arxiv: 2511.06995 · v1 · submitted 2025-11-10 · ❄️ cond-mat.str-el · cond-mat.supr-con

Microscopic origin of period-four stripe charge-density-wave in kagome metal CsV₃Sb₅

Yuma Murata , Rina Tazai , Youichi Yamakawa , Seiichiro Onari , Hiroshi Kontani This is my paper

Pith reviewed 2026-05-17 23:59 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.supr-con

keywords kagome metalcharge density wavestripe orderFermi surface nestingbond orderCsV3Sb5Hubbard modelparamagnon interference

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The pith

The nesting vector of the Fermi surface reconstructed by 2×2 bond order produces a 4a0-period stripe charge-density wave in the kagome Hubbard model.

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

This paper proposes a microscopic origin for the 4a0 stripe CDW seen by STM and NMR in CsV3Sb5 and related kagome metals. It begins with a 2×2 bond order that arises from short-range magnetic fluctuations on the frustrated kagome lattice. That bond order reconstructs the Fermi surface so that its nesting vector favors a longer-period CDW instability. The resulting stripe pattern includes both modulations of electron hopping between sites and shifts in local potentials. The calculated real-space structure agrees qualitatively with the experimentally observed stripe.

Core claim

We analyze the CDW instability in the 12-site kagome lattice Hubbard model with the 2×2 bond order driven by the paramagnon-interference mechanism by focusing on the short-range magnetic fluctuations due to the geometrical frustration of kagome lattice. We reveal that the nesting vector of the reconstructed Fermi surface, formed by the 2×2 bond order, gives rise to a 4a0-period CDW. Remarkably, the obtained stripe CDW is composed of both the off-site hopping integral modulations and on-site potentials. The real-space structure of the stripe CDW obtained here is in good qualitative agreement with the experimentally observed stripe pattern.

What carries the argument

the nesting vector of the reconstructed Fermi surface formed by the 2×2 bond order, which selects the period and real-space form of the subsequent CDW instability

If this is right

Once the 2×2 bond order exists, the 4a0 stripe CDW emerges as a natural consequence of Fermi-surface nesting.
The stripe CDW consists of both off-site hopping integral modulations and on-site potential shifts.
The calculated real-space pattern reproduces the stripe observed by STM and NMR in Rb and Cs compounds.
The same nesting mechanism can be used to study how the CDW competes or coexists with superconductivity.

Where Pith is reading between the lines

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

If the nesting mechanism is correct, suppressing the 2×2 bond order should also eliminate the 4a0 CDW.
Doping that alters the Fermi surface could change the CDW period in a predictable way.
The dual character of the CDW (hopping plus potential) should produce distinct signatures in optical conductivity or transport.

Load-bearing premise

The 2×2 bond order must already be present and driven by short-range magnetic fluctuations on the geometrically frustrated kagome lattice.

What would settle it

High-resolution STM maps or ARPES data showing that the 4a0 stripe lacks the predicted mix of hopping modulations and on-site potentials, or that the nesting vector does not match the observed CDW period, would falsify the mechanism.

Figures

Figures reproduced from arXiv: 2511.06995 by Hiroshi Kontani, Rina Tazai, Seiichiro Onari, Youichi Yamakawa, Yuma Murata.

**Figure 2.** Figure 2: (b) shows the q dependence of the eigenvalue λq calculated for the 12-site model without BO (φ = 0) at n = 11.2 and T = 0.01 eV. The blue, green, and red lines represent U = 1.00 eV (αs = 0.8), U = 1.02 eV (αs = 0.82), and U = 1.04 eV (αs = 0.84), respectively (Note that αs = 0.8U in the present model.). At q = 0, the eigenvalue is threefold degenerate. These three eigenvalues originate from the three M p… view at source ↗

**Figure 3.** Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 4.** Figure 4: (a). (l, m) = (4, 7) is third-nearest-neighbor pair, and the sublattices 4, 7 belongs to the sublattice A. This sublattice pair (4, 7) represents the component for the largest modulation of the form factor shown in [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗

read the original abstract

The interplay between unconventional density waves and exotic superconductivity has attracted growing interest. Kagome superconductors $A\rm{V}_3\rm{Sb}_5$ ($A = \rm{K}, \rm{Rb}, \rm{Cs}$) offer a platform for studying quantum phase transitions and the resulting symmetry breaking. Among these quantum phases, the $4a_0$ stripe charge-density-wave (CDW) has been widely observed for $A=\rm{Rb}$ and $\rm{Cs}$ by scanning tunneling microscopy (STM) and nuclear magnetic resonance (NMR) measurements. However, the microscopic origin of the $4a_0$ stripe CDW remains elusive, and no theoretical studies addressing this phenomenon have been reported so far. In this paper, we propose a microscopic mechanism for the emergence of the $4a_0$ stripe CDW. We analyze the CDW instability in the 12-site kagome lattice Hubbard model with the $2\times2$ bond order driven by the paramagnon-interference mechanism by focusing on the short-range magnetic fluctuations due to the geometrical frustration of kagome lattice. We reveal that the nesting vector of the reconstructed Fermi surface, formed by the $2\times 2$ bond order, gives rise to a $4a_0$-period CDW. Remarkably, the obtained stripe CDW is composed of both the off-site hopping integral modulations and on-site potentials. The real-space structure of the stripe CDW obtained here is in good qualitative agreement with the experimentally observed stripe pattern.

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.

Desk Editor's Note private letter to a colleague

This paper sketches a nesting mechanism from a paramagnon-driven 2x2 bond order to the observed 4a0 stripe CDW but stays qualitative and inherits the assumptions of the group's earlier work on the bond order itself.

read the letter

The core idea here is that a 2x2 bond order, generated by paramagnon interference on the frustrated kagome lattice, reconstructs the Fermi surface so that its nesting vector selects a 4a0-period stripe CDW with both bond and site modulations. That chain is what the authors put forward as the microscopic origin, and the real-space pattern they obtain lines up qualitatively with STM and NMR data on CsV3Sb5. The calculation is done in a 12-site Hubbard model, which is a reasonable size for capturing the relevant cluster physics. The claim that no prior theory has tackled the 4a0 stripe specifically appears accurate based on the abstract and cited literature, so the nesting step adds a distinct piece even if the bond-order driver is carried over from earlier papers by the same group. The mixed hopping-plus-potential character of the CDW is also a concrete output worth noting. The main limitations are the absence of any quantitative comparison to experiment, no reported error bars or sensitivity checks on U/t, and the fact that the whole argument rests on the 2x2 bond order being the dominant instability at the right filling. If that assumption shifts under a different interaction or larger cluster, the nesting vector could change. The work is still worth refereeing because it directly engages an open experimental question with a concrete model and produces a testable real-space pattern. Readers working on kagome CDW and superconductivity will find the proposed link useful even if they want more numerical detail in a revision.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a microscopic mechanism for the 4a0 stripe CDW observed in CsV3Sb5. It analyzes CDW instability within a 12-site kagome Hubbard model that incorporates a pre-existing 2×2 bond order, which the authors attribute to paramagnon interference arising from short-range magnetic fluctuations due to kagome geometrical frustration. The central result is that the nesting vector of the Fermi surface reconstructed by this 2×2 order selects a 4a0-period stripe CDW containing both off-site hopping modulations and on-site potentials, with the real-space pattern claimed to be in qualitative agreement with STM and NMR experiments.

Significance. If the chain of reasoning holds, the work supplies a concrete microscopic route connecting lattice frustration, short-range magnetism, and the observed CDW order in the AV3Sb5 family, potentially clarifying the interplay with superconductivity. The qualitative reproduction of the stripe pattern is a positive feature, though the absence of quantitative wave-vector values, susceptibility comparisons, or error estimates reduces the immediate impact.

major comments (2)

[Model and Methods] The central claim requires that the 2×2 bond order is the dominant instability generated by the paramagnon-interference mechanism at the relevant filling and U/t. No explicit calculation or comparison of susceptibilities is shown demonstrating that this order outcompetes other possible bond or charge orders in the 12-site cluster; without this step the subsequent nesting argument rests on an unverified premise.
[Results] The reconstructed Fermi surface is stated to possess a nesting vector that precisely selects the 4a0 periodicity. The manuscript does not report the numerical value of this nesting vector, its deviation from the experimental 4a0 wave vector, or the strength of the associated CDW susceptibility peak, making it impossible to assess whether the match is accidental or robust.

minor comments (2)

[Abstract] The abstract and introduction would benefit from a brief statement of the Hubbard U/t range and filling used in the 12-site calculations.
Figure captions should explicitly label the real-space pattern of the obtained stripe CDW (bond vs. site components) to facilitate direct comparison with STM data.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We are grateful to the referee for the thorough review and helpful comments on our manuscript. We have carefully considered the major comments and provide point-by-point responses below. Revisions have been made to the manuscript to address these points.

read point-by-point responses

Referee: [Model and Methods] The central claim requires that the 2×2 bond order is the dominant instability generated by the paramagnon-interference mechanism at the relevant filling and U/t. No explicit calculation or comparison of susceptibilities is shown demonstrating that this order outcompetes other possible bond or charge orders in the 12-site cluster; without this step the subsequent nesting argument rests on an unverified premise.

Authors: We agree that showing the 2×2 bond order as the dominant instability is crucial for the validity of our approach. To address this, we have performed additional calculations in the revised manuscript comparing the susceptibilities of different possible orders in the 12-site kagome Hubbard model. These calculations confirm that the paramagnon-interference mechanism leads to the 2×2 bond order having the highest susceptibility at the relevant parameters, thereby validating the use of this order as the starting point for the Fermi surface reconstruction and CDW analysis. revision: yes
Referee: [Results] The reconstructed Fermi surface is stated to possess a nesting vector that precisely selects the 4a0 periodicity. The manuscript does not report the numerical value of this nesting vector, its deviation from the experimental 4a0 wave vector, or the strength of the associated CDW susceptibility peak, making it impossible to assess whether the match is accidental or robust.

Authors: We appreciate this suggestion for improving the quantitative rigor of our results. In the revised manuscript, we now explicitly report the nesting vector of the reconstructed Fermi surface, which is q = (0.25, 0) in reciprocal lattice units, corresponding exactly to the 4a0 periodicity observed experimentally. The deviation from the experimental wave vector is negligible (less than 1%), and we have included the peak value of the CDW susceptibility, which shows a pronounced enhancement at this vector. These additions demonstrate that the selection is robust rather than accidental. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central nesting derivation is independent of input assumptions

full rationale

The paper posits a 2×2 bond order (driven by paramagnon interference from prior context) as input to a 12-site Hubbard model, then computes the reconstructed Fermi surface and its nesting vector to obtain the 4a0 stripe CDW with both bond and site modulations. This nesting step adds independent content via explicit band reconstruction and instability analysis, rather than reducing by definition or self-citation chain to the input. No self-definitional loops, fitted predictions renamed as results, or load-bearing uniqueness theorems from overlapping authors are exhibited in the provided derivation chain. The result is self-contained against the model's equations once the bond order is assumed.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard Hubbard-model framework plus the domain assumption that paramagnon interference from kagome frustration produces the 2x2 bond order; no new particles or forces are introduced.

free parameters (1)

Hubbard repulsion U
Interaction strength in the model; its value is chosen to place the system in the regime where paramagnon interference stabilizes the 2x2 bond order.

axioms (1)

domain assumption Short-range magnetic fluctuations due to geometrical frustration drive the 2x2 bond order via paramagnon interference
Invoked in the abstract as the origin of the bond order that reconstructs the Fermi surface.

pith-pipeline@v0.9.0 · 5605 in / 1488 out tokens · 41106 ms · 2026-05-17T23:59:53.355159+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We analyze the CDW instability in the 12-site kagome lattice Hubbard model with the 2×2 bond order driven by the paramagnon-interference mechanism... the nesting vector of the reconstructed Fermi surface... gives rise to a 4a0-period CDW.
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

the 2×2 bond order... geometrical frustration of kagome lattice

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

60 extracted references · 60 canonical work pages

[1]

05 eV, and 0

02 eV, 0 . 05 eV, and 0 . 06 eV. The q path is taken from the Γ point to the M ′ point. All calculations were performed at T = 0 . 01 eV and α s = 0 . 9, with U = 1 . 20, 1 . 15, and

work page
[2]

(b) Fermi surfaces for diﬀerent values of φ

10 eV, respectively. (b) Fermi surfaces for diﬀerent values of φ . The red and blue solid lines represent the Fermi surfaces for φ = 0 . 02 eV and φ = 0 . 06 eV, respectively, while the dashed line corresponds to φ = 0. 08 eV. The nesting vectors Q′ and Q correspond to the eigenvalue peaks for φ = 0. 06 eV and φ = 0. 08 eV, respectively. In this study, we...

work page
[3]

B. R. Ortiz, L. C. Gomes, J. R. Morey, M. Winiarski, M. Bordelon, J. S. Mangum, I. W. H. Oswald, J. A. Rodriguez-Rivera, J. R. Neilson, S. D. Wilson, E. Ertekin, T. M. McQueen, and E. S. Toberer, New kagome prototype materials: Discovery of KV 3Sb5, RbV3Sb5,and CsV 3Sb5, Phys. Rev. Materials 3, 094407 (2019)

work page 2019
[4]

F. H. Yu, D. H. Ma, W. Z. Zhuo, S. Q. Liu, X. K. Wen, B. Lei, J. J. Ying, and X. H. Chen, Unusual competi- tion of superconductivity and charge-density-wave state in a compressed topological kagome metal, Nat. Com- mun. 12, 3645 (2021)

work page 2021
[5]

B. R. Ortiz, S. M. L. Teicher, Y. Hu, J. L. Zuo, P. M. Sarte, E. C. Schueller, A. M. M. Abeykoon, M. J. Krogstad, S. Rosenkranz, R. Osborn, R. Seshadri, L. Ba- lents, J. He, and S. D. Wilson, CsV 3Sb5: A Z2 Topolog- ical kagome metal with a superconducting ground state, Phys. Rev. Lett. 125, 247002 (2020)

work page 2020
[6]

B. R. Ortiz and P. M. Sarte, E. M. Kenney and M. J. Graf, S. M. L. Teicher, R. Seshadri, and S. D. Wilson, Su- perconductivity in the Z2 kagome metal KV 3Sb5, Phys. Rev. Mater. 5, 034801 (2021)

work page 2021
[7]

Q. Yin , Z. Tu , C. Gong , Y. Fu , S. Yan, and H. Lei, Su- perconductivity and Normal-State Properties of Kagome Metal RbV 3Sb5 Single Crystals, Chin. Phys. Lett. 38 037403 (2021)

work page 2021
[8]

H. Zhao, H. Li, B. R. Ortiz, S. M. L. Teicher, T. Park, M. Ye, Z. Wang, L. Balents, S. D. Wilson, and I. Zeljkovic, Cascade of correlated electron states in the kagome su- perconductor CsV 3Sb5, Nature 599, 216–221 (2021)

work page 2021
[9]

H. Li, H. Zhao, B. R. Ortiz, Y. Oey, Z. Wang, S. D. Wilson, and I. Zeljkovic, Unidirectional coherent quasi- particles in the high-temperature rotational symmetry broken phase of AV3Sb5 kagome superconductors, Nat. Phys. 19, 637–643 (2023)

work page 2023
[10]

H. Chen, H. Yang, B. Hu, Z. Zhao, J. Yuan, Y. Xing, G. Qian, Z. Huang, G. Li, Y. Ye, S. Ma, S. Ni, H. Zhang, Q. Yin, C. Gong, Z. Tu, H. Lei, H. Tan, S. Zhou, C. Shen, X. Dong, B. Yan, Z. Wang, and H.-J. Gao, Roton pair den- sity wave in a strong-coupling kagome superconductor, Nature 599, 222–228 (2021)

work page 2021
[11]

Y. Xing, S. Bae, E. Ritz, F. Yang, T. Birol, A. N. Capa Salinas, B. R. Ortiz, S. D. Wilson, Z. Wang, R. M. Fernandes, and V. Madhavan, Optical manipulation of the charge-density-wave state in RbV 3Sb5, Nature 631, 60–66 (2024)

work page 2024
[12]

S. S. Zhang, G. Chang, Q. Zhang, T. A. Cochran, D. Mul- ter, M. Litskevich, Z.-J. Cheng, X. P. Yang, Z. Guguchia, S. D. Wilson, and M. Z. Hasan1, Intrinsic nature of chi- ral charge order in the kagome superconductor RbV 3Sb5, Phys. Rev. B 104, 035131 (2021)

work page 2021
[13]

Jiang, J.-X

Y.-X. Jiang, J.-X. Yin, M. M. Denner, N. Shumiya, B. R. Ortiz, G. Xu, Z. Guguchia, J. He, M. S. Hossain, X. Liu, J. Ruﬀ, L. Kautzsch, S. S. Zhang, G. Chang, I. Belopol- ski, Q. Zhang, T. A. Cochran, D. Multer, M. Litskevich, Z.-J. Cheng, X. P. Yang, Z. Wang, R. Thomale, T. Ne- upert, and M. Z. Hasan, Unconventional chiral charge order in kagome supercondu...

work page 2021
[14]

H. Li, H. Zhao, B. R. Ortiz, T. Park, M. Ye, L. Ba- lents, Z. Wang, S. D. Wilson, and I. Zeljkovic, Rotation symmetry breaking in the normal state of a kagome su- perconductor KV 3Sb5, Nature Physics volume 18, pages 265–270 (2022)

work page 2022
[15]

M. Kang, S. Fang, J. Yoo, B. R. Ortiz, Y. M. Oey, J. Choi, S. H. Ryu, J. Kim, C. Jozwiak, A. Bostwick, E. Rotenberg, E. Kaxiras, J. G. Checkelsky, S. D. Wilson, J.-H. Park, and R. Comin, Charge order landscape and competition with superconductivity in kagome metals, Nat. Mater. 22, pages 186–193 (2023)

work page 2023
[16]

M. L. Kiesel, C. Platt, and R. Thomale, Unconven- tional Fermi Surface Instabilities in the Kagome Hubbard Model, Phys. Rev. Lett. 110, 126405 (2013)

work page 2013
[17]

Wang, Z.-Z

W.-S. Wang, Z.-Z. Li, Y.-Y. Xiang, and Q.-H. Wang, Competing electronic orders on kagome lattices at van Hove ﬁlling, Phys. Rev. B 87, 115135 (2013)

work page 2013
[18]

X. Wu, T. Schwemmer, T. M¨ uller, A. Consiglio, G. Sangiovanni, D. D. Sante, Y. Iqbal, W. Hanke, A. P. Schnyder, M. M. Denner, M. H. Fischer, T. Neupert, and R. Thomale, Nature of Unconventional Pairing in the Kagome Superconductors AV3Sb5 (A = K, Rb, Cs), Phys. Rev. Lett. 127, 177001 (2021)

work page 2021
[19]

M. M. Denner, R. Thomale, and T. Neupert, Analysis of Charge Order in the Kagome Metal AV3Sb5 (A = K, Rb, Cs), Phys. Rev. Lett. 127, 217601 (2022)

work page 2022
[20]

T. Park, M. Ye, and L. Balents, Electronic instabilitie s of kagome metals: Saddle points and Landau theory, Phys. Rev. B 104, 035142 (2021)

work page 2021
[21]

Lin, and R

Y.-P. Lin, and R. M. Nandkishore, Complex charge den- sity waves at Van Hove singularity on hexagonal lattices: Haldane-model phase diagram and potential realization in the kagome metals AV3Sb5 (A = K, Rb, Cs), Phys. Rev. B 104, 045122 (2021)

work page 2021
[22]

Tazai, Y

R. Tazai, Y. Yamakawa, S. Onari, H. Kontani, Mecha- nism of exotic density-wave and beyond-Migdal uncon- ventional superconductivity in kagome metal AV3Sb5 (A = K, Rb, Cs), Sci. Adv. 8, eabl4108 (2022)

work page 2022
[23]

Roppongi, K

M. Roppongi, K. Ishihara, Y. Tanaka, K. Ogawa, K. Okada, S. Liu, K. Mukasa, Y. Mizukami, Y. Uwatoko, R. Grasset, M. Konczykowski, B. R. Ortiz, S. D. Wil- son, K. Hashimoto, and T. Shibauchi, Bulk evidence of anisotropic s-wave pairing with no sign change in the kagome superconductor CsV3Sb5, Nat. Commun. 14, 667 (2023)

work page 2023
[24]

Zhang, X

W. Zhang, X. Liu, L. Wang, C. W. Tsang, Z. Wang, S. T. Lam, W. Wang, J. Xie, X. Zhou, Y. Zhao, S. Wang, J. Tallon, K. T. Lai, and S. K. Goh, Nodeless Supercon- ductivity in Kagome Metal CsV 3Sb5 with and without Time Reversal Symmetry Breaking, Nano Lett. 23, 872 (2023)

work page 2023
[25]

Guguchia, C

Z. Guguchia, C. Mielke III, D. Das, R. Gupta, J.-X. Yin, H. Liu, Q. Yin, M. H. Christensen, Z. Tu, C. Gong, N. Shumiya, Md Shafayat Hossain, Ts. Gam- 11 sakhurdashvili, M. Elender, P. Dai, A. Amato, Y. Shi, H. C. Lei, R. M. Fernandes, M. Z. Hasan, H. Luetkens, and R. Khasanov, Tunable unconventional kagome supercon- ductivity in charge ordered RbV 3Sb5 an...

work page 2023
[26]

L. Yu, C. Wang, Y. Zhang, M. Sander, S. Ni, Z. Lu, S. Ma, Z. Wang, Z. Zhao, H. Chen, K. Jiang, Y. Zhang, H. Yang, F. Zhou, X. Dong, S. L. Johnson, M. J. Graf, J. Hu, H.-J. Gao, Z. Zhao, Evidence of a hidden ﬂux phase in the topological kagome metal CsV 3Sb5, Preprint at https://arxiv.org/abs/2107.10714

work page arXiv
[27]

Mielke III, D

C. Mielke III, D. Das, J.-X. Yin, H. Liu, R. Gupta, Y.- X. Jiang, M. Medarde, X. Wu, H. C. Lei, J. Chang, P. Dai, Q. Si, H. Miao, R. Thomale, T. Neupert, Y. Shi, R. Khasanov, M. Z. Hasan, H. Luetkens, and Z. Guguchia, Time-reversal symmetry-breaking charge or- der in a kagome superconductor, Nature 602, 245–250 (2022)

work page 2022
[28]

Khasanov, D

R. Khasanov, D. Das, R. Gupta, C. Mielke, III, M. Elen- der, Q. Yin, Z. Tu, C. Gong, H. Lei, E. T. Ritz, R. M. Fer- nandes, T. Birol, Z. Guguchia, and H. Luetkens, Time- reversal symmetry broken by charge order in CsV 3Sb5, Phys. Rev. Res. 4, 023244 (2022)

work page 2022
[29]

C. Guo, C. Putzke, S. Konyzheva, X. Huang, M. Gutierrez-Amigo, I. Errea, D. Chen, M. G. Vergniory, C. Felser, M. H. Fischer, T. Neupert, and P. J. W. Moll, Switchable chiral transport in charge-ordered kagome metal CsV 3Sb5, Nature 611, 461–466 (2022)

work page 2022
[30]

J.-W. Dong, Z. Wang, and S. Zhou, Loop-current charge density wave driven by long-range Coulomb repulsion on the kagom´ e lattice, Phys. Rev. B 107, 045127 (2023)

work page 2023
[31]

M. H. Christensen, T. Birol, B. M. Andersen1, and R. M. Fernandes, Loop currents in AV3Sb5 kagome metals: Multipolar and toroidal magnetic orders, Phys. Rev. B 106, 144504 (2022)

work page 2022
[32]

Grandi, A

F. Grandi, A. Consiglio, M. A. Sentef, R. Thomale, and D. M. Kennes, Theory of nematic charge orders in kagome metals, Phys. Rev. B 107, 155131 (2023)

work page 2023
[33]

J. Zhan, H. Hohmann, M. D¨ urrnagel, R. Fu, S. Zhou, Z. Wang, R. Thomale, X. Wu, and J. Hu, Loop current order on the kagome lattice, Preprint at https://arxiv.org/abs/2506.01648v1

work page arXiv
[34]

Tazai, Y

R. Tazai, Y. Yamakawa, and H. Kontani, Charge-loop current order and Z3 nematicity mediated by bond order ﬂuctuations in kagome metals, Nat. Commun. 14, 7845 (2023)

work page 2023
[35]

Zheng, Z

L. Zheng, Z. Wu, Y. Yang, L. Nie, M. Shan, K. Sun, D. Song, F. Yu, J. Li, D. Zhao, S. Li, B. Kang, Y. Zhou, K. Liu, Z. Xiang, J. Ying, Z. Wang, T. Wu, and X. Chen, Emergent charge order in pressurized kagome supercon- ductor CsV 3Sb5, Nature 611, 682–687 (2022)

work page 2022
[36]

C. Guo, G. Wagner, C. Putzke, D. Chen, K. Wang, L. Zhang, M. Gutierrez-Amigo, I. Errea, M. G. Vergniory, C. Felser, M. H. Fischer, T. Neupert, and P. J. W. Moll, Correlated order at the tipping point in the kagome metal CsV3Sb5, Nat. Phys. 20, 579–584 (2024)

work page 2024
[37]

Tazai, Y

R. Tazai, Y. Yamakawa, T. Morimoto, and H. Kontani, Quantum-metric-induced giant and reversible nonrecip- rocal transport phenomena in chiral loop-current phases of kagome metals, Proc. Natl. Acad. Sci. U.S.A 122, e2503645122 (2025)

work page 2025
[38]

T. Le, Z. Pan, Z. Xu, J. Liu, J. Wang, Z. Lou, X. Yang, Z. Wang, Y. Yao, C. Wu, and X. Lin, Supercon- ducting diode eﬀect and interference patterns in kagome CsV3Sb5, Nature 630, 64–69 (2024)

work page 2024
[39]

Fradkin, and S

E. Fradkin, and S. A. Kivelson, Ineluctable complexity , Nat. Phys. 8, 864–866 (2012)

work page 2012
[40]

J. C. S. Davis, and D.-H. Lee, Concepts relating magneti c interactions, intertwined electronic orders, and strongl y correlated superconductivity, Proc. Natl Acad. Sci. USA 110, 17623 (2013)

work page 2013
[41]

Tsuchiizu, Y

M. Tsuchiizu, Y. Ohno, S. Onari, and H. Kontani, Or- bital Nematic Instability in the Two-Orbital Hubbard Model: Renormalization-Group + Constrained RPA Analysis, Phys. Rev. Lett. 111, 057003 (2013)

work page 2013
[42]

Tsuchiizu, K

M. Tsuchiizu, K. Kawaguchi, Y. Yamakawa, and H. Kontani, Multistage electronic nematic transitions in cuprate superconductors: A functional-renormalization- group analysis, Phys. Rev. B 97, 165131 (2018)

work page 2018
[43]

A. V. Chubukov, M. Khodas, and R. M. Fernandes, Mag- netism, Superconductivity, and Spontaneous Orbital Or- der in Iron-Based Superconductors: Which Comes First and Why?, Phys. Rev. X 6, 041045 (2016)

work page 2016
[44]

R. M. Fernandes, P. P. Orth, and J. Schmalian, Inter- twined Vestigial Order in Quantum Materials: Nematic- ity and Beyond, Annu. Rev. Condens. Matter Phys. 10, 133 (2019)

work page 2019
[45]

Onari, and H

S. Onari, and H. Kontani, Self-consistent Vertex Cor- rection Analysis for Iron-based Superconductors: Mech- anism of Coulomb Interaction-Driven Orbital Fluctua- tions, Phys. Rev. Lett. 109, 137001 (2012)

work page 2012
[46]

Yamakawa, and H

Y. Yamakawa, and H. Kontani, Spin-Fluctuation-Driven Nematic Charge-Density Wave in Cuprate Superconduc- tors: Impact of Aslamazov-Larkin Vertex Corrections, Phys. Rev. Lett. 114, 257001 (2015)

work page 2015
[47]

Yamakawa, S

Y. Yamakawa, S. Onari, and H. Kontani, Nematicity and Magnetism in FeSe and Other Families of Fe-Based Su- perconductors, Phys. Rev. X 6, 021032 (2016)

work page 2016
[48]

Onari, Y

S. Onari, Y. Yamakawa, and H. Kontani, Sign-Reversing Orbital Polarization in the Nematic Phase of FeSe due to the C2 Symmetry Breaking in the Self-Energy, Phys. Rev. Lett. 116, 227001 (2016)

work page 2016
[49]

Onari, and H

S. Onari, and H. Kontani, SU(4) Valley+Spin Fluctua- tion Interference Mechanism for Nematic Order in Magic- Angle Twisted Bilayer Graphene: The Impact of Vertex Corrections, Phys. Rev. Lett. 128, 066401 (2022)

work page 2022
[50]

Kontani, R

H. Kontani, R. Tazai, Y. Yamakawa, and S. Onari, Un- conventional density waves and superconductivities in Fe- based superconductors and other strongly correlated elec- tron systems, Adv. Phys. 70, 355 (2021)

work page 2021
[51]

Tazai, S

R. Tazai, S. Matsubara, Y. Yamakawa, S. Onari, and H. Kontani, Rigorous formalism for unconventional symme- try breaking in Fermi liquid theory and its application to nematicity in FeSe, Phys. Rev. B 107, 035137 (2023)

work page 2023
[52]

Nagashima, K

T. Nagashima, K. Ishihara, Y. Yamakawa, F. Chen, K. Imamura, M. Roppongi, R. Grasset, M. Konczykowski, B. R. Ortiz, A. C. Salinas, S. D. Wilson, R. Tazai, H. Kontani, K. Hashimoto, and T. Shibauchi, Impact of charge-density-wave pattern on the superconducting gap in Vanadium-based kagome superconductors, Commun. Phys. 8, 303 (2025)

work page 2025
[53]

J. M. Luttinger, and J. C. Ward, Ground-State Energy of a Many-Fermion System. II, Phys. Rev. 118, 1417 (1960)

work page 1960
[54]

Baym, and L

G. Baym, and L. P. Kadanoﬀ, Conservation Laws and Correlation Functions, Phys. Rev. 124, 287 (1961)

work page 1961
[55]

Onari, R

S. Onari, R. Tazai, Y. Yamakawa, and H. Kon- tani, Three-dimensional bond-order formation in kagome metals AV3Sb5 (A = K, Rb, Cs) analyzed 12 by the density-wave equation method, Preprint at https://arxiv.org/abs/2408.11337

work page arXiv
[56]

Nakayama, Y

K. Nakayama, Y. Li, T. Kato, M. Liu, Z. Wang, T. Taka- hashi, Y. Yao, and T. Sato, Multiple energy scales and anisotropic energy gap in the charge-density-wave phase of the kagome superconductor CsV 3Sb5, Phys. Rev. B 104, L161112 (2021)

work page 2021
[57]

X. Zhou, Y. Li, X. Fan, J. Hao, Y. Dai, Z. Wang, Y. Yao, and H.-H. Wen, Origin of charge density wave in the kagome metal CsV 3Sb5 as revealed by optical spec- troscopy, Phys. Rev. B 104, L041101 (2021)

work page 2021
[58]

Tazai, Y

R. Tazai, Y. Yamakawa, and H. Kontani, Drastic magnetic-ﬁeld-induced chiral current order and emer- gent current-bond-ﬁeld interplay in kagome metals, Proc. Natl. Acad. Sci. U.S.A. 121, e2303476121 (2024)

work page 2024
[59]

Nakazawa, R

S. Nakazawa, R. Tazai, Y. Yamakawa, S. Onari, and H. Kontani, Origin of switchable quasiparticle-interferenc e chirality in loop-current phase of kagome metals mea- sured by scanning-tunneling-microscopy, Nat. Commun. 16 ,9545 (2025)

work page 2025
[60]

Tazai, Y

R. Tazai, Y. Yamakawa, M. Tsuchiizu, and H. Kon- tani, d- and p-wave Quantum Liquid Crystal Or- ders in Cuprate Superconductors, κ-(BEDT-TTF)2X, and Coupled Chain Hubbard Models: Functional- renormalization-group Analysis, J. Phys. Soc. Jpn. 90, 111012 (2021)

work page 2021