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arxiv: 2604.05506 · v1 · submitted 2026-04-07 · ❄️ cond-mat.supr-con

Visualizing the interplay of dual electronic nematicities in kagome superconductors

Yunmei Zhang , Jun Zhan , Ping Wu , Yun-Peng Huang , Qixiao Yuan , Hongyu Li , Zhuying Wang , Wanru Ma
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Shuikang Yu Kunming Zhang Wanlin Cheng Deshu Chen Minrui Chen Tao Wu Ziji Xiang Xianxin Wu Zhenyu Wang Xianhui Chen
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Pith reviewed 2026-05-10 19:21 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con
keywords nematic orderkagome superconductorCsV3Sb5charge density wavescanning tunneling microscopyFermi surfaceorbital orderGinzburg-Landau
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The pith

STM reveals two distinct nematic orders in the kagome superconductor CsV3Sb5

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

The paper uses scanning tunneling microscopy on CsV3Sb5 with varying temperature and Ti doping to separate two nematic order parameters. One is induced by the triple-Q charge density wave, while the other appears as a C2 symmetry breaking in the vanadium dx2-y2 Fermi surface pockets. This second order survives to higher temperatures and dopings where the CDW vanishes. Their preferred directions differ at intermediate doping but coincide in the clean material, suggesting they come from different kagome lattice orbitals and interact in complex ways.

Core claim

By using scanning tunneling microscopy to study the electronic structures of CsV3Sb5 as a function of temperature and Ti doping, we disentangle the interrelation between two distinct nematic order parameters, one associated with the CDW and the other manifested as C2 distortion of the V-dx2-y2 Fermi pockets without breaking transition symmetry. The latter persists to high doping levels and high temperatures where the long-range CDW is fully suppressed. Moreover, its nematic director is oriented in a lattice direction distinct from that of the CDW-induced nematicity at intermediate doping, and eventually aligns with the strong nematic CDW order in the pristine compound where the quasiparticle

What carries the argument

Dual nematic order parameters assigned to distinct kagome-lattice orbitals, distinguished by STM through their doping-temperature dependence and director orientations.

If this is right

  • The second nematic order from orbital distortion can exist without the long-range CDW.
  • The two nematic directors are oriented differently at intermediate doping levels.
  • The directors align in the pristine compound below the vanadium quasiparticle coherence temperature.
  • The orders arise from different orbitals on the kagome lattice and their coupling produces unusual phenomena.

Where Pith is reading between the lines

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

  • This could provide a way to tune the dominant nematic order by doping to study their interactions.
  • Similar dual nematic orders may be found in other materials with geometric frustration.
  • The persistence of the second order suggests it could influence superconductivity in the doped regime.

Load-bearing premise

The observed C2 distortion of the V-dx2-y2 Fermi pockets is a genuine distinct nematic order parameter that can be clearly separated from CDW-induced effects by STM without significant surface or artifact issues.

What would settle it

If the C2 distortion of the Fermi pockets disappears at the same temperature as the CDW even when doping suppresses the CDW, or if the director orientations always match regardless of doping level.

Figures

Figures reproduced from arXiv: 2604.05506 by Deshu Chen, Hongyu Li, Jun Zhan, Kunming Zhang, Minrui Chen, Ping Wu, Qixiao Yuan, Shuikang Yu, Tao Wu, Wanlin Cheng, Wanru Ma, Xianhui Chen, Xianxin Wu, Yunmei Zhang, Yun-Peng Huang, Zhenyu Wang, Zhuying Wang, Ziji Xiang.

Figure 2
Figure 2. Figure 2: FIG. 2. Observation of a 𝑞𝑞 = 0 nematic state at x = 0.18. (a) STM topography of the Sb-terminated surface. The bright protrusions correspond to Ti atoms that replace V atoms in the underneath kagome layer. (b) FFT of the Sb-terminated surface topography acquired at 20 mV, showing only the Bragg peaks. (c, d) Differential conductance map 𝐿𝐿(𝐫𝐫,−10 mV) and its Fourier transform. A, B, and C indicate the thr… view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Electronic orders in pristine CsV3Sb5 and statistical analysis of the dopant-induced anisotropy. (a) FT of L(r, -10 mV) for the pristine sample which exhibits prominent unidirectional features. (b) Energy dispersions of the QPI scattering vectors, extracted along the three Γ𝐾𝐾 directions. (c) FT intensity profiles along the three atomic directions of the corresponding topographic image of (a), show… view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Ginzburg-Landau phase diagram of the coupled CDW and nematic orders in the 𝛼𝛼𝜙𝜙 − 𝛽𝛽𝜂𝜂 plane. Here 𝛼𝛼𝜙𝜙 is the quadratic coefficient of the nematic CDW component, and 𝛽𝛽𝜂𝜂 characterizes the coupling between the CDW-induced nematic order ϕ and the intrinsic nematic order η. Different colors indicate the three phases: a coexistence phase with aligned nematic directors for 𝛽𝛽𝜂𝜂 < 0, a coexistence phas… view at source ↗
read the original abstract

Kagome superconductor AV$_3$Sb$_5$ (A stands for K, Rb, and Cs) hosts a wealth of intertwined electronic orders driven by geometric frustration and electron correlations. Among them, the breaking of rotational and/or time-reversal symmetry, observed within the triple-$Q$ charge density wave (CDW) phase yet exhibiting a more complex temperature dependence, remains a central puzzle. Here, by using scanning tunneling microscopy to study the electronic structures of CsV$_3$Sb$_5$ as a function of temperature and Ti doping, we disentangle the interrelation between two distinct nematic order parameters, one associated with the CDW and the other manifested as $C_2$ distortion of the V-$d_{x^{2}-y^{2}}$ Fermi pockets without breaking transition symmetry. The latter persists to high doping levels and high temperatures where the long-range CDW is fully suppressed. Moreover, its nematic director is oriented in a lattice direction distinct from that of the CDW-induced nematicity at intermediate doping, and eventually aligns with the strong nematic CDW order in the pristine compound where the quasiparticles of vanadium orbitals become coherent below a lower characteristic temperature. These observations, combined with Ginzburg-Landau analysis, reveal a rich interplay between two nematic orders that can be assigned to distinct kagome-lattice orbitals. Our results shed new light on the enigmatic intertwined orders in this family and establish a rare material platform in which dual nematic orders coexist and couple to give rise to unusual correlated phenomena.

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 / 0 minor

Summary. The manuscript uses scanning tunneling microscopy (STM) to investigate the electronic structures of CsV₃Sb₅ as a function of temperature and Ti doping. It disentangles two distinct nematic order parameters: one associated with the triple-Q CDW and the other as a C₂ distortion of the V-d_{x²-y²} Fermi pockets that persists without breaking transition symmetry even when the long-range CDW is suppressed. The nematic director reorients with doping, and Ginzburg-Landau analysis is employed to describe their interplay, assigning them to distinct kagome-lattice orbitals.

Significance. If the experimental distinction between the two nematic orders is robust, this work would be significant for the field of kagome superconductors. It provides direct visualization of dual electronic nematicities coexisting and coupling, which could explain the complex temperature dependence of symmetry breaking in AV₃Sb₅. The doping-tuned suppression of CDW while observing the persistent C2 distortion offers a rare platform to study orbital-specific correlated phenomena.

major comments (3)
  1. The central claim that the C2 distortion represents a distinct nematic order independent of CDW-induced nematicity is load-bearing for the paper's conclusions. However, the STM data interpretation lacks quantitative LDOS simulations for the two scenarios or cross-checks with bulk probes to exclude surface effects or residual short-range CDW order, as noted in the skeptic's assessment of the weakest assumption.
  2. The Ginzburg-Landau analysis is phenomenological with assumptions on the coupling between the two orders not fully specified. This limits the ability to derive the observed director reorientation and characteristic temperatures from first principles, making the analysis more descriptive than predictive.
  3. The assignment of the two nematic orders to distinct kagome-lattice orbitals is based on the STM observations and GL analysis, but without supporting microscopic calculations or additional experimental evidence, this assignment remains tentative and central to the significance claim.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for highlighting both its potential significance and areas where the evidence could be strengthened. We address each major comment below with specific responses and indicate where revisions will be made.

read point-by-point responses

  1. Referee: The central claim that the C2 distortion represents a distinct nematic order independent of CDW-induced nematicity is load-bearing for the paper's conclusions. However, the STM data interpretation lacks quantitative LDOS simulations for the two scenarios or cross-checks with bulk probes to exclude surface effects or residual short-range CDW order, as noted in the skeptic's assessment of the weakest assumption.

    Authors: We agree that quantitative LDOS simulations would provide stronger support and that cross-checks with bulk probes help address potential surface or short-range order concerns. The distinction in our data rests on the orthogonal doping and temperature dependencies of the two features, the reorientation of the nematic director at intermediate doping, and the spatial uniformity of the C2 distortion across large areas. In the revised manuscript we will add an expanded discussion section that references existing ARPES and transport data showing C2 symmetry breaking persisting above the CDW transition temperature and at doping levels where long-range CDW order is absent. We will also include qualitative arguments, based on the observed coherence of quasiparticles and lack of domain fragmentation, against residual short-range CDW as the sole origin. Full quantitative LDOS simulations for the doped, multi-orbital case are computationally intensive and beyond the present scope, but we will note this limitation explicitly. revision: partial

  2. Referee: The Ginzburg-Landau analysis is phenomenological with assumptions on the coupling between the two orders not fully specified. This limits the ability to derive the observed director reorientation and characteristic temperatures from first principles, making the analysis more descriptive than predictive.

    Authors: We acknowledge that the Ginzburg-Landau treatment is phenomenological, as is standard when modeling competing symmetry-breaking orders whose microscopic origins are not yet fully established. The coupling terms were selected according to the point-group symmetries of the kagome lattice and the experimentally observed director reorientation with doping. In the revised manuscript we will explicitly list all assumed coupling constants, show the free-energy minimization steps that reproduce the director switch and the two distinct onset temperatures, and clarify that the model is intended to organize the observations rather than to predict them ab initio. We will also add a brief statement that first-principles derivation of the coupling strengths remains an open theoretical task. revision: partial

  3. Referee: The assignment of the two nematic orders to distinct kagome-lattice orbitals is based on the STM observations and GL analysis, but without supporting microscopic calculations or additional experimental evidence, this assignment remains tentative and central to the significance claim.

    Authors: The orbital assignment follows directly from the STM observation that the persistent C2 distortion selectively affects the V d_{x²-y²} Fermi pockets while the CDW-linked nematicity involves a different set of states, combined with the symmetry-allowed couplings in the GL model. We agree that this remains an interpretation rather than a first-principles result. In the revised text we will rephrase the relevant sections to present the assignment as a data-consistent hypothesis, cite existing theoretical works that anticipate orbital-selective nematicity in kagome lattices, and explicitly state that microscopic calculations are needed for confirmation. No new calculations are added because they lie outside the experimental focus of the present study. revision: no

Circularity Check

0 steps flagged

No significant circularity; experimental STM data and standard post-hoc GL analysis are independent of inputs.

full rationale

The paper's derivation chain begins with direct STM measurements of electronic structure versus temperature and Ti doping in CsV3Sb5, which constitute independent experimental inputs. These data are used to identify C2 distortions of V-dx2-y2 pockets and their director orientations. The subsequent Ginzburg-Landau analysis is a standard phenomenological tool applied after data collection to interpret the interplay of two nematic orders; it does not fit parameters to a subset and rename them as predictions, nor does it rely on self-definitional loops or load-bearing self-citations for uniqueness. No equations or claims reduce by construction to the input observations, and the central distinction between CDW-induced and orbital nematicities is assigned from the measured features rather than derived tautologically. The work is self-contained against external benchmarks via the raw STM spectra and doping series.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The claim rests on STM observations interpreted through standard Ginzburg-Landau phenomenology and domain assumptions about surface sensitivity; no new particles or forces are introduced.

free parameters (2)
  • Ti doping levels
    Selected to progressively suppress the CDW while tracking the second nematicity
  • Characteristic temperatures
    Identified from data for coherence onset and order suppression
axioms (2)
  • domain assumption Ginzburg-Landau theory applies to the coupling of the two nematic orders
    Invoked to analyze the interplay and director alignment
  • domain assumption STM images reflect bulk electronic structure without dominant surface reconstruction
    Required to assign the C2 distortion to V-dx2-y2 Fermi pockets

pith-pipeline@v0.9.0 · 5652 in / 1514 out tokens · 55049 ms · 2026-05-10T19:21:20.566254+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

58 extracted references · 58 canonical work pages

  1. [1]

    Fradkin, S

    E. Fradkin, S. A. Kivelson, and J. M. Tranquada, Colloquium: Theory of intertwined orders in high- temperature superconductors, Rev. Mod. Phys. 87, 457 (2015)

    work page 2015

  2. [2]

    R. M. Fernandes, P. P. Orth, and J. Schmalian, Intertwined vestigial order in quantum materials: Nematicity and beyond, Annu. Rev. Condens. Matter Phys. 10, 133 (2019)

    work page 2019

  3. [3]

    D. F. Agterberg, J. C. S. Davis, S. D. Edkins, E. Fradkin, D. J. V an Harlingen, S. A. Kivelson, P. A. Lee, L. Radzihovsky, J. M. Tranquada, and Y . Wang, The physics of pair-density waves: Cuprate superconductors and beyond, Annu. Rev. Condens. Matter Phys. 11, 231 (2020)

    work page 2020

  4. [4]

    Balents, Spin liquids in frustrated magnets, Nature 464, 199 (2010)

    L. Balents, Spin liquids in frustrated magnets, Nature 464, 199 (2010)

    work page 2010

  5. [5]

    W.-H. Ko, P. A. Lee, and X.- G. Wen, Doped kagome system as exotic superconductor, Phys. Rev. B 79, 214502 (2009)

    work page 2009

  6. [6]

    Nandkishore, L

    R. Nandkishore, L. S. Levitov, and A. V . Chubukov, Chiral superconductivity from repulsive interactions in doped graphene, Nat. Phys. 8, 158 (2012)

    work page 2012

  7. [7]

    Syôzi, Statistics of kagomé lattice, Prog

    I. Syôzi, Statistics of kagomé lattice, Prog. Theor. Phys. 6, 306 (1951)

    work page 1951

  8. [8]

    J.-X. Yin, B. Lian, and M. Z. Hasan, Topological kagome magnets and superconductors, Nature 612, 647 (2022)

    work page 2022

  9. [9]

    Y u and J.-X

    S.-L. Y u and J.-X. Li, Chiral superconducting phase and chiral spin-density-wave phase in a Hubbard model on the kagome lattice, Phys. Rev. B 85, 144402 (2012). 7

    work page 2012

  10. [10]

    M. L. Kiesel and R. Thomale, Sublattice interference in the kagome Hubbard model, Phys. Rev. B 86, 121105 (2012)

    work page 2012

  11. [11]

    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

  12. [12]

    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

  13. [13]

    B. R. Ortiz et al., New kagome prototype materials: Discovery of KV 3Sb5, RbV3Sb5, and CsV3Sb5, Phys. Rev. Materials 3, 094407 (2019)

    work page 2019

  14. [14]

    B. R. Ortiz et al., CsV3Sb5: A Z2 topological kagome metal with a superconducting ground state, Phys. Rev. Lett. 125, 247002 (2020)

    work page 2020

  15. [15]

    Neupert, M

    T. Neupert, M. M. Denner, J.-X. Yin, R. Thomale, and M. Z. Hasan, Charge order and superconductivity in kagome materials, Nat. Phys. 18, 137 (2022)

    work page 2022

  16. [16]

    Jiang, T

    K. Jiang, T. Wu, J.- X. Yin, Z. Wang, M. Z. Hasan, S. D. Wilson, X. Chen, and J. Hu, Kagome superconductors A V3Sb5 (A = K, Rb, Cs), Natl. Sci. Rev. 10, nwac199 (2023)

    work page 2023

  17. [17]

    S. D. Wilson and B. R. Ortiz, A V3Sb5 kagome superconductors, Nat. Rev. Mater. 9, 420 (2024)

    work page 2024

  18. [18]

    Kang et al., Twofold van Hove singularity and origin of charge order in topological kagome superconductor CsV 3Sb5, Nat

    M. Kang et al., Twofold van Hove singularity and origin of charge order in topological kagome superconductor CsV 3Sb5, Nat. Phys. 18, 301 (2022)

    work page 2022

  19. [19]

    Hu et al., Rich nature of van Hove singularities in kagome superconductor CsV3Sb5, Nat

    Y . Hu et al., Rich nature of van Hove singularities in kagome superconductor CsV3Sb5, Nat. Commun. 13, 2220 (2022)

    work page 2022

  20. [20]

    Y . Hu, X. Wu, A. P. Schnyder, and M. Shi, Electronic landscape of kagome superconductors A V3Sb5 (A = K, Rb, Cs) from angle-resolved photoemission spectroscopy, npj Quantum Mater. 8, 67 (2023)

    work page 2023

  21. [21]

    M. H. Christensen, T. Birol, B. M. Andersen, and R. M. Fernandes, Theory of the charge density wave in AV3Sb5 kagome metals, Phys. Rev. B 104, 214513 (2021)

    work page 2021

  22. [22]

    M. M. Denner, R. Thomale, and T. Neupert, Analysis of charge order in the kagome metal A V3Sb5 (A = K, Rb, Cs), Phys. Rev. Lett. 127, 217601 (2021)

    work page 2021

  23. [23]

    Wu et al., Nature of unconventional pairing in the kagome superconductors A V 3Sb5 (A = K, Rb, Cs), Phys

    X. Wu et al., Nature of unconventional pairing in the kagome superconductors A V 3Sb5 (A = K, Rb, Cs), Phys. Rev. Lett. 127, 177001 (2021)

    work page 2021

  24. [24]

    Zhou and Z

    S. Zhou and Z. Wang, Chern Fermi pocket, topological pair -density wave, and charge -4e and charge -6e superconductivity in kagome superconductors, Nat. Commun. 13, 7288 (2022)

    work page 2022

  25. [25]

    Tazai, Y

    R. Tazai, Y . Yamakawa, and H. Kontani, Charge-loop current order and Z 3 nematicity mediated by bond- order fluctuations in kagome metals, Nat. Commun. 14, 7845 (2023)

    work page 2023

  26. [26]

    H. Li, Y . B. Kim, and H.-Y . Kee, Intertwined van Hove singularities as a mechanism for loop current order in kagome metals, Phys. Rev. Lett. 132, 146501 (2024)

    work page 2024

  27. [27]

    X. Han, A. P. Schnyder, and X. Wu, Enhanced nematicity emerging from higher -order Van Hove singularities, Phys. Rev. B 107, 184504 (2023)

    work page 2023

  28. [28]

    R. Fu, J. Zhan, M. Dürrnagel, H. Hohmann, R. Thomale , J. Hu, Z. Wang, S. Zhou, and X. Wu, Exotic charge-density waves and superconductivity on the kagome lattice, Natl. Sci. Rev. 12, nwaf414 (2025)

    work page 2025

  29. [29]

    J. Zhan, H. Hohmann, M. Dürrnagel, R. Fu, S. Zhou, Z. Wang, R. Thomale, X. Wu, and J. Hu, Loop current order on the kagome lattice, Phys. Rev. Lett. 136, 126001 (2026)

    work page 2026

  30. [30]

    Jiang et al., Unconventional chiral charge order in kagome superconductor KV 3Sb5, Nat

    Y.-X. Jiang et al., Unconventional chiral charge order in kagome superconductor KV 3Sb5, Nat. Mater. 20, 1353 (2021). 8

    work page 2021

  31. [31]

    Mielke III et al., Time -reversal symmetry-breaking charge order in a kagome superconductor, Nature 602, 245 (2022)

    C. Mielke III et al., Time -reversal symmetry-breaking charge order in a kagome superconductor, Nature 602, 245 (2022)

    work page 2022

  32. [32]

    Guo et al., Switchable chiral transport in charge-ordered kagome metal CsV3Sb5, Nature 611, 461 (2022)

    C. Guo et al., Switchable chiral transport in charge-ordered kagome metal CsV3Sb5, Nature 611, 461 (2022)

    work page 2022

  33. [33]

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

    work page 2022

  34. [34]

    Xing et al., Optical manipulation of the charge-density-wave state in RbV3Sb5, Nature 631, 60 (2024)

    Y . Xing et al., Optical manipulation of the charge-density-wave state in RbV3Sb5, Nature 631, 60 (2024)

    work page 2024

  35. [35]

    Hu et al., Time-reversal symmetry breaking in charge density wave of CsV 3Sb5 detected by polar Kerr effect, arXiv:2208.08036 (2022)

    Y . Hu et al., Time-reversal symmetry breaking in charge density wave of CsV 3Sb5 detected by polar Kerr effect, arXiv:2208.08036 (2022)

    work page arXiv 2022

  36. [36]

    Gui et al., Probing orbital magnetism of a kagome metal CsV 3Sb5 by a tuning fork resonator, Nat

    H. Gui et al., Probing orbital magnetism of a kagome metal CsV 3Sb5 by a tuning fork resonator, Nat. Commun. 16, 4275 (2025)

    work page 2025

  37. [37]

    H. Zhao, H. Li, B. R. Ortiz, S. M. Teicher, T. Park, M. Ye, Z. Wang, L. Balents, S. D. Wilson, and I. Zeljkovic, Cascade of correlated electron states in the kagome superconductor CsV3Sb5, Nature 599, 216 (2021)

    work page 2021

  38. [38]

    Xiang, Q

    Y . Xiang, Q. Li, Y . Li, W. Xie, H. Yang, Z. Wang, Y . Yao, and H. H. Wen, Twofold symmetry of c-axis resistivity in topological kagome superconductor CsV3Sb5 with in-plane rotating magnetic field, Nat. Commun. 12, 6727 (2021)

    work page 2021

  39. [39]

    Nie et al., Charge -density-wave-driven electronic nematicity in a kagome superconductor, Nature 604, 59 (2022)

    L. Nie et al., Charge -density-wave-driven electronic nematicity in a kagome superconductor, Nature 604, 59 (2022)

    work page 2022

  40. [40]

    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

  41. [41]

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

    work page 2023

  42. [42]

    Wu et al., Unidirectional electron–phonon coupling in the nematic state of a kagome superconductor, Nat

    P. Wu et al., Unidirectional electron–phonon coupling in the nematic state of a kagome superconductor, Nat. Phys. 19, 1143 (2023)

    work page 2023

  43. [43]

    Chen et al., Roton pair density wave in a strong- coupling kagome superconductor, Nature 599, 222 (2021)

    H. Chen et al., Roton pair density wave in a strong- coupling kagome superconductor, Nature 599, 222 (2021)

    work page 2021

  44. [44]

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

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

    work page 2024

  45. [45]

    Chen et al., Anomalous thermoelectric effects and quantum oscillations in the kagome metal CsV 3Sb5, Phys

    D. Chen et al., Anomalous thermoelectric effects and quantum oscillations in the kagome metal CsV 3Sb5, Phys. Rev. B 105, L201109 (2022)

    work page 2022

  46. [46]

    Guo et al., Correlated order at the tipping point in the kagome metal CsV3Sb5, Nat

    C. Guo et al., Correlated order at the tipping point in the kagome metal CsV3Sb5, Nat. Phys. 20, 579 (2024)

    work page 2024

  47. [48]

    Li et al., Small Fermi pockets intertwined with charge stripes and pair density wave order in a kagome superconductor, Phys

    H. Li et al., Small Fermi pockets intertwined with charge stripes and pair density wave order in a kagome superconductor, Phys. Rev. X 13, 031030 (2023)

    work page 2023

  48. [49]

    Yang et al., Titanium doped kagome superconductor CsV3−xTixSb5 and two distinct phases, Sci

    H. Yang et al., Titanium doped kagome superconductor CsV3−xTixSb5 and two distinct phases, Sci. Bull. 67, 2176 (2022)

    work page 2022

  49. [50]

    Liu et al., Doping evolution of superconductivity, charge order, and band topology in hole -doped topological kagome superconductors Cs(V1−xTix)3Sb5, Phys

    Y . Liu et al., Doping evolution of superconductivity, charge order, and band topology in hole -doped topological kagome superconductors Cs(V1−xTix)3Sb5, Phys. Rev. Materials 7, 064801 (2023)

    work page 2023

  50. [51]

    Wu et al., Competitive charge density waves in the doped kagome superconductor CsV3−xTixSb5, Phys

    Z. Wu et al., Competitive charge density waves in the doped kagome superconductor CsV3−xTixSb5, Phys. Rev. B 112, 144512 (2025). 9

    work page 2025

  51. [52]

    Huang et al., Revealing the orbital origins of exotic electronic states with Ti substitution in kagome superconductor CsV3Sb5, Phys

    Z. Huang et al., Revealing the orbital origins of exotic electronic states with Ti substitution in kagome superconductor CsV3Sb5, Phys. Rev. Lett. 134, 056001 (2025)

    work page 2025

  52. [53]

    Li et al., Electronic nematicity without charge density waves in titanium-based kagome metal, Nat

    H. Li et al., Electronic nematicity without charge density waves in titanium-based kagome metal, Nat. Phys. 19, 1591 (2023)

    work page 2023

  53. [54]

    Yang et al., Superconductivity and nematic order in a new titanium-based kagome metal CsTi3Bi5 without charge density wave order, Nat

    H. Yang et al., Superconductivity and nematic order in a new titanium-based kagome metal CsTi3Bi5 without charge density wave order, Nat. Commun. 15, 9626 (2024)

    work page 2024

  54. [55]

    Hu et al., Non- trivial band topology and orbital -selective electronic nematicity in a titanium- based kagome superconductor, Nat

    Y . Hu et al., Non- trivial band topology and orbital -selective electronic nematicity in a titanium- based kagome superconductor, Nat. Phys. 19, 1827 (2023)

    work page 2023

  55. [56]

    See Supplemental Material at : for transport characterization, a table of Ti concentration by counting, more QPI data for x=0.12 and 0.18, more data showing misalignment between the nematic axes of the CDW and the q=0 nematic state in x=0.12 samples , QPI linecuts for x=0.12 and 0.18, a Ginzburg- Landau analysis of intertwined CDW and electronic nematic o...

    work page

  56. [57]

    Guo et al., Many-body interference in kagome crystals, Nature 647, 68 (2025)

    C. Guo et al., Many-body interference in kagome crystals, Nature 647, 68 (2025)

    work page 2025

  57. [58]

    Huang et al., The parent state in kagome metals and superconductors: Chiral-nematic Fermi liquid state, arXiv:2511.09402 (2025)

    Z. Huang et al., The parent state in kagome metals and superconductors: Chiral-nematic Fermi liquid state, arXiv:2511.09402 (2025)

    work page arXiv 2025

  58. [59]

    Xu et al., Pervasive electronic nematicity as the parent state of kagome superconductors, arXiv:2511.22002 (2025)

    M. Xu et al., Pervasive electronic nematicity as the parent state of kagome superconductors, arXiv:2511.22002 (2025). Acknowledgements We thank Yingying Peng and Hui Chen for valuable discussions. This work is supported by the National Natural Science Foundation of China (Grant Nos. 52261135638, 12488201, 52373309), the Quantum Science and Technology-Nati...

    work page arXiv 2025