Abstract
Electronic nematicity has been commonly observed in juxtaposition with unconventional superconductivity. Understanding the nature of the nematic state and its consequences for the electronic band structure and superconductivity has therefore become a key issue in condensed matter physics. Here we visualize the organization of the interacting quasiparticles in the nematic state of the kagome superconductor CsV3−xTixSb5 using scanning tunnelling microscopy. Two-fold symmetric quasiparticle scattering interference of the vanadium kagome bands emerges below the bulk nematic transition temperature deep inside the charge density wave phase. We find that electron–phonon coupling alters the self-energy of the electrons and renormalizes the Fermi velocity of the in-plane vanadium bands only along the symmetry-breaking direction, making the low-energy dispersion and electron dynamics highly non-equivalent along the three lattice directions. The anti-correlation between the nematic transition temperature and the superconducting transition temperature with Ti substitution suggests a possible competition between superconductivity and electronic nematicity, with principal superconducting gaps opening on the same vanadium bands once the nematic state is totally suppressed. This provides a platform for modelling electronic nematicity in systems where electron correlations and lattice degree of freedom act together.
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Data availability
The data supporting the findings of this study are available at https://doi.org/10.5281/zenodo.7641861. Additional data are available from the corresponding author upon reasonable request. Source data are provided with this paper.
Code availability
The code used for STM data analysis is available from the corresponding author upon reasonable request.
References
Kivelson, S., Fradkin, E. & Emery, V. Electronic liquid crystal phases of a doped Mott insulator. Nature 393, 550–553 (1998).
Fradkin, E., Kivelson, S., Lawler, M. J., Eisenstein, J. P. & Mackenzie, A. P. Nematic Fermi fluids in condensed matter physics. Annu. Rev. Condens. Matter Phys. 1, 153–178 (2010).
Fernandes, R. M., Orth, P. P. & Schmalian, J. Intertwined vestigial order in quantum materials: nematicity and beyond. Annu. Rev. Condens. Matter Phys. 10, 133–154 (2019).
Hinkov, V. et al. Electronic liquid crystal state in the high-temperature superconductor YBa2Cu3O6.45. Science 319, 597–600 (2008).
Daou, R. et al. Broken rotational symmetry in the pseudogap phase of a high-Tc superconductor. Nature 463, 519–522 (2010).
Chu, J. H. et al. In-plane resistivity anisotropy in an underdoped iron arsenide superconductor. Science 329, 824–826 (2010).
Chuang, T. M. et al. Nematic electronic structure in the ‘parent’ state of the iron-based superconductor Ca (Fe1–xCox)2As2. Science 327, 181–184 (2010).
Kasahara, S. et al. Electronic nematicity above the structural and superconducting transition in BaFe2(As1−xPx)2. Nature 486, 382–385 (2012).
Rosenthal, E. et al. Visualization of electron nematicity and unidirectional antiferroic fluctuations at high temperatures in NaFeAs. Nat. Phys. 10, 225–232 (2014).
Fujita, K. et al. Simultaneous transitions in cuprate momentum-space topology and electronic symmetry breaking. Science 344, 612–616 (2014).
Fernandes, R. M., Chubukov, A. V. & Schmalian, J. What drives nematic order in iron-based superconductors? Nat. Phys. 10, 97–104 (2014).
Sato, Y. et al. Thermodynamic evidence for a nematic phase transition at the onset of the pseudogap in YBa2Cu3Oy. Nat. Phys. 13, 1074–1078 (2017).
Lilly, M. P. et al. Evidence for an anisotropic state of two-dimensional electrons in high Landau levels. Phys. Rev. Lett. 82, 394–397 (1999).
Feldman, B. E. et al. Observation of a nematic quantum Hall liquid on the surface of bismuth. Science 354, 316–321 (2016).
Cao, Y. et al. Nematicity and competing orders in superconducting magic-angle graphene. Science 372, 264–271 (2021).
Jiang, Y. et al. Charge order and broken rotational symmetry in magic-angle twisted bilayer graphene. Nature 573, 91–95 (2019).
Rubio-Verdú, C. et al. Moiré nematic phase in twisted double bilayer graphene. Nat. Phys. 18, 196–202 (2022).
Ortiz, B. R. et al. New kagome prototype materials: discovery of KV3Sb5, RbV3Sb5, and CsV3Sb5. Phys. Rev. Mater. 3, 094407 (2019).
Ortiz, B. R. et al. CsV3Sb5: a Z2 topological kagome metal with a superconducting ground state. Phys. Rev. Lett. 125, 247002 (2020).
Kenney, E. M. et al. Absence of local moments in the kagome metal KV3Sb5 as determined by muon spin spectroscopy. J. Phys. Condens. Matter 33, 235801 (2021).
Neupert, T. et al. Charge order and superconductivity in kagome materials. Nat. Phys. 18, 137–143 (2022).
Jiang, K. et al. Kagome superconductors AV3Sb5 (A = K, Rb, Cs). Natl Sci. Rev. 10, nwac199 (2022).
Nie, L. et al. Charge-density-wave-driven electronic nematicity in a kagome superconductor. Nature 604, 59–64 (2022).
Kang, M. et al. Twofold van Hove singularity and origin of charge order in topological kagome superconductor CsV3Sb5. Nat. Phys. 18, 301–308 (2022).
Wang, W. S. et al. Competing electronic orders on kagome lattices at van Hove filling. Phys. Rev. B 87, 115135 (2013).
Kiesel, M., Platt, C. & Thomale, R. Unconventional Fermi Surface Instabilities in the kagome Hubbard model. Phys. Rev. Lett. 110, 126405 (2013).
Jiang, Y. X. et al. Unconventional chiral charge order in kagome superconductor KV3Sb5. Nat. Mater. 20, 1353–1357 (2021).
Zhao, H. et al. Cascade of correlated electron states in the kagome superconductor CsV3Sb5. Nature 599, 216–221 (2021).
Liang, Z. et al. Three-dimensional charge density wave and surface-dependent vortex-core states in a kagome superconductor CsV3Sb5. Phys. Rev. X 11, 031026 (2021).
Chen, H. et al. Roton pair density wave in a strong-coupling kagome superconductor. Nature 599, 222–228 (2021).
Li, H. et al. Observation of unconventional charge density wave without acoustic phonon anomaly in kagome superconductors AV3Sb5 (A = Rb, Cs). Phys. Rev. X 11, 031050 (2021).
Mielke, C. et al. Time-reversal symmetry-breaking charge order in a kagome superconductor. Nature 602, 245–250 (2022).
Xu, Y. et al. Three-state nematicity and magneto-optical Kerr effect in the charge density waves in kagome superconductors. Nat. Phys. 18, 1470–1475 (2022).
Hu, Y. et al. Time-reversal symmetry breaking in charge density wave of CsV3Sb5 detected by polar Kerr effect. Preprint at https://arxiv.org/abs/2208.08036 (2022).
Li, H. et al. Rotation symmetry breaking in the normal state of a kagome superconductor KV3Sb5. Nat. Phys. 18, 265–270 (2022).
Li, H. et al. Unidirectional coherent quasiparticles in the high-temperature rotational symmetry broken phase of AV3Sb5 kagome superconductors. Nat. Phys. 1–7 (2023).
Xiang, Y. et al. Twofold symmetry of c-axis resistivity in topological kagome superconductor CsV3Sb5 with in-plane rotating magnetic field. Nat. Commun. 12, 6727 (2021).
Feenstra, R. M. Tunneling spectroscopy of the (110) surface of direct-gap III–V semiconductors. Phys. Rev. B 50, 456–4570 (1994).
Hanaguri, T. et al. Two distinct superconducting pairing states divided by the nematic end point in FeSe1−xSx. Sci. Adv. 4, eaar6419 (2018).
Kostin, A. et al. Imaging orbital-selective quasiparticles in the Hund’s metal state of FeSe. Nat. Mater. 17, 869–874 (2018).
Luo, H. et al. Electronic nature of charge density wave and electron-phonon coupling in kagome superconductor KV3Sb5. Nat. Commun. 13, 273 (2022).
Xiao, Q. et al. Coexistence of multiple stacking charge density waves in kagome superconductor CsV3Sb5. Phys. Rev. Res. 5, L012032 (2023).
Frassineti, J. et al. Microscopic nature of the charge-density wave in kagome superconductor RbV3Sb5. Phys. Rev. Res. 5, L012017 (2023).
Wang, Y. et al. The structure of kagome superconductors AV3Sb5 in the charge density wave states. Preprint at https://arxiv.org/abs/2210.07585 (2022).
Allan, M. P. et al. Anisotropic impurity states, quasiparticle scattering and nematic transport in underdoped Ca(Fe1−xCox)2As2. Nat. Phys. 9, 220–224 (2013).
Xie, Y. et al. Electron–phonon coupling in the charge density wave state of CsV3Sb5. Phys. Rev. B 105, L140501 (2022).
Ratcliff, N. et al. Coherent phonon spectroscopy and interlayer modulation of charge density wave order in the kagome metal CsV3Sb5. Phys. Rev. Mater. 5, L111801 (2021).
Wang, Z. X. et al. Unconventional charge density wave and photoinduced lattice symmetry change in the kagome metal CsV3Sb5 probed by time-resolved spectroscopy. Phys. Rev. B 104, 165110 (2021).
Wulferding, D., Lee, S. & Choi, Y. et al. Emergent nematicity and intrinsic versus extrinsic electronic scattering processes in the kagome metal CsV3Sb5. Phys. Rev. Res. 4, 023215 (2022).
Christensen, M. H., Birol, T., Andersen, B. M. & Fernandes, R. M. Theory of the charge-density wave in AV3Sb5 kagome metals. Phys. Rev. B 104, 214513 (2021).
Park, T., Ye, M. & Balents, L. Electronic instabilities of kagome metals: saddle points and Landau theory. Phys. Rev. B 104, 035142 (2021).
Denner, M. M., Thomale, R. & Neupert, T. Analysis of charge order in the kagome metal AV3Sb5 (A = K, Rb, Cs). Phys. Rev. Lett. 127, 217601 (2021).
Tazai, R. et al. Mechanism of exotic density-wave and beyond-Migdal unconventional superconductivity in kagome metal AV3Sb5 (A = K, Rb, Cs). Sci. Adv. 8, eabl4108 (2022).
Guo, C. et al. Switchable chiral transport in charge-ordered kagome metal CsV3Sb5. Nature 611, 461–466 (2022).
Lanzara, A. et al. Evidence for ubiquitous strong electron–phonon coupling in high-temperature superconductors. Nature 412, 510–514 (2001).
Yang, H. et al. Titanium doped kagome superconductor CsV3−xTixSb5 and two distinct phases. Sci. Bull 67, 2176–2185 (2022).
Lawler, M. J. et al. Intra-unit-cell electronic nematicity of the high-Tc copper-oxide pseudogap states. Nature 466, 347–351 (2010).
Rhodes, L. et al. kz selective scattering within quasiparticle interference measurements of FeSe. Phys. Rev. Lett. 123, 216404 (2019).
Rhodes, L. et al. Nature of quasiparticle interference in three dimensions. Phys. Rev. B 107, 045107 (2023).
Devereaux, T. P. et al. Anisotropic electron–phonon interaction in the cuprates. Phys. Rev. Lett. 93, 117004 (2004).
Valla, T. et al. Anisotropic electron–phonon coupling and dynamical nesting on the graphene sheets in superconducting CaC6 using angle-resolved photoemission spectroscopy. Phys. Rev. Lett. 102, 107007 (2009).
Wang, V., Xu, N., Liu, J.-C., Tang, G. & Geng, W.-T. VASPKIT: a user-friendly interface facilitating high-throughput computing and analysis using VASP code. Comput. Phys. Commun. 267, 108033 (2021).
Mostofi, A. A. et al. An updated version of wannier90: a tool for obtaining maximally-localised Wannier functions. Comput. Phys. Commun. 185, 2309–2310 (2014).
Wu, Q.-S., Zhang, S.-N., Song, H.-F., Troyer, M. & Soluyanov, A. A. WannierTools: an open-source software package for novel topological materials. Comput. Phys. Commun. 224, 405–416 (2018).
Togo, A. & Tanaka, I. First principles phonon calculations in materials science. Scr. Mater. 108, 1–5 (2015).
Acknowledgements
We thank R.M. Fernandes, V. Madhavan, K. Jiang, X. Wu, Z. Du, R. Sharma, J. He and Y. Sun for valuable discussions. We thank Y. Peng for providing XRD data for the band structure calculation. The work at USTC is supported by the National Key R&D Program of the MOST of China (grants no. 2022YFA1602602), the National Natural Science Foundation of China (grants nos. 11888101, 12074364 and 52261135638), the Strategic Priority Research Program of the Chinese Academy of Sciences (grant no. XDB25000000), the Anhui Initiative in Quantum Information Technologies (grant no. AHY160000) and the Innovation Program for Quantum Science and Technology (grant no. 2021ZD0302802). Zhenyu Wang acknowledges the Fundamental Research Funds for the Central Universities (WK3510000012). L.S. acknowledges the National Key R&D Program of China (grant no. 2018YFA0305602) and the National Natural Science Foundation of China (grant no. 12074002). Z.Q. acknowledges the National Natural Science Foundation of China (grant no. 11974327) and the Fundamental Research Funds for the Central Universities (WK3510000010 and WK2030020032).
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Zhenyu Wang and X.C. conceived the experiments and supervised the project. P.W., Y.T., Zhuying Wang, S.Y. and Y.Z. performed STM experiments and data analysis with assistance of W.M., Z. Liang, X.Z. and L.S. H.L., J.Y. and Z.X. synthesized and characterized the samples. Z. Li, W.M., Y.Y. and Z.Q. performed band calculations. Zhenyu Wang, Z.X., T.W. and X.C. interpreted the results and wrote the manuscript. All authors discussed the results and commented on the manuscript.
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Extended data
Extended Data Fig. 1 Transport characterization of the Ti-substituted CsV3Sb5 samples.
a, Temperature-dependent in-plane resistivity of CsV3-xTixSb5 single crystals, with x ≈ 0, 0.03, 0.05, 0.09, 0.12 and 0.18. Inset: temperature-derivative of the in-plane resistivity showing the charge density wave transition. b, Zoomed-in view of the low-temperature resistivity showing the superconducting transition Tc. In this study, Tc is defined as the zero-resistance temperature.
Extended Data Fig. 2 Determination of the local Ti concentration.
a to d, Typical topographic images of CsV3-xTixSb5. The bright protrusions represent Ti atoms that replace V atoms in the underneath kagome layer. e to h, Distributions of Ti atoms in the field of view shown in a to d. The numbers of Ti atoms by counting are 172, 312, 913, and 1410, respectively. Set-point conditions: a: Vs = 1.5 V, It = 6 nA; b: Vs = 1.5 V, It = 4 nA; c: Vs = 1.5 V, It = 2 nA; d: Vs = 1.5 V, It = 5 nA.
Extended Data Fig. 3 Comparison of the measured ki (ω) to the calculated band dispersion using different CDW configurations.
The orange dots denote the measured QPI dispersion for x = 0 and x ≈ 0.05. b–c, Calculated band structure with the pristine crystal structure in a at kz = 0 and kz = π/c. e–f, Calculated band structure with SoD reconstruction in d at kz = 0 and kz = π/c. h–i, Calculated band structure with Tri-Hex reconstruction in g at kz = 0 and kz = π/c. j–l, Calculated band structure with 2 × 2 × 2 CDW reconstruction in g (Tri-Hex with π-shift) at kz = 0 and kz = π/2c (here π/2c is the boundary of the extended cell). Γ’, K’, M’, A’, H’, L’ are the high-symmetry points of the folded BZ due to 2 × 2 × 2 CDW reconstruction which corresponds to Γ, K, M, A, H, L in the unfolded BZ.
Extended Data Fig. 4 Effective real part of self-energy for the \({{{\mathbf{k}}}}_1^\delta \left( \omega \right)\) band along different lattice directions.
Effective real part of quasiparticle self-energy, Σ′(k,ω), extracted from the measured dispersion \({{{\mathbf{k}}}}_1^\delta \left( \omega \right)\) for x = 0 (a) and x ≈ 0.05 (b) samples. Band dispersion obtained by calculations is used as the ‘bare’ band and slightly shifted in energy to match the measured kF. Peaks located at approximately 15 and 30–40 meV are observed along the C2 lattice direction, while there is no obvious feature along the other two lattice directions. Thick diffuse lines in a and b are visual guides. For x = 0 samples, interference signals along the off-C2 direction are weak at |E| > 20 meV.
Extended Data Fig. 5 Measured \({{{\mathbf{k}}}}_1^\delta \left( \omega \right)\) dispersion for x ≈ 0 samples.
Kinks at approximately 15 and 30 meV are observed only along the C2-direction (a); along the remaining two lattice directions, the measured \({{{\mathbf{k}}}}_1^\delta \left( \omega \right)\) roughly follows the calculated bare band without additional features (b). The determination of \({{{\mathbf{k}}}}_1^\delta \left( \omega \right)\) by fitting is shown in Supplementary Note 3. In the x = 0 samples, a small Fermi surface deformation of the δ band is observed, that is, \({{{\mathbf{k}}}}_1^\delta \left( {E_F} \right)\) is different along the C2-direction than along the remaining two lattice directions (dashed line in b), indicating a possible q = 0 Pomeranchuk instability25,26. However, this effect is very weak in the x ≈ 0.05 samples (Fig. 3e).
Extended Data Fig. 6 Linewidth and peak height in the STM momentum distribution curves for x ≈ 0.05.
a, b, Phenomenological full-width-half-maximum (∆k = ∆q/2) of L (q1, eV) extracted by Lorentzian fits along the C2 direction (a) and off-C2 direction (b). The fitting details are shown in SI Note 3. In principle, the peak widths can be related to the quasiparticle lifetime and thus the imaginary part of the self-energy. A remarkable change in the peak width can be found along the C2 direction at −40 meV, which corresponds to the kink position in the dispersion. This is consistent with C2-symmetric band renormalization. c, d, The anisotropy of the FT peak height at q1 along the C2 direction and off-C2 direction, defined as \({\Delta}I\left( {{{{\mathbf{q}}}}_1} \right) = {\textstyle{{I\left( {{{{\mathbf{q}}}}_1^{C2}} \right) - I\left( {{{{\mathbf{q}}}}_1^{other}} \right)} \over {I\left( {{{{\mathbf{q}}}}_1^{C2}} \right) + I\left( {{{{\mathbf{q}}}}_1^{other}} \right)}}}\), for two different samples. The anisotropy of the peak height shows a significant increase at |E| < 40 meV, again consistent with C2-symmetric band renormalization by electron-mode coupling.
Extended Data Fig. 7 Temperature dependence of the 1Q-4a0 charge order.
a, Atomically resolved STM topography of the Sb-terminated surface at 45 K, for x = 0. b, The FT of the topography shown in a. c, d, STM topography obtained at 45 K for x ≈ 0.05 samples and its FT. The dark circles, orange circles and blue circles denote the Bragg peaks, triple-Q 2a0 × 2a0 CDW peaks and 1Q-4a0 charge order peaks, respectively. e, f, Temperature-dependent FT linecuts of STM topographic images along the 1Q-4a0 ordering direction. All the linecuts are normalized with the amplitude of the associated Bragg peaks for comparison. One can find that the onset temperature of the 1Q-4a0 order is suppressed in the x ≈ 0.05 samples.
Extended Data Fig. 8 Calculated phonon density of states.
The phonon density of states shows a series of peaks in similar energy windows where we see kinks in the electron dispersion: some near 15 meV and others between 30 and 40 meV. The amplitudes of these peaks are largely enhanced when entering the CDW phase (calculated for Tri-Hex configuration; see Method).
Extended Data Fig. 9 BQPI maps at 0 T, 0.04 T and 2 T for x ≈ 0.18.
a-d, Measured g(q, eV) at 0.4 K with zero magnetic field. e-h, Measured g(q, eV) at 0.4 K with 0.04 T perpendicular magnetic field. i-l, Measured g(q, eV) at 0.4 K with 2 T perpendicular magnetic field (above HC2). Raw data were symmetrized to increase the signal-to-noise ratio, and the central core is suppressed using a Gaussian. The q-space range for spectral weight analysis is colour-marked in a, e, and i. m, averaged dI/dV spectra at 0 T, 0.04 T and 2 T. n, Difference between the spectral weight \(\bar g\left( {{{{\mathbf{q}}}}_{{{\mathbf{i}}}},eV} \right)\) on the vanadium and Sb bands as a function of energy, \({\Delta}\bar g\left( {eV} \right) = {\textstyle{{\left[ {\bar g\left( {{{{\mathbf{q}}}}_1,\,eV} \right) + \bar g\left( {{{{\mathbf{q}}}}_2,\,eV} \right)} \right]/2 - \bar g\left( {{{{\mathbf{q}}}}_0,\,eV} \right)} \over {\left[ {\overline g \left( {{{{\mathbf{q}}}}_1,\,eV} \right) + \bar g\left( {{{{\mathbf{q}}}}_2,\,eV} \right)} \right]/2 + \overline g \left( {{{{\mathbf{q}}}}_0,\,eV} \right)}}}\), where \(\bar g\left( {{{{\mathbf{q}}}}_1,eV} \right)\) and \(\bar g\left( {{{{\mathbf{q}}}}_2,eV} \right)\) are the averaged spectral weight per pixel on the V bands and \(\bar g\left( {{{{\mathbf{q}}}}_0,eV} \right)\) is that on the Sb band (see Method). The drop to negative values of \({\Delta}\bar g\left( {eV} \right)\) inside the superconducting gap at 0 T and 0.04 T suggests a faster suppression of spectral weight on the V bands in the superconducting state. o, p, FT line-cuts along the pink line in a, showing the evolution of q0, q1 and q3 with energy for B = 0 T and 0.04 T, respectively. r, Same line-cuts as shown in p but vertically shifted to highlight the change of q0, q1 and q3 within the superconducting gap. It is clear that the peak intensities of q1 and q3 (V-bands) drop faster than that of q0 (Sb-band).
Extended Data Fig. 10 BQPI maps at 0 T and 2 T for x = 0.
a–f, Measured g(q, eV) at 0.4 K with zero magnetic field. The spectra weight located at the vector of q2 persists to zero energy inside the superconducting gap, suggesting a gap minimum on the V- \(d_{xy}/d_{x^2 - y^2}\) band near the M point. g–h, Measured g(q, eV) at 0.4 K with perpendicular magnetic field of 2 T (above HC2).
Supplementary information
Supplementary Information
Supplementary Table 1, discussion, Notes 1–8 and Figs. 1–13.
Supplementary Video 1
QPI images for x = 0.
Supplementary Video 2
QPI images for x = 0.05 #1.
Supplementary Video 3
QPI images for x = 0.05 #3.
Supplementary Video 4
QPI images for x = 0.18.
Source data
Source Data Fig. 1
STM topography data.
Source Data Fig. 2
Quasiparticle interference data.
Source Data Fig. 3
Band dispersion data.
Source Data Fig. 4
Temperature-dependent QPI and BQPI data.
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Wu, P., Tu, Y., Wang, Z. et al. Unidirectional electron–phonon coupling in the nematic state of a kagome superconductor. Nat. Phys. 19, 1143–1149 (2023). https://doi.org/10.1038/s41567-023-02031-5
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DOI: https://doi.org/10.1038/s41567-023-02031-5
