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Decoupling of static and dynamic charge correlations revealed by uniaxial strain in a cuprate superconductor
Phys. Rev. B 112, L041124 – Published 28 July, 2025
DOI: https://doi.org/10.1103/n834-dkyh
Abstract
We use uniaxial strain in combination with ultra-high-resolution resonant inelastic x-ray scattering (RIXS) at the oxygen- and copper- edges to study the excitations stemming from the charge ordering wave vector in . By detwinning stripe ordering, we demonstrate that the optical phonon anomalies do not show any stripe anisotropy. The low-energy charge excitations also retain an in-plane fourfold symmetry. As such, we find that both phonon and charge excitations are decoupled entirely from the strength of static charge ordering. The almost isotropic character of charge excitations is indicative of a quantum critical behavior and remains a possible source for the strange metal properties found in the normal state of cuprate superconductors.
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References (57)
- R. Arpaia and G. Ghiringhelli, Charge order at high temperature in cuprate superconductors, J. Phys. Soc. Jpn. 90, 111005 (2021).
- L. Chaix, G. Ghiringhelli, Y. Y. Peng, M. Hashimoto, B. Moritz, K. Kummer, N. B. Brookes, Y. He, S. Chen, S. Ishida, Y. Yoshida, H. Eisaki, M. Salluzzo, L. Braicovich, Z.-X. Shen, T. P. Devereaux, and W.-S. Lee, Dispersive charge density wave excitations in , Nat. Phys. 13, 952 (2017).
- R. Arpaia, S. Caprara, R. Fumagalli, G. De Vecchi, Y. Y. Peng, E. Andersson, D. Betto, G. M. De Luca, N. B. Brookes, F. Lombardi, M. Salluzzo, L. Braicovich, C. Di Castro, M. Grilli, and G. Ghiringhelli, Dynamical charge density fluctuations pervading the phase diagram of a Cu-based high- superconductor, Science 365, 906 (2019).
- H. Miao, J. Lorenzana, G. Seibold, Y. Y. Peng, A. Amorese, F. Yakhou-Harris, K. Kummer, N. B. Brookes, R. M. Konik, V. Thampy, G. D. Gu, G. Ghiringhelli, L. Braicovich, and M. P. M. Dean, High-temperature charge density wave correlations in without spin–charge locking, Proc. Natl. Acad. Sci. USA 114, 12430 (2017).
- H. Miao, R. Fumagalli, M. Rossi, J. Lorenzana, G. Seibold, F. Yakhou-Harris, K. Kummer, N. B. Brookes, G. D. Gu, L. Braicovich, G. Ghiringhelli, and M. P. M. Dean, Formation of incommensurate charge density waves in cuprates, Phys. Rev. X 9, 031042 (2019).
- W. S. Lee, K.-J. Zhou, M. Hepting, J. Li, A. Nag, A. C. Walters, M. Garcia-Fernandez, H. C. Robarts, M. Hashimoto, H. Lu, B. Nosarzewski, D. Song, H. Eisaki, Z. X. Shen, B. Moritz, J. Zaanen, and T. P. Devereaux, Spectroscopic fingerprint of charge order melting driven by quantum fluctuations in a cuprate, Nat. Phys. 17, 53 (2021).
- H. Y. Huang, A. Singh, C. Y. Mou, S. Johnston, A. F. Kemper, J. van den Brink, P. J. Chen, T. K. Lee, J. Okamoto, Y. Y. Chu, J. H. Li, S. Komiya, A. C. Komarek, A. Fujimori, C. T. Chen, and D. J. Huang, Quantum fluctuations of charge order induce phonon softening in a superconducting cuprate, Phys. Rev. X 11, 041038 (2021).
- R. Arpaia, L. Martinelli, M. M. Sala, S. Caprara, A. Nag, N. B. Brookes, P. Camisa, Q. Li, Q. Gao, X. Zhou, M. Garcia-Fernandez, K.-J. Zhou, E. Schierle, T. Bauch, Y. Y. Peng, C. Di Castro, M. Grilli, F. Lombardi, L. Braicovich, and G. Ghiringhelli, Signature of quantum criticality in cuprates by charge density fluctuations, Nat. Commun. 14, 7198 (2023).
- S. Caprara, C. D. Castro, G. Mirarchi, G. Seibold, and M. Grilli, Dissipation-driven strange metal behavior, Commun. Phys. 5, 10 (2022).
- G. Grissonnanche, Y. Fang, A. Legros, S. Verret, F. Laliberté, C. Collignon, J. Zhou, D. Graf, P. A. Goddard, L. Taillefer, and B. J. Ramshaw, Linear-in temperature resistivity from an isotropic Planckian scattering rate, Nature (London) 595, 667 (2021).
- S. Caprara, C. Di Castro, G. Seibold, and M. Grilli, Dynamical charge density waves rule the phase diagram of cuprates, Phys. Rev. B 95, 224511 (2017).
- G. Seibold, R. Arpaia, Y. Y. Peng, R. Fumagalli, L. Braicovich, C. Di Castro, M. Grilli, G. C. Ghiringhelli, and S. Caprara, Strange metal behaviour from charge density fluctuations in cuprates, Commun. Phys. 4, 7 (2021).
- J. Li, A. Nag, J. Pelliciari, H. Robarts, A. Walters, M. Garcia-Fernandez, H. Eisaki, D. Song, H. Ding, S. Johnston, R. Comin, and K.-J. Zhou, Multiorbital charge-density wave excitations and concomitant phonon anomalies in , Proc. Natl. Acad. Sci. USA 117, 16219 (2020).
- J. Chang, C. Niedermayer, R. Gilardi, N. B. Christensen, H. M. Rønnow, D. F. McMorrow, M. Ay, J. Stahn, O. Sobolev, A. Hiess, S. Pailhes, C. Baines, N. Momono, M. Oda, M. Ido, and J. Mesot, Tuning competing orders in cuprate superconductors by the application of an external magnetic field, Phys. Rev. B 78, 104525 (2008).
- C. Lin, M. Ochi, R. Noguchi, K. Kuroda, M. Sakoda, A. Nomura, M. Tsubota, P. Zhang, C. Bareille, K. Kurokawa, Y. Arai, K. Kawaguchi, H. Tanaka, K. Yaji, A. Harasawa, M. Hashimoto, D. Lu, S. Shin, R. Arita, S. Tanda, and T. Kondo, Visualization of the strain-induced topological phase transition in a quasi-one-dimensional superconductor , Nat. Mater. 20, 1093 (2021).
- C. Lin, A. Consiglio, O. K. Forslund, J. Küspert, M. M. Denner, H. Lei, A. Louat, M. D. Watson, T. K. Kim, C. Cacho, D. Carbone, M. Leandersson, C. Polley, T. Balasubramanian, D. D. Sante, R. Thomale, Z. Guguchia, G. Sangiovanni, T. Neupert, and J. Chang, Uniaxial strain tuning of charge modulation and singularity in a kagome superconductor, Nat. Commun. 15, 10466 (2024).
- J. Choi, Q. Wang, S. Jöhr, N. B. Christensen, J. Küspert, D. Bucher, D. Biscette, M. H. Fischer, M. Hücker, T. Kurosawa, N. Momono, M. Oda, O. Ivashko, M. V. Zimmermann, M. Janoschek, and J. Chang, Unveiling unequivocal charge stripe order in a prototypical cuprate superconductor, Phys. Rev. Lett. 128, 207002 (2022).
- T. L. Meyer, L. Jiang, S. Park, T. Egami, and H. N. Lee, Strain-relaxation and critical thickness of epitaxial films, APL Mater. 3, 126102 (2015).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/n834-dkyh for details on experimental configurations, fitting of RIXS spectra, data normalization and background subtraction, which includes Refs. [11, 12, 22, 24, 37, 38, 42, 43, 44, 45, 46, 47, 48, 54, 55, 56]
- T. P. Croft, C. Lester, M. S. Senn, A. Bombardi, and S. M. Hayden, Charge density wave fluctuations in and their competition with superconductivity, Phys. Rev. B 89, 224513 (2014).
- Q. Wang, K. von Arx, D. G. Mazzone, S. Mustafi, M. Horio, J. Küspert, J. Choi, D. Bucher, H. Wo, J. Zhao, W. Zhang, T. C. Asmara, Y. Sassa, M. Månsson, N. B. Christensen, M. Janoschek, T. Kurosawa, N. Momono, M. Oda, M. H. Fischer, T. Schmitt, and J. Chang, Uniaxial pressure induced stripe order rotation in , Nat. Commun. 13, (2022).
- V. Thampy, M. P. M. Dean, N. B. Christensen, L. Steinke, Z. Islam, M. Oda, M. Ido, N. Momono, S. B. Wilkins, and J. P. Hill, Rotated stripe order and its competition with superconductivity in , Phys. Rev. B 90, 100510(R) (2014).
- S. B. Wilkins, M. P. M. Dean, J. Fink, M. Hücker, J. Geck, V. Soltwisch, E. Schierle, E. Weschke, G. Gu, S. Uchida, N. Ichikawa, J. M. Tranquada, and J. P. Hill, Comparison of stripe modulations in and , Phys. Rev. B 84, 195101 (2011).
- N. B. Christensen, J. Chang, J. Larsen, M. Fujita, M. Oda, M. Ido, N. Momono, E. M. Forgan, A. T. Holmes, J. Mesot, M. Huecker, and M. v. Zimmermann, Bulk charge stripe order competing with superconductivity in (x=0.12), arXiv:1404.3192.
- H.-H. Kim, E. Lefrançois, K. Kummer, R. Fumagalli, N. B. Brookes, D. Betto, S. Nakata, M. Tortora, J. Porras, T. Loew, M. E. Barber, L. Braicovich, A. P. Mackenzie, C. W. Hicks, B. Keimer, M. Minola, and M. Le Tacon, Charge density waves in probed by resonant x-ray scattering under uniaxial compression, Phys. Rev. Lett. 126, 037002 (2021).
- H.-H. Kim, S. M. Souliou, M. E. Barber, E. Lefrançois, M. Minola, M. Tortora, R. Heid, N. Nandi, R. A. Borzi, G. Garbarino, A. Bosak, J. Porras, T. Loew, M. König, P. J. W. Moll, A. P. Mackenzie, B. Keimer, C. W. Hicks, and M. Le Tacon, Uniaxial pressure control of competing orders in a high-temperature superconductor, Science 362, 1040 (2018).
- L. Pintschovius and M. Braden, Anomalous dispersion of LO phonons in , Phys. Rev. B 60, R15039 (1999).
- R. J. McQueeney, Y. Petrov, T. Egami, M. Yethiraj, G. Shirane, and Y. Endoh, Anomalous dispersion of LO phonons in at low temperatures, Phys. Rev. Lett. 82, 628 (1999).
- X. J. Zhou, J. Shi, T. Yoshida, T. Cuk, W. L. Yang, V. Brouet, J. Nakamura, N. Mannella, S. Komiya, Y. Ando, F. Zhou, W. X. Ti, J. W. Xiong, Z. X. Zhao, T. Sasagawa, T. Kakeshita, H. Eisaki, S. Uchida, A. Fujimori, Z. Zhang, E. W. Plummer, R. B. Laughlin, Z. Hussain, and Z.-X. Shen, Multiple bosonic mode coupling in the electron self-energy of , Phys. Rev. Lett. 95, 117001 (2005).
- C. Falter, M. Klenner, G. A. Hoffmann, and Q. Chen, Origin of phonon anomalies in , Phys. Rev. B 55, 3308 (1997).
- D. Reznik, L. Pintschovius, M. Ito, S. Iikubo, M. Sato, H. Goka, M. Fujita, K. Yamada, G. D. Gu, and J. M. Tranquada, Electron–phonon coupling reflecting dynamic charge inhomogeneity in copper oxide superconductors, Nature (London) 440, 1170 (2006).
- D. Reznik, Giant electron-phonon anomaly in doped and other cuprates, Adv. Condens. Matter Phys. 2010, 1 (2010).
- S. R. Park, T. Fukuda, A. Hamann, D. Lamago, L. Pintschovius, M. Fujita, K. Yamada, and D. Reznik, Evidence for a charge collective mode associated with superconductivity in copper oxides from neutron and x-ray scattering measurements of , Phys. Rev. B 89, 020506(R) (2014).
- T. P. Devereaux, A. M. Shvaika, K. Wu, K. Wohlfeld, C. J. Jia, Y. Wang, B. Moritz, L. Chaix, W.-S. Lee, Z.-X. Shen, G. Ghiringhelli, and L. Braicovich, Directly characterizing the relative strength and momentum dependence of electron-phonon coupling using resonant inelastic x-ray scattering, Phys. Rev. X 6, 041019 (2016).
- A. Geondzhian and K. Gilmore, Demonstration of resonant inelastic x-ray scattering as a probe of exciton-phonon coupling, Phys. Rev. B 98, 214305 (2018).
- K. Bieniasz, S. Johnston, and M. Berciu, Beyond the single-site approximation modeling of electron-phonon coupling effects on resonant inelastic x-ray scattering spectra, SciPost Phys. 11, 062 (2021).
- L. Braicovich, M. Rossi, R. Fumagalli, Y. Peng, Y. Wang, R. Arpaia, D. Betto, G. M. De Luca, D. Di Castro, K. Kummer, M. Moretti Sala, M. Pagetti, G. Balestrino, N. B. Brookes, M. Salluzzo, S. Johnston, J. van den Brink, and G. Ghiringhelli, Determining the electron-phonon coupling in superconducting cuprates by resonant inelastic x-ray scattering: Methods and results on , Phys. Rev. Res. 2, 023231 (2020).
- K. Bieniasz, S. Johnston, and M. Berciu, Theory of dispersive optical phonons in resonant inelastic x-ray scattering experiments, Phys. Rev. B 105, L180302 (2022).
- F. Giustino, M. L. Cohen, and S. G. Louie, Small phonon contribution to the photoemission kink in the copper oxide superconductors, Nature (London) 452, 975 (2008).
- L. Pintschovius, D. Reznik, W. Reichardt, Y. Endoh, H. Hiraka, J. M. Tranquada, H. Uchiyama, T. Masui, and S. Tajima, Oxygen phonon branches in , Phys. Rev. B 69, 214506 (2004).
- J. Graf, M. d'Astuto, C. Jozwiak, D. R. Garcia, N. L. Saini, M. Krisch, K. Ikeuchi, A. Q. R. Baron, H. Eisaki, and A. Lanzara, Bond stretching phonon softening and kinks in the angle-resolved photoemission spectra of optimally doped superconductors, Phys. Rev. Lett. 100, 227002 (2008).
- E. Kaneshita, M. Ichioka, and K. Machida, Phonon anomalies due to collective stripe modes in high cuprates, Phys. Rev. Lett. 88, 115501 (2002).
- M. d'Astuto, G. Dhalenne, J. Graf, M. Hoesch, P. Giura, M. Krisch, P. Berthet, A. Lanzara, and A. Shukla, Sharp optical-phonon softening near optimal doping in observed via inelastic x-ray scattering, Phys. Rev. B 78, 140511(R) (2008).
- M. Maschek, S. Rosenkranz, R. Heid, A. H. Said, P. Giraldo-Gallo, I. R. Fisher, and F. Weber, Wave-vector-dependent electron-phonon coupling and the charge-density-wave transition in , Phys. Rev. B 91, 235146 (2015).
- S.-K. Chan and V. Heine, Spin density wave and soft phonon mode from nesting Fermi surfaces, J. Phys. F 3, 795 (1973).
- K.-J. Zhou, A. Walters et al., I21: an advanced high-resolution resonant inelastic x-ray scattering beamline at diamond light source, Journal of Synchrotron Radiation 29, 563 (2022).
- Y. Peng, L. Martinelli et al., Doping dependence of the electron-phonon coupling in two families of bilayer superconducting cuprates, Phys. Rev. B 105, 115105 (2022).
- Y. Y. Peng, E. W. Huang et al., Dispersion, damping, and intensity of spin excitations in the monolayer cuprate superconductor family, Phys. Rev. B 98, 144507 (2018).
- B. Yu, W. Tabis, I. Bialo, F. Yakhou, N. B. Brookes, Z. Anderson, Y. Tang, G. Yu, and M. Greven, Unusual dynamic charge correlations in simple-tetragonal , Phys. Rev. X 10, 021059 (2020).
- E. Wahlberg, R. Arpaia, G. Seibold, M. Rossi, R. Fumagalli, E. Trabaldo, N. B. Brookes, L. Braicovich, S. Caprara, U. Gran, G. Ghiringhelli, T. Bauch, and F. Lombardi, Restored strange metal phase through suppression of charge density waves in underdoped , Science 373, 1506 (2021).
- L. Nie, G. Tarjus, and S. A. Kivelson, Quenched disorder and vestigial nematicity in the pseudogap regime of the cuprates, Proc. Natl. Acad. Sci. USA 111, 7980 (2014).
- H. Jang, W.-S. Lee, H. Nojiri, S. Matsuzawa, H. Yasumura, L. Nie, A. V. Maharaj, S. Gerber, Y.-J. Liu, A. Mehta, D. A. Bonn, R. Liang, W. N. Hardy, C. A. Burns, Z. Islam, S. Song, J. Hastings, T. P. Devereaux, Z.-X. Shen, S. A. Kivelson, C.-C. Kao, D. Zhu, and J.-S. Lee, Ideal charge-density-wave order in the high-field state of superconducting YBCO, Proc. Natl. Acad. Sci. USA 113, 14645 (2016).
- S. A. Kivelson, I. P. Bindloss, E. Fradkin, V. Oganesyan, J. M. Tranquada, A. Kapitulnik, and C. Howald, How to detect fluctuating stripes in the high-temperature superconductors, Rev. Mod. Phys. 75, 1201 (2003).
- J. G. Vale, C. D. Dashwood, E. Paris, L. S. I. Veiga, M. Garcia-Fernandez, A. Nag, A. Walters, K.-J. Zhou, I.-M. Pietsch, A. Jesche, P. Gegenwart, R. Coldea, T. Schmitt, and D. F. McMorrow, High-resolution resonant inelastic x-ray scattering study of the electron-phonon coupling in honeycomb , Phys. Rev. B 100, 224303 (2019).
- S. Johnston, C. Monney, V. Bisogni, K.-J. Zhou, R. Kraus, G. Behr, V. N. Strocov, J. Málek, S.-L. Drechsler, J. Geck, T. Schmitt, and J. van den Brink, Electron-lattice interactions strongly renormalize the charge-transfer energy in the spin-chain cuprate , Nat. Commun. 7, 10563 (2016).
- C. Weber, C. Yee, K. Haule, and G. Kotliar, Scaling of the transition temperature of hole-doped cuprate superconductors with the charge-transfer energy, Europhys. Lett. 100, 37001 (2012).
- Decoupled static and dynamical charge correlations in a cuprate superconductor, Zenodo (2025), https://doi.org/10.5281/zenodo.15789939.