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arxiv: 2405.09451 · v2 · submitted 2024-05-15 · ❄️ cond-mat.str-el · cond-mat.supr-con

Exotic charge density waves and superconductivity on the Kagome Lattice

Rui-Qing Fu , Jun Zhan , Matteo D\"urrnagel , Hendrik Hohmann , Ronny Thomale , Jiangping Hu , Ziqiang Wang , Sen Zhou
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Xianxin Wu
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Pith reviewed 2026-05-24 01:15 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.supr-con
keywords kagome latticecharge density waveloop current ordervan Hove fillingnematic ordersuperconductivityCoulomb interactionsbond order
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The pith

Next nearest-neighbor Coulomb repulsion favors a 2×2 loop current order on the kagome lattice at van Hove filling.

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

The paper examines charge instabilities on the spinless kagome lattice model including inter-site Coulomb interactions, specifically at the pure-sublattice van Hove filling. It finds that onsite charge order is suppressed while bond charge orders are enhanced at the nesting vectors due to the Fermi surface texture. Nearest-neighbor bonds support real fluctuations and next-nearest-neighbor bonds support imaginary fluctuations, making the 2×2 loop current order the favored state under next nearest-neighbor repulsion. Further increase in interactions produces a nematic phase that breaks rotational symmetry through intra-cell density modulation. Superconducting pairing channels arising from these charge fluctuations are also analyzed.

Core claim

In the spinless kagome lattice at van Hove filling with inter-site Coulomb repulsion, the charge susceptibility shows that next-nearest-neighbor interactions stabilize a 2×2 loop current order through imaginary bond fluctuations on the next-nearest-neighbor bonds, while nearest-neighbor interactions promote real bond orders, and stronger interactions drive a nematic sublattice density wave that breaks C6 symmetry.

What carries the argument

The charge susceptibility computed for the non-interacting or weakly interacting spinless kagome model, which identifies enhanced bond charge orders at nesting vectors due to sublattice texture on the hexagonal Fermi surface.

If this is right

  • The 2×2 loop current order is favored specifically by next nearest-neighbor Coulomb repulsion.
  • A nematic state with intra-cell sublattice density modulation emerges at stronger interactions.
  • Superconducting orders can descend from both onsite and bond charge fluctuations.
  • Bond charge orders are substantially enhanced at nesting vectors while onsite order is suppressed.

Where Pith is reading between the lines

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

  • Tuning the relative strength of nearest versus next-nearest neighbor repulsion could switch the dominant charge order between real bond and imaginary loop-current phases.
  • The mechanism offers a route to time-reversal symmetry breaking without local moments through bond-order fluctuations alone.
  • Extensions that include spin degrees of freedom could compete with or modify the charge-driven instabilities identified here.

Load-bearing premise

The charge susceptibility in the non-interacting spinless model at van Hove filling identifies the leading instabilities correctly when inter-site Coulomb interactions are included.

What would settle it

A full self-consistent calculation or experiment at van Hove filling showing that the leading instability is not the 2×2 loop current when next-nearest-neighbor repulsion dominates would falsify the result.

Figures

Figures reproduced from arXiv: 2405.09451 by Hendrik Hohmann, Jiangping Hu, Jun Zhan, Matteo D\"urrnagel, Ronny Thomale, Rui-Qing Fu, Sen Zhou, Xianxin Wu, Ziqiang Wang.

Figure 1
Figure 1. Figure 1: FIG. 1. Kagome lattice and charge susceptibility bubbles. (a) [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Bare and RPA susceptibilities along the high-symmetry [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Phase diagram and real-space patterns of relevant charge or [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. E [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Superconducting phase diagram and leading gap functions away from the p-type VH filling. (a) Pairing eigenvalues [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
read the original abstract

Recent experiments have identified fascinating electronic orders in kagome materials, including intriguing superconductivity, charge density wave (CDW) and nematicity. In particular, some experimental evidence for AV$_3$Sb$_5$ (A = K,Rb,Cs) and related kagome metals hints at the formation of orbital currents in the charge density wave ordered regime, providing a mechanism for spontaneous time-reversal symmetry breaking in the absence of local moments. In this work, we comprehensively explore the competitive charge instabilities of the spinless kagome lattice with inter-site Coulomb interactions at the pure-sublattice van Hove filling. From the analysis of the charge susceptibility, we find that, at the nesting vectors, while the onsite charge order is dramatically suppressed, the bond charge orders are substantially enhanced owing to the sublattice texture on the hexagonal Fermi surface. Furthermore, we demonstrate that nearest-neighbor and next nearest-neighbor bonds are characterized by significant intrinsic real and imaginary bond fluctuations, respectively. The 2$\times$2 loop current order is thus favored by the next nearest-neighbor Coulomb repulsion. Interestingly, increasing interactions further leads to a nematic state with intra-cell sublattice density modulation that breaks the $C_6$ rotational symmetry. We further explore superconducting orders descending from onsite and bond charge fluctuations, and discuss our model's implications on the experimental status quo.

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

1 major / 1 minor

Summary. The manuscript examines charge instabilities on the spinless kagome lattice at pure-sublattice van Hove filling with inter-site Coulomb interactions. Charge susceptibility analysis indicates that nearest-neighbor repulsion enhances bond charge orders while next-nearest-neighbor repulsion favors 2×2 loop-current (imaginary bond) order; stronger interactions drive a nematic state with intra-cell sublattice modulation breaking C6 symmetry. Superconducting instabilities descending from these fluctuations are explored, with implications discussed for time-reversal symmetry breaking in AV3Sb5 kagome metals.

Significance. If the central results hold, the work supplies a microscopic route from the model Hamiltonian and susceptibility peaks to orbital-current CDW order without local moments, offering a plausible explanation for experimental hints of TRS breaking in kagome metals. The non-interacting susceptibility framework is standard and directly ties nesting vectors to favored channels.

major comments (1)
  1. [Abstract] Abstract and main susceptibility analysis: the conclusion that next-nearest-neighbor Coulomb repulsion favors the 2×2 loop-current order rests on peaks computed in the non-interacting or weakly interacting spinless model. Adding finite inter-site Coulomb terms can renormalize effective interactions, so the non-interacting ranking may not survive a self-consistent treatment (RPA or mean-field decoupling) that determines which channel actually condenses; the manuscript does not demonstrate that the ranking is robust to this step.
minor comments (1)
  1. [Abstract] The superconductivity section is described as sketched; including at least one explicit gap equation or pairing kernel derived from the bond fluctuations would clarify the descent from the charge instabilities.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for identifying this important point about the robustness of the instability ranking. We address the comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract and main susceptibility analysis: the conclusion that next-nearest-neighbor Coulomb repulsion favors the 2×2 loop-current order rests on peaks computed in the non-interacting or weakly interacting spinless model. Adding finite inter-site Coulomb terms can renormalize effective interactions, so the non-interacting ranking may not survive a self-consistent treatment (RPA or mean-field decoupling) that determines which channel actually condenses; the manuscript does not demonstrate that the ranking is robust to this step.

    Authors: We agree that the current analysis identifies favored channels from the peaks of the charge susceptibility (computed with the inter-site interactions included at the RPA level) but does not include a full self-consistent mean-field or RPA decoupling to confirm which order actually condenses. This is a valid concern. In the revised manuscript we will add a mean-field treatment of the leading channels to explicitly demonstrate that the 2×2 loop-current order is stabilized by next-nearest-neighbor repulsion, thereby addressing the robustness of the ranking. revision: yes

Circularity Check

0 steps flagged

No circularity: conclusions follow from direct susceptibility computation on the model Hamiltonian

full rationale

The paper identifies leading charge instabilities by computing the charge susceptibility in the spinless kagome model at van Hove filling, both without and with weak interactions, then examines how inter-site Coulomb terms enhance specific bond orders. No parameters are fitted to target observables, no self-citations supply load-bearing uniqueness theorems or ansatzes, and no predictions reduce to the inputs by construction. The derivation chain consists of standard diagrammatic or mean-field susceptibility evaluation whose outputs are independent of the final claims about favored orders.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claims rest on a standard tight-binding plus Coulomb model whose interaction strengths are free parameters varied across regimes; no new particles or forces are postulated.

free parameters (1)
  • nearest-neighbor and next-nearest-neighbor Coulomb strengths
    Varied to determine which bond order dominates; values not fixed by external data in the abstract.
axioms (2)
  • domain assumption Spinless fermion model on kagome lattice at pure-sublattice van Hove filling captures the relevant physics.
    Stated explicitly as the setting for the susceptibility analysis.
  • domain assumption Peaks in the charge susceptibility identify the leading instabilities.
    Used to conclude which orders are favored.

pith-pipeline@v0.9.0 · 5807 in / 1426 out tokens · 31912 ms · 2026-05-24T01:15:42.920666+00:00 · methodology

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Forward citations

Cited by 2 Pith papers

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

  1. Floquet X-Ray Scattering as a Probe of Hidden Electronic Orders

    cond-mat.str-el 2026-04 unverdicted novelty 8.0

    Floquet X-ray scattering provides direct access to bond and current correlations in hidden electronic orders, with distinct polarization fingerprints on the Kagome lattice that can be tuned by drive frequency.

  2. Time-reversal symmetry breaking superconductivity in the presence of loop-current fluctuations

    cond-mat.supr-con 2025-10 unverdicted novelty 5.0

    Unbiased QMC simulations of a bilayer t-J⊥-V model map a doping-driven transition from a spontaneous interlayer loop-current state to interlayer s-wave superconductivity, including a coexisting time-reversal-symmetry-...

Reference graph

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