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arxiv: 2604.14538 · v1 · submitted 2026-04-16 · ❄️ cond-mat.str-el · cond-mat.mes-hall

Discovery of an odd-parity f-wave charge order in a kagome metal

Jiangchang Zheng , Caiyun Chen , Ruiqin Fu , Luca Buiarelli , Zihan Lin , Fazhi Yang , Tianhao Guo , Ganesh Pokharel
show 8 more authors
Andrea Capa Salinas Sen Zhou Turan Birol Stephen D. Wilson Junzhang Ma Daniel J. Schultz Xianxin Wu Berthold J\"ack
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Pith reviewed 2026-05-10 10:24 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.mes-hall
keywords CsV3Sb5kagome metalf-wave charge orderinversion symmetry breakingodd-parity orderGross-Neveu modelDirac point gapcharge bond order
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The pith

An f-wave charge order breaks inversion symmetry in the kagome metal CsV3Sb5.

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

The paper sets out to show that electrons in CsV3Sb5 form a charge pattern that breaks inversion symmetry while leaving the lattice translations unchanged. This pattern has f-wave symmetry and is odd under parity reversal. The order appears to be held in place by electrons spontaneously opening an energy gap at a Dirac point that had been missed before, mirroring the dynamical mass generation in the Gross-Neveu model. The phase exists only inside a narrow temperature window and disappears below 10 K, implying that it hands over to a different, locally invisible electronic state at still lower temperatures.

Core claim

The authors report the discovery of an inversion symmetry-breaking f-wave charge bond order in CsV3Sb5 that preserves translation symmetry. This phase is stabilized by the spontaneous opening of a spectral gap at a previously overlooked Dirac point, providing a condensed-matter realization of the Gross-Neveu model for dynamical mass generation and parity breaking. The f-wave order vanishes abruptly below 10 K, pointing to a transition into a hidden electronic state invisible to local STM probes.

What carries the argument

The f-wave charge bond order, an odd-parity electronic order on the kagome lattice that breaks inversion symmetry without breaking translation symmetry and is stabilized by gap opening at the Dirac point.

Load-bearing premise

The patterns seen in scanning tunneling microscopy and angle-resolved photoemission uniquely match f-wave symmetry, and the gap at the Dirac point drives the order rather than resulting from it.

What would settle it

High-resolution ARPES or STM data that show either no gap at the predicted Dirac point or an even-parity rather than odd-parity charge modulation would falsify the central identification.

Figures

Figures reproduced from arXiv: 2604.14538 by Andrea Capa Salinas, Berthold J\"ack, Caiyun Chen, Daniel J. Schultz, Fazhi Yang, Ganesh Pokharel, Jiangchang Zheng, Junzhang Ma, Luca Buiarelli, Ruiqin Fu, Sen Zhou, Stephen D. Wilson, Tianhao Guo, Turan Birol, Xianxin Wu, Zihan Lin.

Figure 1
Figure 1. Figure 1: FIG. 1: Inversion symmetry breaking charge order on the kagome lattice. [PITH_FULL_IMAGE:figures/full_fig_p015_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Detection of inversion symmetry-breaking density of states at the surface of [PITH_FULL_IMAGE:figures/full_fig_p016_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Intervening nature of inversion symmetry-breaking charge order detected in [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Insensitivity of inversion symmetry-breaking charge order to titanium doping [PITH_FULL_IMAGE:figures/full_fig_p018_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Odd-parity charge order with [PITH_FULL_IMAGE:figures/full_fig_p019_5.png] view at source ↗
read the original abstract

The spontaneous breaking of symmetries is a cornerstone of physics, defining the phases of matter from the cosmological scale to the quantum realm. In condensed matter, electronic orders are classified by their behavior under fundamental symmetries like spatial inversion (parity). While even-parity orders, such as conventional superconductivity and charge density waves, are ubiquitous, their odd-parity counterparts--predicted to host exotic phenomena such as gapless quasiparticle excitations and novel collective modes--are comparatively elusive states of quantum matter. Here, using high-resolution scanning tunneling microscopy and angle-resolved photoemission spectroscopy on the kagome metal CsV$_3$Sb$_5$, we report the discovery of an inversion symmetry-breaking $f$-wave charge bond order. We show that this phase, which preserves translation symmetry, is stabilized by the spontaneous opening of a spectral gap at a previously overlooked Dirac point, providing a textbook condensed-matter realization of the Gross-Neveu model for dynamical mass generation and parity breaking. Intriguingly, this $f$-wave order is itself a intervening phase, vanishing abruptly below a temperature of 10\,K and pointing to a subsequent transition into a `hidden' electronic state that is invisible to local STM probes. Our findings establish odd-parity charge order as a novel phase of matter, here, embedded within the intricate hierarchy of correlated electronic orders on the kagome lattice.

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

3 major / 2 minor

Summary. The manuscript reports the experimental discovery, via STM and ARPES on CsV3Sb5, of an inversion-symmetry-breaking but translation-preserving f-wave charge bond order. This order is claimed to be stabilized by spontaneous gap opening at a previously overlooked Dirac point, furnishing a condensed-matter realization of the Gross-Neveu mechanism for dynamical mass generation and parity breaking; the f-wave phase is further described as an intervening state that vanishes abruptly below ~10 K, implying a subsequent transition into a hidden electronic order invisible to local STM probes.

Significance. If the symmetry assignment and the proposed stabilization mechanism hold, the result would constitute a notable advance: the first clear identification of odd-parity charge order in a kagome metal and a direct experimental analog of the Gross-Neveu-Yukawa paradigm. The observation of an intervening phase within the known hierarchy of orders in AV3Sb5 would also sharpen understanding of the material’s complex low-temperature phase diagram.

major comments (3)
  1. [Symmetry identification] Symmetry identification section: the assignment of the observed STM bond-order pattern and ARPES gap to a pure f-wave (odd-parity, translation-invariant) form factor is not shown to be unique. No exhaustive forward-modeling comparison against other inversion-odd charge-order channels (e.g., mixed-parity or higher-multipole form factors) is provided, leaving open the possibility that alternative symmetries could reproduce the same local and momentum-space signatures.
  2. [Stabilization mechanism] Stabilization mechanism (Gross-Neveu claim): the assertion that gap opening at the Dirac point supplies the dominant energy gain and thereby stabilizes the f-wave order rests on temperature-dependent evolution alone. Without a quantitative free-energy comparison, doping-dependent measurements, or explicit calculation showing that the gap provides a larger condensation energy than the order itself, the causal direction remains an inference rather than a demonstrated result.
  3. [Low-temperature behavior] Hidden-state transition: the claim that the f-wave order vanishes abruptly below 10 K and gives way to a hidden state invisible to STM requires additional supporting data (e.g., bulk thermodynamic or transport signatures, or complementary probes) to establish that a genuine subsequent transition occurs rather than a gradual suppression or experimental artifact.
minor comments (2)
  1. [Methods/Figures] Figure captions and methods should explicitly state the energy resolution, temperature stability, and background-subtraction procedures used in the ARPES Dirac-point gap analysis.
  2. [Discussion] The manuscript would benefit from a brief comparison table listing the expected STM/ARPES signatures for the leading candidate odd-parity orders.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their positive evaluation of our work and for the constructive comments, which have prompted us to clarify and strengthen several aspects of the manuscript. We address each major comment in turn below.

read point-by-point responses

  1. Referee: [Symmetry identification] Symmetry identification section: the assignment of the observed STM bond-order pattern and ARPES gap to a pure f-wave (odd-parity, translation-invariant) form factor is not shown to be unique. No exhaustive forward-modeling comparison against other inversion-odd charge-order channels (e.g., mixed-parity or higher-multipole form factors) is provided, leaving open the possibility that alternative symmetries could reproduce the same local and momentum-space signatures.

    Authors: We agree that an explicit demonstration of uniqueness would strengthen the symmetry assignment. The manuscript's symmetry analysis shows that the observed STM bond-order pattern (with its characteristic phase winding around the kagome plaquettes) and the momentum-space gap opening exclusively at the Dirac point are reproduced by the f-wave form factor while preserving translation symmetry and breaking inversion. To address the referee's concern, the revised manuscript will include forward-modeling of alternative inversion-odd channels (including mixed-parity and higher-multipole form factors), demonstrating that they produce incompatible STM contrast or fail to open a gap at the observed Dirac point location. revision: yes

  2. Referee: [Stabilization mechanism] Stabilization mechanism (Gross-Neveu claim): the assertion that gap opening at the Dirac point supplies the dominant energy gain and thereby stabilizes the f-wave order rests on temperature-dependent evolution alone. Without a quantitative free-energy comparison, doping-dependent measurements, or explicit calculation showing that the gap provides a larger condensation energy than the order itself, the causal direction remains an inference rather than a demonstrated result.

    Authors: The referee correctly identifies that the proposed Gross-Neveu stabilization rests on the experimental observation that the Dirac-point gap opens concurrently with the onset of the f-wave order in temperature-dependent ARPES and STM. No quantitative free-energy comparison or doping series is presented. In the revision we will rephrase the relevant sections to describe the gap opening as providing the dominant energy scale that stabilizes the order, while explicitly noting that this remains an inference drawn from the temperature evolution and that dedicated theoretical calculations would be required to quantify the condensation energies. revision: partial

  3. Referee: [Low-temperature behavior] Hidden-state transition: the claim that the f-wave order vanishes abruptly below 10 K and gives way to a hidden state invisible to STM requires additional supporting data (e.g., bulk thermodynamic or transport signatures, or complementary probes) to establish that a genuine subsequent transition occurs rather than a gradual suppression or experimental artifact.

    Authors: The abrupt disappearance of the f-wave signatures below 10 K is documented in our STM data through dense temperature sampling. We acknowledge that the manuscript does not contain bulk thermodynamic or transport measurements that could independently confirm a phase transition. In the revision we will (i) present additional high-resolution STM temperature scans that quantify the sharpness of the suppression and (ii) moderate the language to state that the data suggest a subsequent transition into a hidden state, while noting the limitations of local probes and the consistency with the broader phase diagram reported in the literature. revision: partial

Circularity Check

0 steps flagged

No circularity: experimental discovery with data-driven symmetry assignment

full rationale

The paper is an experimental report using STM and ARPES to identify inversion-breaking f-wave charge order in CsV3Sb5. The central claims rest on direct imaging of bond-order patterns, spectral gap observations at a Dirac point, and temperature evolution, interpreted as a Gross-Neveu realization. No equations, first-principles derivations, or predictions are presented that reduce by construction to fitted inputs, self-citations, or ansatze. Symmetry assignment and stabilization mechanism are inferences from data comparison, not self-referential loops. This is the expected outcome for a discovery paper without theoretical modeling chains.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Experimental discovery; no free parameters, axioms, or invented entities are introduced in the abstract. The claim relies on standard interpretations of STM/ARPES data and the Gross-Neveu model from prior theory.

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