arxiv: 2604.20546 · v1 · submitted 2026-04-22 · ❄️ cond-mat.supr-con

Recognition: unknown

Discovery of parity-violating chiral polar-nematic charge density wave and superconductivity in kagome metals

Xingwei Shi , Geng Li , Zhan Wang , Chuqi Zhang , Ke Zhu , Keyu Zeng , Zikun Tang , Li Huang

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Zhen Zhao Jianping Sun Xiao Liu Jin-Guang Cheng Chengmin Shen Shu Ping Lau Kian Ping Loh Haitao Yang Xiao Lin Ziqiang Wang Hong-Jun Gao

Authors on Pith no claims yet

Pith reviewed 2026-05-09 23:01 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con

keywords kagome metalscharge density waveparity violationchiralitynematic ordersuperconductivityinversion symmetry breaking

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The pith

Kagome metals spontaneously break inversion symmetry in their charge density wave state, producing a chiral polar-nematic order that also affects the superconducting phase.

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

The paper shows that the charge density wave in nonmagnetic kagome metals AV3Sb5 breaks inversion symmetry within the kagome plane, even though the underlying crystal is centrosymmetric. This creates a mixed-parity state with both ferroelectric dipolar moments and nematic quadrupolar moments that couple together. The coupling produces noncollinear alignments that eliminate all mirror symmetries and establish robust electronic chirality. The same parity violation appears in the superconducting state as modulations in pair density at the original and CDW wavevectors. These observations open routes to electric-field control of the chiral order.

Core claim

Using scanning tunneling microscopy, atomic force microscopy, and optical second-harmonic generation, the authors find that the 3Q charge density wave spontaneously breaks inversion symmetry in the kagome plane. The resulting mixed-parity CDW carries ferroelectric dipolar and nematic quadrupolar ordered moments whose coexistence and coupling drive noncollinear ferro-polar and nematic alignments. These alignments break all mirror symmetries and generate electronic chirality. The multipolar moments also couple to in-plane electric fields, allowing field control of the chiral state. Below the superconducting transition, parity-violating pair-density modulations appear at both the lattice and CD

What carries the argument

The mixed-parity 3Q CDW state whose dipolar and quadrupolar moments couple to produce noncollinear ferro-polar and nematic order that breaks all mirror symmetries.

If this is right

Electric fields can manipulate the chirality of the CDW state through coupling to the multipolar moments.
The chiral CDW provides a microscopic origin for magnetoelectric responses and nonreciprocal transport in kagome metals.
Parity-violating pair density modulations appear in the superconducting state at both the original lattice and CDW wavevectors.
Loop-current order and unconventional superconductivity may be linked to the same multipolar chiral order.

Where Pith is reading between the lines

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

If the chiral CDW survives into the superconducting dome, it could template a chiral superconducting order parameter.
Similar multipolar coupling might be searched for in other centrosymmetric kagome or triangular lattices that host 3Q CDWs.
Electric-field control of chirality offers a route to switchable nonreciprocal devices without magnetic fields.

Load-bearing premise

The observed STM, AFM, and second-harmonic generation signals reflect spontaneous bulk inversion-symmetry breaking in the CDW rather than surface effects or extrinsic fields.

What would settle it

A measurement showing that the second-harmonic generation signal or the observed dipolar and quadrupolar moments persist only under applied surface fields or disappear in bulk-sensitive probes would falsify the claim of spontaneous bulk parity breaking.

read the original abstract

Nonmagnetic kagome metals and superconductors AV3Sb5 (A = K, Rb, Cs) host unconventional charge density wave (CDW) and superconducting (SC) phases accompanied by multiple electronic symmetry breaking. Due to the centrosymmetric crystal structure, inversion symmetry has generally been assumed to hold. Here, using scanning tunneling microscopy complemented by atomic force microscopy and optical second-harmonic generation, we directly reveal that inversion symmetry in the kagome plane is spontaneously broken in the CDW state. The mixed-parity CDW state exhibits ferroelectric dipolar and nematic quadrupolar ordered moments. The coexistence and coupling between the dipole and quadrupole favor noncollinear ferro-polar and nematic alignment that breaks all mirror symmetries and gives rise to robust electronic chirality in the 3Q CDW. The multipolar coupling to in-plane electric field enables electric field control and manipulation of the chiral polar-nematic CDW state, including its chirality. Below the SC transition, we observe parity-violating pair density modulations at both the original and the CDW lattice wavevectors. Our findings of parity-violating electronic chiral multipolar order provide microscopic insights into the magnetoelectric and nonreciprocal transport, loop current order, pairing density waves, and unconventional superconductivity in kagome metals and related 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 / 1 minor

Summary. The manuscript reports the discovery of a parity-violating chiral polar-nematic charge density wave (CDW) in nonmagnetic kagome metals AV3Sb5 (A = K, Rb, Cs). Using scanning tunneling microscopy (STM), atomic force microscopy (AFM), and optical second-harmonic generation (SHG), the authors claim to directly observe spontaneous breaking of inversion symmetry in the kagome plane within the CDW state. They interpret the data as evidence for mixed-parity CDW order with ferroelectric dipolar and nematic quadrupolar moments whose coupling produces noncollinear ferro-polar and nematic alignment, breaking all mirror symmetries and generating robust electronic chirality in the 3Q CDW. The work further reports electric-field control of the chiral state and parity-violating pair-density modulations below the superconducting transition.

Significance. If the central attribution of the observed multipolar signals to bulk spontaneous inversion-symmetry breaking holds, the result would be significant for the field of kagome superconductors. It would provide a microscopic mechanism linking CDW order to magnetoelectric responses, nonreciprocal transport, loop-current order, and unconventional pairing. The use of three orthogonal experimental techniques (STM, AFM, SHG) to probe the same symmetry-breaking phenomenon is a methodological strength that strengthens the case for the claimed mixed-parity order.

major comments (2)

[Abstract, §3] Abstract and §3 (STM/AFM data): The central claim that the observed dipolar and quadrupolar moments 'directly reveal' spontaneous bulk inversion-symmetry breaking rests on surface-sensitive probes. No thickness-dependent SHG measurements, cleaved-surface versus as-grown comparisons, or cross-checks with bulk-sensitive techniques (e.g., neutron diffraction for structural multipoles) are presented to exclude surface reconstruction, adsorbates, or tip-induced fields. This attribution is load-bearing for the parity-violation and chirality narrative.
[Abstract, §4] Abstract and §4 (SHG): SHG is symmetry-allowed at any inversion-breaking interface even if the bulk remains centrosymmetric. The manuscript does not report quantitative SHG intensity versus temperature, polarization dependence, or thickness scaling that would distinguish bulk versus interface contributions, leaving the bulk interpretation under-constrained.

minor comments (1)

[Abstract] Abstract: No quantitative values, error bars, or statistical significance are provided for the reported STM/AFM contrasts or SHG intensities, making it difficult to assess the robustness of the symmetry-breaking signals.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the positive assessment of its potential significance. We address each major comment below with point-by-point responses, providing clarifications based on the data and indicating where revisions will be made to improve the presentation.

read point-by-point responses

Referee: [Abstract, §3] Abstract and §3 (STM/AFM data): The central claim that the observed dipolar and quadrupolar moments 'directly reveal' spontaneous bulk inversion-symmetry breaking rests on surface-sensitive probes. No thickness-dependent SHG measurements, cleaved-surface versus as-grown comparisons, or cross-checks with bulk-sensitive techniques (e.g., neutron diffraction for structural multipoles) are presented to exclude surface reconstruction, adsorbates, or tip-induced fields. This attribution is load-bearing for the parity-violation and chirality narrative.

Authors: We agree that STM and AFM are surface-sensitive and that direct bulk confirmation via neutron diffraction or thickness-dependent studies would further strengthen the claim. The CDW itself is established as a bulk order by prior X-ray and neutron diffraction work, and our SHG signal onsets precisely at the bulk CDW transition temperature across multiple samples. Reproducibility across different tips and cleaved surfaces argues against tip-induced or adsorbate artifacts. In the revised manuscript we will expand §3 and the abstract to explicitly discuss these points, cite the bulk CDW literature, and note the surface-bulk distinction as a limitation while emphasizing the consistency of the three techniques. We view this as a partial revision since new experimental data cannot be added at this stage. revision: partial
Referee: [Abstract, §4] Abstract and §4 (SHG): SHG is symmetry-allowed at any inversion-breaking interface even if the bulk remains centrosymmetric. The manuscript does not report quantitative SHG intensity versus temperature, polarization dependence, or thickness scaling that would distinguish bulk versus interface contributions, leaving the bulk interpretation under-constrained.

Authors: We acknowledge that SHG alone does not automatically prove bulk inversion breaking. The revised §4 will include quantitative SHG intensity versus temperature data demonstrating that the signal appears below the CDW transition and disappears above it, together with an expanded polarization-dependence analysis that matches the symmetry expected for the proposed mixed-parity order. Thickness scaling is experimentally difficult for these materials but will be noted as a desirable future measurement. These additions will better constrain the interpretation while transparently stating the current limitations of the SHG data. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental claims rest on direct measurements without derivation or self-referential fitting

full rationale

The paper is an experimental report using STM, AFM, and SHG to observe signals interpreted as spontaneous inversion-symmetry breaking in the CDW phase of AV3Sb5. No mathematical derivations, equations, fitted parameters, or predictions appear in the provided text. Claims of mixed-parity CDW, dipolar/quadrupolar moments, chirality, and parity-violating PDW are presented as direct revelations from data via standard condensed-matter symmetry analysis. No self-citations function as load-bearing uniqueness theorems, no ansatzes are smuggled, and no results reduce to inputs by construction. The derivation chain is absent; the work is self-contained against external benchmarks of experimental interpretation.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The abstract relies on standard experimental interpretations rather than new postulates. No free parameters are fitted to produce the central claim. Two domain assumptions are implicit.

axioms (2)

domain assumption SHG intensity reports broken inversion symmetry via standard electric-dipole selection rules
Invoked when the abstract states that SHG reveals spontaneous inversion-symmetry breaking.
domain assumption The CDW is a 3Q state whose real-space structure is known from prior work
Used when the abstract refers to 'the 3Q CDW' and its wavevectors.

pith-pipeline@v0.9.0 · 5604 in / 1431 out tokens · 29141 ms · 2026-05-09T23:01:12.047903+00:00 · methodology

discussion (0)

Reference graph

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