pith. sign in

arxiv: 2503.07015 · v2 · submitted 2025-03-10 · ❄️ cond-mat.str-el · cond-mat.supr-con

Origin of switchable quasiparticle-interference chirality in loop-current phase of kagome metals measured by scanning-tunneling-microscopy

Seigo Nakazawa , Rina Tazai , Youichi Yamakawa , Seiichiro Onari , Hiroshi Kontani This is my paper

Pith reviewed 2026-05-23 01:13 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.supr-con
keywords kagome metalsloop-current phasequasiparticle interferencescanning tunneling microscopychiralitystar-of-David CDWZ3 nematicityimpurity scattering
0
0 comments X

The pith

A single impurity induces switchable quasiparticle interference chirality in the loop-current phase of kagome metals.

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

The paper establishes that in kagome superconductors AV3Sb5, the dissipationless loop-current phase coexisting with star-of-David charge-density-wave order produces a pronounced chiral quasiparticle interference signal in scanning tunneling microscopy when impurities are extremely dilute. A single impurity at site Z creates a chirality value of plus or minus one that is fixed by the direction of Z3 nematicity, which itself follows from the relative position of the loop-current order. This chirality switches smoothly under a small applied magnetic field and produces associated shear lattice strain that matches experimental reports. A sympathetic reader would care because the result supplies a direct microscopic link between the symmetry-breaking loop-current state and an observable STM signature, offering a concrete way to confirm the phase through controlled impurity and field effects.

Core claim

In the extremely dilute impurity regime below 0.1 percent, a single impurity at site Z induces a quasiparticle interference chirality χ_Z equal to plus or minus one. This value is determined by the direction of the Z3 nematicity, which is set by the relative position of the loop-current order inside the star-of-David charge-density-wave phase. Even a small magnetic field can switch the chirality smoothly and generates field-induced shear lattice strain consistent with recent experiments.

What carries the argument

The impurity-induced quasiparticle interference chirality χ_Z, whose sign is fixed by Z3 nematicity arising from the relative placement of loop-current order within the star-of-David CDW.

If this is right

  • The observed QPI chirality in STM directly encodes the direction of the loop-current order through Z3 nematicity.
  • Application of a small magnetic field provides a reversible control knob for both the chirality and the induced lattice strain.
  • The chiral signal appears only in the dilute-impurity regime, explaining why it has been seen in certain high-quality samples.
  • The mechanism accounts for the connection between loop-current symmetry breaking and measurable STM features in AV3Sb5 compounds.

Where Pith is reading between the lines

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

  • If the same loop-current plus CDW coexistence occurs in related kagome systems, analogous switchable chirality should appear under comparable dilute-impurity conditions.
  • Varying the magnetic-field direction relative to the lattice could map out the full set of allowed strain responses and test the Z3 symmetry assignment.
  • The single-impurity calculation suggests that controlled introduction of isolated defects could serve as a local probe of hidden loop-current order in other correlated materials.

Load-bearing premise

The model requires that a loop-current phase with specific symmetry properties coexists with the star-of-David charge-density-wave and that impurity scattering occurs in the extremely dilute single-impurity limit.

What would settle it

Absence of any magnetic-field-induced switching in the quasiparticle interference chirality, or failure to observe the chiral signal at all in samples with impurity concentrations below 0.1 percent, would falsify the central claim.

Figures

Figures reproduced from arXiv: 2503.07015 by Hiroshi Kontani, Rina Tazai, Seigo Nakazawa, Seiichiro Onari, Youichi Yamakawa.

Figure 1
Figure 1. Figure 1: FIG. 1: (a) Kagome lattice model. The unit cell is composed [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a) represents the modulation of the LDOS (δρi ≡ ρi − ρ V =0 i ) at E = −0.04 induced by the single impurity at A-site (=Imp A), whose location is shown in [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: (a) LDOS under the LC order ( [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: (a) Adiabatic change from [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

In the kagome superconductors AV3Sb5 (A=Cs,Rb,K), a cascade of correlated electron phases cause exotic symmetry-breaking quantum states. In particular, the dissipationless chiral loop-current phase has been attracting increasing attention. A crucial clue is offered by the chirality of the quasiparticle interference signal observed in scanning tunneling microscopy. However, the connection between loop-current chirality and quasiparticle interference chirality remains poorly understood. Here, we reveal theoretically that a pronounced chiral quasiparticle interference signal emerges in the extremely dilute impurity regime ($lesssim$ 0.1 %). A single impurity at site Z induces a quasiparticle interference chirality $\chi_Z=\pm1$, determined by the direction of the Z3 nematicity, itself set by the relative position of the loop-current order in the star-of-David charge-density-wave phase. Notably, even a small magnetic field can smoothly switch the chirality, leading to field-induced shear lattice strain consistent with recent experiments. Our theoretical study provide key insights into the nature of the loop-current-induced symmetry-breaking states in kagome metals.

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 theoretically examines the connection between loop-current order and quasiparticle interference (QPI) chirality in the kagome superconductors AV3Sb5. It argues that, in the extremely dilute single-impurity limit, an impurity at site Z produces a chiral QPI signal with χ_Z = ±1 whose sign is fixed by the Z3 nematicity direction, itself determined by the relative positioning of the loop-current order inside the star-of-David CDW. The central additional claim is that an applied magnetic field can smoothly reverse this chirality through an induced shear lattice strain, consistent with recent experiments.

Significance. If the central derivation holds, the work supplies a concrete microscopic mechanism linking the loop-current phase to the observed switchable QPI chirality and to field-induced lattice strain, thereby strengthening the experimental case for loop-current order in these materials. The explicit treatment of the dilute-impurity regime and the Z3 degeneracy provides falsifiable predictions for STM measurements.

major comments (2)
  1. [Discussion of magnetic-field switching (near the free-energy analysis)] The assertion that laboratory-scale magnetic fields (~few T) suffice to switch the QPI chirality rests on an effective free-energy term coupling B to the nematic director. No microscopic calculation (electron-phonon, orbital magnetism, or magneto-elastic) of the coupling coefficient is reported; the magnitude required to overcome the anisotropy barrier is therefore unquantified. This assumption is load-bearing for the field-switching claim.
  2. [§ on dilute-impurity QPI calculation] The QPI chirality χ_Z is stated to be determined solely by the Z3 nematicity set by the loop-current positioning inside the star-of-David CDW. The manuscript does not demonstrate that this mapping remains robust once realistic band-structure details, finite impurity potential strength, or weak inter-impurity interference are restored; the single-impurity, parameter-free limit is used throughout.
minor comments (2)
  1. Notation for the chirality index χ_Z and the nematic director should be defined explicitly at first use, with a clear statement of the sign convention relative to the lattice.
  2. The abstract states the impurity concentration ≲ 0.1 %; the main text should specify the precise density at which the single-impurity approximation begins to break down.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address the two major comments below, clarifying the scope of our calculations while agreeing where additional discussion is warranted.

read point-by-point responses

  1. Referee: The assertion that laboratory-scale magnetic fields (~few T) suffice to switch the QPI chirality rests on an effective free-energy term coupling B to the nematic director. No microscopic calculation (electron-phonon, orbital magnetism, or magneto-elastic) of the coupling coefficient is reported; the magnitude required to overcome the anisotropy barrier is therefore unquantified. This assumption is load-bearing for the field-switching claim.

    Authors: We agree that the magnetic-field switching is treated at the effective free-energy level without a microscopic derivation of the magneto-elastic or orbital coupling coefficient. The manuscript's primary focus is the microscopic origin of the QPI chirality from loop-current order in the dilute-impurity limit; the field-switching scenario is introduced phenomenologically to connect with existing experiments on field-induced strain. We will revise the relevant section to explicitly state that the coupling strength is not computed from first principles and that the claim of laboratory-scale fields is therefore qualitative, resting on consistency with the observed strain response rather than a calculated barrier height. revision: partial

  2. Referee: The QPI chirality χ_Z is stated to be determined solely by the Z3 nematicity set by the loop-current positioning inside the star-of-David CDW. The manuscript does not demonstrate that this mapping remains robust once realistic band-structure details, finite impurity potential strength, or weak inter-impurity interference are restored; the single-impurity, parameter-free limit is used throughout.

    Authors: The calculation is deliberately restricted to the extremely dilute (≲0.1 %), single-impurity, parameter-free limit precisely to isolate the direct mapping between the loop-current-determined Z3 nematicity and the emergent QPI chirality χ_Z. In this controlled regime the chirality is fixed by symmetry and the impurity site. We will add a dedicated paragraph explaining the rationale for this limit and outlining why the chirality assignment is expected to persist under weak perturbations (finite potential, realistic bands, low-density inter-impurity effects), while acknowledging that a full numerical survey of those extensions lies beyond the present scope. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation is model-based prediction from assumed loop-current order

full rationale

The abstract and available text present a theoretical calculation of QPI chirality χ_Z induced by a single impurity in a presupposed loop-current + star-of-David CDW background. The Z3 nematicity direction is an input symmetry choice of the model, and the resulting χ_Z=±1 plus field-induced switching are outputs of that model rather than redefinitions of the inputs. No equations are shown that equate a fitted parameter to a claimed prediction, no self-citation chain is invoked to justify a uniqueness theorem, and no ansatz is smuggled via prior work. The magneto-elastic coupling is treated as an external consistency check with experiment rather than derived inside the paper, but this is an assumption gap, not a definitional loop. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review; the ledger is therefore minimal and limited to the central modeling assumption stated in the text.

axioms (1)
  • domain assumption Existence of loop-current phase with Z3 nematicity inside the star-of-David CDW
    Invoked as the background state whose relative position sets the nematicity that in turn sets χ_Z

pith-pipeline@v0.9.0 · 5759 in / 1336 out tokens · 43436 ms · 2026-05-23T01:13:16.324395+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

62 extracted references · 62 canonical work pages

  1. [1]

    1 (c) and (d) in the folded Brillouin zone (BZ) for η = − φ = 0

    Figure 1 (b) shows the SoD BO by φ0 (φ < 0) and the LC order by ηI (η > 0): The band structure and the density-of-states (DOS) are shown in Figs. 1 (c) and (d) in the folded Brillouin zone (BZ) for η = − φ = 0 . 01. The equal-energy surfaces for E = 0 (Fermi level) and − 0. 04 are shown in Fig. 1 (e). Importantly, the coexisting state ( ηα, φ0) is nematic...

    work page

  2. [2]

    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, RbV 3Sb5, and CsV 3Sb5, Phys. Rev. Materials 3, 094407 (2019)

    work page 2019

  3. [3]

    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

  4. [4]

    H. Li, H. Zhao, B. R. Ortiz, T. Park, M. Ye, L. Balents, Z. Wang, S. D. Wilson, and I. Zeljkovic, Rotation symmetry breaking in the normal state of a kagome superconductor KV3Sb5, Nat. Phys. 18, 265 (2022)

    work page 2022

  5. [5]

    L. Nie, K. Sun, W. Ma, D. Song, L. Zheng, Z. Liang, P. Wu, F. Yu, J. Li, M. Shan, D. Zhao, S. Li, B. Kang, Z. Wu, Y. Zhou, K. Liu, Z. Xiang, J. Ying, Z. Wang, T. Wu, and X. Chen, Charge-density-wave-driven electronic nematicity in a kagome superconductor, Nature 604, 59 (2022)

    work page 2022

  6. [6]

    T. Kato, Y. Li, T. Kawakami, M. Liu, K. Nakayama, Z. Wang, A. Moriya, K. Tanaka, T. Takahashi, Y. Yao, and T. Sato, Three-dimensional energy gap and origin of charge-density wave in kagome superconductor KV 3Sb5, Commun. Mater. 3, 30 (2022)

    work page 2022

  7. [7]

    L. Nie, K. Sun, W. Ma, D. Song, L. Zheng, Z. Liang, P. Wu, F. Yu, J. Li, M. Shan, D. Zhao, S. Li, B. Kang, Z. Wu, Y. Zhou, K. Liu, Z. Xiang, J. Ying, Z. Wang, T. 6 Wu, and X. Chen, Charge-density-wave-driven electronic nematicity in a kagome superconductor, Nature 604, 59 (2022)

    work page 2022

  8. [8]

    Y. Xu, Z. Ni, Y. Liu, B. R. Ortiz, Q. Deng, S. D. Wilson, B. Yan, L. Balents, and L. Wu, Three-state nematic- ity and magneto-optical Kerr effect in the charge density waves in kagome superconductors, Nat. Phys. 18, 1470 (2022)

    work page 2022

  9. [11]

    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 CsV 3Sb5, Nat Commun 14, 667 (2023)

    work page 2023

  10. [12]

    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 superconduc- tivity in kagome metal CsV 3Sb5 with and without time reversal symmetry breaking, Nano Lett. 23, 872 (2023)

    work page 2023

  11. [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, S. D. Wilson, and M. Z. Hasan, Unconventional chiral charge order in kag...

    work page 2021

  12. [14]

    Deng et al ., Chiral kagome superconductivity modu- lations with residual Fermi arcs, Nature 632, 775 (2024)

    H. Deng et al ., Chiral kagome superconductivity modu- lations with residual Fermi arcs, Nature 632, 775 (2024)

    work page 2024

  13. [16]

    Wang et al ., Electronic nature of chiral charge order in the kagome superconductor CsV 3Sb5, Phys

    Z. Wang et al ., Electronic nature of chiral charge order in the kagome superconductor CsV 3Sb5, Phys. Rev. B 104, 075148 (2021)

    work page 2021

  14. [17]

    Shumiya et al ., Intrinsic nature of chiral charge order in the kagome superconductor RbV 3Sb5, Phys

    N. Shumiya et al ., Intrinsic nature of chiral charge order in the kagome superconductor RbV 3Sb5, Phys. Rev. B 104, 035131 (2021)

    work page 2021

  15. [18]

    C. M. Varma, Non-Fermi-liquid states and pairing insta - bility of a general model of copper oxide metals, Phys. Rev. B 55, 14554 (1997)

    work page 1997

  16. [19]

    Weber, T

    C. Weber, T. Giamarchi, and C. M. Varma, Phase Dia- gram of a Three-Orbital Model for High- Tc Cuprate Su- perconductors, Phys. Rev. Lett. 112, 117001 (2014)

    work page 2014

  17. [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

  18. [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 A V3Sb5 (A=K, Rb, Cs), Phys. Rev. B 104, 045122 (2021)

    work page 2021

  19. [22]

    M. L. Kiesel, C. Platt, and R. Thomale, Unconventional Fermi surface instabilities in the kagome Hubbard model, Phys. Rev. Lett. 110, 126405 (2013)

    work page 2013

  20. [23]

    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

  21. [24]

    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 A V 3Sb5 (A = K, Rb, Cs), Phys. Rev. Lett. 127, 177001 (2021)

    work page 2021

  22. [25]

    M. M. Denner, R. Thomale, and T. Neupert, Analysis of Charge Order in the Kagome Metal A V 3Sb5 (A = K, Rb, Cs), Phys. Rev. Lett. 127, 217601 (2021)

    work page 2021

  23. [26]

    M. H. Christensen, T. Biro, B. M. Andersen, and R. M. Fernandes, Loop currents in A V 3Sb5 kagome met- als: Multipolar and toroidal magnetic order, Phys. Rev. B 106, 144504 (2022)

    work page 2022

  24. [27]

    S.-Y. Yang, Y. Wang, B. R. Ortiz, D. Liu, J. Gayles, E. Derunova, R. Gonzalez-Hernandez, Sejkal, Y. Chen, S. S. P. Parkin, S. D. Wilson, E. S. Toberer, T. McQueen, and M. N. Ali, Giant, unconventional anomalous Hall effect in the metallic frustrated magnet candidate, KV 3Sb5, Sci. Adv. 6, eabb6003 (2020)

    work page 2020

  25. [28]

    F. H. Yu, T. Wu, Z. Y. Wang, B. Lei, W. Z. Zhuo, J. J. Ying, and X. H. Chen, Concurrence of anomalous Hall effect and charge density wave in a superconducting topo- logical kagome metal, Phys. Rev. B 104, L041103 (2021)

    work page 2021

  26. [29]

    Y. Wang, Z. Chen, Y. Nie, Y. Zhang, Q. Niu, G. Zheng, X. Zhu, W. Ning, and M. Tian, Nontrivial Fermi surface topology and large anomalous Hall effect in the kagome superconductor RbV 3Sb5, Phys. Rev. B 108, 035117 (2023)

    work page 2023

  27. [31]

    Supplementary Information

    work page

  28. [33]

    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. John- son, M. J. Graf, J. Hu, H.-J. Gao, and Z. Zhao, Evidence of a hidden flux phase in the topological kagome metal CsV 3Sb5, arXiv:2107.10714 (avalable at https://arxiv.org/abs/2107.10714)

    work page arXiv

  29. [34]

    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 (2022)

    work page 2022

  30. [35]

    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

  31. [36]

    Guguchia, C

    Z. Guguchia, C. Mielke III, D. Das, R. Gupta, J.-X. Yin, 7 H. Liu, Q. Yin, M. H. Christensen, Z. Tu, C. Gong, N. Shumiya, M. S. Hossain, T. Gamsakhurdashvili, M. Elen- der, P. Dai, A. Amato, Y. Shi, H. C. Lei, R. M. Fernan- des, M. Z. Hasan, H. Luetkens, and R. Khasanov, Tun- able unconventional kagome superconductivity in charge ordered RbV 3Sb5 and KV 3...

    work page 2023

  32. [37]

    J. Luo, Z. Zhao, Y. Z. Zhou, J. Yang, A. F. Fang, H. T. Yang, H. J. Gao, R. Zhou, and G.-q. Zheng, Possible star- of-David pattern charge density wave with additional modulation in the kagome superconductor CsV 3Sb5, npj Quantum Mater. 7, 30 (2022)

    work page 2022

  33. [38]

    Y. Hu, S. Yamane, G. Mattoni, K. Yada, K. Obata, Y. Li, Y. Yao, Z. Wang, J. Wang, C. Farhang, J. Xia, Y. Maeno, and S. Yonezawa, Time-reversal sym- metry breaking in charge density wave of CsV 3Sb5 de- tected by polar Kerr effect, arXiv:2208.08036 (avalable at https://arxiv.org/abs/2208.08036)

    work page arXiv

  34. [39]

    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, Nature Physics 20, 579 (2024)

    work page 2024

  35. [41]

    Fujita, C

    K. Fujita, C. K. Kim, I. Lee, J. Lee, M. H. Hamidian, I. A. Firmo, S. Mukhopadhyay, H. Eisaki, S. Uchida, M. J. Lawler, E. -A. Kim, and J. C. Seamus Davis, Simultane- ous transitions in cuprate momentum-space topology and electronic symmetry breaking, Science 344, 612 (2014)

    work page 2014

  36. [42]

    C. J. Butler, Y. Kohsaka, Y. Yamakawa, M. S. Bahramy, S. Onari, H. Kontani, T. Hanaguri, and S. Shamoto, Correlation-driven electronic nematicity in the Dirac semimetal BaNiS 2, Proc. Natl. Acad. Sci. USA, 119, e2212730119 (2022)

    work page 2022

  37. [43]

    S. Wang, P. Choubey, Y. X. Chong, W. Chen, W. Ren, H. Eisaki, S. Uchida, P. J. Hirschfeld, and J. C. Seamus Davis, Scattering interference signature of a pair density wave state in the cuprate pseudogap phase, Nat. Com- mun. 12, 6087 (2021)

    work page 2021

  38. [44]

    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

  39. [45]

    H. D. Scammell, J. Ingham, T. Li, and O. P. Sushkov, Chiral excitonic order from twofold van Hove singularities in kagome metals, Nat. Commun. 14, 605 (2023)

    work page 2023

  40. [47]

    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

  41. [48]

    Tazai, Y

    R. Tazai, Y. Yamakawa, and H. Kontani, Emergence of charge loop current in the geometrically frustrated Hub- bard model: A functional renormalization group study, Phys. Rev. B 103, L161112 (2021)

    work page 2021

  42. [49]

    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

  43. [50]

    Huang, R

    J. Huang, R. Tazai, Y. Yamakawa, S. Onari, and H. Kon- tani, Low temperature phase transitions inside the CDW phase in the kagome metals A V 3Sb5 (A=Cs,Rb,K): Sig- nificance of mixed-type Fermi surface electron correla- tions, Phys. Rev. B 109, L041110 (2024)

    work page 2024

  44. [51]

    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

  45. [52]

    Nakazawa, R

    S. Nakazawa, R. Tazai, Y. Yamakawa, S. Onari, and H. Kontani, Giant Impurity Effects on Charge Loop Cur- rent Order States in Kagome Metals, Phys. Rev. B 111, 075161 (2025)

    work page 2025

  46. [56]

    The enlarged unit cell contains twelve sublattices ( l = 1 ∼ 12)

    The TrH (SoD) bond-order is realized for φ > 0 ( φ < 0). The enlarged unit cell contains twelve sublattices ( l = 1 ∼ 12). Sites A, B, and C in the main text respectively correspond to sites 10, 8, and 12. Next, we explain the 3 Q current order between the nearest V atoms. Its form factor with q = q1, f (1) ij , is + i for sites ( i, j ) belongs to sublat...

    work page

  47. [57]

    ) + c3(η4 1 + η4 2 + η4

    + c2(φ 2 1φ 2 2 + cycl. ) + c3(η4 1 + η4 2 + η4

    work page

  48. [58]

    ) + 2c5(φ 2 1η2 1 + φ 2 2η2 2 + φ 2 3η2

    + c4(η2 1η2 2 + cycl. ) + 2c5(φ 2 1η2 1 + φ 2 2η2 2 + φ 2 3η2

    work page

  49. [59]

    + c6(φ 2 1(η2 2 + η2

    work page

  50. [60]

    # $ % & ' !

    + cycl . ), where ab ∝ (Tcdw − T ) and ac ∝ (Tlc − T ) are the second-order, b1 and b2 are the third-order, and c1 ∼ c6 are the fourth-order param- eters. Here, we assume φ = φ0. Then, the φ 3 term becomes b1φ 3/ 3 √ 3, so the relation b1φ < 0 is satisfied to stabilize the 3Q BO. Then, the GL free energy is simpli- fied as F [η, φ0] = ( ac − b1φ/ 2 √ 3 + 2(...

    work page

  51. [61]

    Tazai, Y

    R. Tazai, Y. Yamakawa, S. Onari, and H. Kontani, Mech- anism of exotic density-wave and beyond-Migdal uncon- ventional superconductivity in kagome metal A V 3Sb5 (A=K, Rb, Cs), Sci. Adv. 8, eabl4108 (2022)

    work page 2022

  52. [62]

    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

  53. [63]

    Shimura, R

    K. Shimura, R. Tazai, Y. Yamakawa, S. Onari, and H. Kontani, Real-space loop current pattern in time- reversal-symmetry breaking phase in kagome metals, J. Phys. Soc. Jpn. 93, 033704 (2024)

    work page 2024

  54. [64]

    Nakazawa, R

    S. Nakazawa, R. Tazai, Y. Yamakawa, S. Onari, and H. Kontani, Giant Impurity Effects on Charge Loop Current Order States in Kagome Metals, arXiv:2405.12141

    work page arXiv

  55. [65]

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

    work page 2021

  56. [66]

    Asaba, A

    T. Asaba, A. Onishi, Y. Kageyama, T. Kiyosue, K. Oht- suka, S. Suetsugu, Y. Kohsaka, T. Gaggl, Y. Kasahara, H. Murayama, K. Hashimoto, R. Tazai, H. Kontani, B. R. Ortiz, S. D. Wilson, Q. Li, H.-H. Wen, T. Shibauchi, and Y. Matsuda, Evidence for an odd-parity nematic phase above the charge-density-wave transition in a kagome metal, Nat. Phys. 20, 40 (2024)

    work page 2024

  57. [67]

    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. of Sci. (PNAS) 121, e2303476121 (2024)

    work page 2024

  58. [68]

    Zhao et al

    H. Zhao et al. , Cascade of correlated electron states in the kagome superconductor CsV 3Sb5, Nature 599, 216 (2021)

    work page 2021

  59. [69]

    H. Li, H. Zhao, B. R. Ortiz, Y. Oey, Z. Wang, S. D. Wil- son, and I. Zeljkovic, Unidirectional coherent quasiparti- cles in the high-temperature rotational symmetry broken phase of A V3Sb5 kagome superconductors, Nat. Phys. 19, 637 (2023)

    work page 2023

  60. [70]

    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, arXiv:2408.04233

    work page arXiv

  61. [71]

    C. Guo, C. Putzke, C. Konyzheva, 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 (2022)

    work page 2022

  62. [72]

    Y. Xing, S. Bae, E. Ritz, Fan Yang, Turan Birol, Andrea N. Capa Salinas, Brenden R. Ortiz, Stephen D. Wilson, Z. Wang, R. M. Fernandes, and V. Madhavan, Nature 631, 60 (2024)

    work page 2024