It constructs a model where conduction electrons couple to localized spins through Kondo interaction. The key finding is that an in-plane magnetic field turns a multi-Q cycloid into a Skyrmion lattice, which folds the bands and changes the transport. If correct, this links magnetic textures directly to unusual electron scattering that breaks standard Fermi liquid predictions. Readers interested in topological materials would care because it suggests new routes to control conductivity without impurities.

Core claim

In the lattice model of Weyl fermions coupled to magnetic moments, the Skyrmion lattice formed under an in-plane Zeeman field modifies the band structure via magnetic Brillouin zone folding. This leads to significant changes in longitudinal and Hall conductivities calculated via the Kubo formula. The temperature-dependent resistivity deviates from the Fermi-liquid T squared dependence to a non-Fermi liquid power law with exponent alpha between 3 and 5 in the clean limit.

What carries the argument

The Skyrmion lattice arising from a multi-Q cycloid magnetic configuration under an in-plane Zeeman field, which induces magnetic Brillouin zone folding and interacts with Weyl fermions through Kondo coupling to alter conductivities.

If this is right

  • The longitudinal resistivity shows non-Fermi liquid scaling rho_xx ~ T^alpha with 3 < alpha < 5 rather than the usual T^2.
  • Hall conductivity exhibits large magnitudes and can change sign depending on parameters.
  • The system enters a non-Fermi liquid state due to the Skyrmion-induced modifications to the electronic structure.

Where Pith is reading between the lines

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

  • If the mechanism holds, similar non-Fermi liquid behavior might appear in other systems with Skyrmion lattices and topological bands.
  • External magnetic fields could be used to switch between Fermi liquid and non-Fermi liquid regimes in these materials.

Load-bearing premise

The multi-Q cycloid configuration transitions into a Skyrmion lattice under an in-plane Zeeman field, and the Kondo coupling combined with magnetic Brillouin zone folding produces the non-Fermi liquid transport in the clean limit.

What would settle it

Measurement of the resistivity temperature dependence in ReAlX compounds under applied in-plane magnetic fields that stabilize the Skyrmion phase, checking if the exponent falls between 3 and 5.

Figures

Figures reproduced from arXiv: 2602.21643 by Xi Luo, Yue Yu.

Figure 1
Figure 1. Figure 1: FIG. 1. (color online) The band structures of [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (color online) The distributions of (a) the ( [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (color online) The scaling behavior of anomalous Hall [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
read the original abstract

We investigate the interplay between complex magnetic orders and topological electronic states in nonsymmorphic magnetic Weyl semimetals of the ReAlX family (Re is a rare earth element and X is Si or Ge). We show that a Skyrmion lattice can fundamentally alter the behavior of Weyl fermions, driving the system into a non-Fermi liquid state and producing large, sign-tunable Hall responses. To this end, we construct a lattice model incorporating conduction Weyl fermions coupled to localized magnetic moments via Kondo interaction. Considering a multi-${\bf Q}$ cycloid magnetic configuration that evolves into a Skyrmion lattice under an in-plane Zeeman field, we analyze its profound impact on the band structure through magnetic Brillouin zone and band-folding. Using the Kubo formula, we calculate the conductivity tensor and examine the transport properties in the clean limit. Our results reveal that the Skyrmion lattice induces significant changes in both longitudinal and Hall conductivities. Remarkably, the temperature-dependent resistivity deviates from standard Fermi-liquid behavior ($\rho_{xx}\sim T^2$), exhibiting a non-Fermi liquid power-law scaling ($\rho_{xx}\sim T^\alpha$ with $\alpha$ between 3 and 5). This work provides a unified theoretical framework connecting multi-${\bf Q}$ magnetic textures, Skyrmion physics, and anomalous transport in topological semimetals, bridging the fields of topological magnetism and topological fermions.

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 constructs a lattice model for Weyl fermions in nonsymmorphic ReAlX compounds coupled to localized moments via Kondo interaction. It considers a multi-Q cycloid magnetic order that evolves into a Skyrmion lattice under an in-plane Zeeman field, examines the resulting magnetic Brillouin-zone folding and band reconstruction, and computes the conductivity tensor via the Kubo formula in the clean limit. The central claims are that the Skyrmion texture produces large, sign-tunable Hall responses and drives non-Fermi-liquid longitudinal resistivity with power-law exponent α between 3 and 5 rather than the conventional T² Fermi-liquid form.

Significance. If the transport calculations are correct, the work would supply a concrete microscopic route by which a static Skyrmion lattice, through zone folding and Kondo coupling, can generate non-Fermi-liquid scaling and tunable anomalous Hall conductivity in a Weyl semimetal. The explicit lattice Hamiltonian and the focus on the ReAlX family provide a falsifiable framework that could be tested against experiment. The strength lies in linking multi-Q magnetism directly to topological transport without invoking additional dynamical scattering channels.

major comments (2)
  1. [Transport calculations] Transport section (Kubo-formula results for ρ_xx): the reported non-Fermi-liquid exponents α = 3–5 in the clean limit with a static Skyrmion texture require explicit justification. In the DC Kubo formula the temperature dependence enters only through the Fermi window −∂f/∂ω and any T-dependent band renormalization; for Weyl dispersions this ordinarily produces linear or quadratic scaling. The manuscript must show the spectral function, the effective density of states after magnetic folding, or the precise manner in which the Kondo term generates the higher powers, or else demonstrate that the exponents are robust against reasonable variations in Kondo strength and Zeeman field.
  2. [Hall conductivity results] Results on Hall conductivity: the claim of sign-tunable Hall responses is load-bearing for the Skyrmion-phase narrative, yet the manuscript does not report the separate contributions from Berry curvature versus scattering asymmetry or quantify how the in-plane Zeeman field reverses the sign. A plot or table of σ_xy versus Zeeman magnitude at fixed temperature would make the tunability verifiable.
minor comments (2)
  1. [Abstract] The abstract states α lies “between 3 and 5” without indicating whether these values are obtained from a fit, from an analytic approximation, or from a specific parameter set; a brief statement of the fitting procedure or the range of parameters explored would improve clarity.
  2. [Model Hamiltonian] Notation for the multi-Q vectors and the magnetic Brillouin zone should be defined once in the model section and used consistently; occasional redefinition of Q_i or the folding procedure obscures the band-structure discussion.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and valuable comments on our manuscript. We address each major point below and will revise the manuscript to incorporate the requested clarifications and additional data.

read point-by-point responses

  1. Referee: [Transport calculations] Transport section (Kubo-formula results for ρ_xx): the reported non-Fermi-liquid exponents α = 3–5 in the clean limit with a static Skyrmion texture require explicit justification. In the DC Kubo formula the temperature dependence enters only through the Fermi window −∂f/∂ω and any T-dependent band renormalization; for Weyl dispersions this ordinarily produces linear or quadratic scaling. The manuscript must show the spectral function, the effective density of states after magnetic folding, or the precise manner in which the Kondo term generates the higher powers, or else demonstrate that the exponents are robust against reasonable variations in Kondo strength and Zeeman field.

    Authors: We agree that explicit justification is needed for the reported exponents. The non-Fermi-liquid scaling originates from the magnetic Brillouin-zone folding by the Skyrmion lattice, which reconstructs the Weyl bands and produces a modified density of states with van Hove features that, when integrated against the Fermi window in the Kubo formula, yield α between 3 and 5. The Kondo coupling further renormalizes the effective bandwidth in a T-dependent manner. In the revision we will add plots of the spectral function A(k,ω) and the folded density of states, together with a brief derivation showing how these features produce the higher powers. We will also include supplementary calculations demonstrating that the exponents remain in the 3–5 range for moderate variations of Kondo strength and Zeeman field. revision: yes

  2. Referee: [Hall conductivity results] Results on Hall conductivity: the claim of sign-tunable Hall responses is load-bearing for the Skyrmion-phase narrative, yet the manuscript does not report the separate contributions from Berry curvature versus scattering asymmetry or quantify how the in-plane Zeeman field reverses the sign. A plot or table of σ_xy versus Zeeman magnitude at fixed temperature would make the tunability verifiable.

    Authors: In the clean limit employed throughout the work there is no impurity scattering, so the Hall conductivity is entirely intrinsic and arises from the Berry curvature of the magnetically folded bands. The in-plane Zeeman field continuously distorts the Skyrmion texture, altering the real-space topological charge and thereby the integrated Berry curvature, which produces the sign change. We will add a new figure plotting σ_xy versus Zeeman-field magnitude at fixed temperature and will explicitly state in the text that scattering-asymmetry (skew-scattering) contributions are absent in this limit. This will make the tunability both quantitative and directly verifiable. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected; derivation remains self-contained

full rationale

The paper constructs an explicit lattice model of Weyl fermions with Kondo coupling to localized moments, adopts a multi-Q cycloid texture that evolves into a Skyrmion lattice under an in-plane Zeeman field, folds the bands via the magnetic Brillouin zone, and applies the Kubo formula to compute the conductivity tensor in the clean limit. The reported non-Fermi-liquid exponent range (α = 3–5) is presented as the numerical or analytic outcome of that calculation rather than a parameter fitted to data or a quantity defined into the model by construction. No self-citations, ansatz smuggling, or uniqueness theorems imported from prior work by the same authors appear in the provided text, and the central transport claim retains independent content from the model and formula. The derivation is therefore scored as non-circular.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on a constructed lattice model whose magnetic texture and interaction parameters are not fully enumerated in the abstract; several free parameters and domain assumptions are therefore expected but cannot be exhaustively listed.

free parameters (2)
  • Kondo coupling strength
    Strength of interaction between localized moments and conduction Weyl fermions; required to stabilize the magnetic orders and scattering rates.
  • In-plane Zeeman field magnitude
    Field strength chosen to drive the cycloid-to-Skyrmion transition.
axioms (2)
  • domain assumption The system remains in the clean limit with negligible disorder scattering.
    Invoked for the Kubo-formula conductivity calculation.
  • domain assumption Magnetic Brillouin zone folding due to the Skyrmion lattice accurately captures the modification of Weyl fermion bands.
    Central premise for linking the magnetic texture to altered transport.

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Reference graph

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