Dispersive charge excitations are observed in a stripe-ordered cuprate.
Their velocity is comparable to that of spin excitations, linking charge and spin dynamics.
Phonon modeling separates weak charge signals from overlapping lattice vibrations.
| [1] | Dean M. P. M., Dellea G., Springell R. S., et al. (2013). Persistence of magnetic excitations in La2−xSrxCuO4 from the undoped insulator to the heavily overdoped non-superconducting metal. Nat. Mater. 12:1019−1023. DOI:10.1038/nmat3723 |
| [2] | Scalapino D. J. (2012). A common thread: The pairing interaction for unconventional superconductors. Rev. Mod. Phys. 84:1383−1417. DOI:10.1103/RevModPhys.84.1383 |
| [3] | Monthoux P., Pines D., and Lonzarich G. G. (2007). Superconductivity without phonons. Nature 450:1177−1183. DOI:10.1038/nature06480 |
| [4] | Ghiringhelli G., Le Tacon M., Minola M., et al. (2012). Long-range incommensurate charge fluctuations in (Y,Nd)Ba2Cu3O6+x. Science 337:821−825. DOI:10.1126/science.1223532 |
| [5] | Peng Y. Y., Salluzzo M., Sun X., et al. (2016). Direct observation of charge order in underdoped and optimally doped Bi2(Sr,La)2CuO6+δ by resonant inelastic x-ray scattering. Phys. Rev. B 94:184511. DOI:10.1103/PhysRevB.94.184511 |
| [6] | da Silva Neto E. H., Aynajian P., Frano A., et al. (2014). Ubiquitous interplay between charge ordering and high-temperature superconductivity in cuprates. Science 343:393−396. DOI:10.1126/science.1243479 |
| [7] | Chaix L., Lebert B., Miao H., et al. (2022). Bulk charge density wave and electron-phonon coupling in superconducting copper oxychlorides. Phys. Rev. Research 4:033004. DOI:10.1103/PhysRevResearch.4.033004 |
| [8] | Tabis W., Yu B., Bialo I., et al. (2017). Synchrotron x-ray scattering study of charge-density-wave order in HgBa2CuO4+δ. Phys. Rev. B 96:134510. DOI:10.1103/PhysRevB.96.134510 |
| [9] | Caprara S., Di Castro C., Seibold G., et al. (2017). Dynamical charge density waves rule the phase diagram of cuprates. Phys. Rev. B 95:224511. DOI:10.1103/PhysRevB.95.224511 |
| [10] | Perali A., Castellani C., Di Castro C., et al. (1996). d-wave superconductivity near charge instabilities. Phys. Rev. B 54:16216. DOI:10.1103/PhysRevB.54.16216 |
| [11] | Yue Z.-Y., Xu Z.-T., Yang S., et al. (2024). Pseudogap phase as fluctuating pair density wave. arXiv: 2404.16770. DOI: 10.48550/arXiv.2404.16770 |
| [12] | Yu B., Tabis W., Bialo I., et al. (2020). Unusual dynamic charge correlations in simple-tetragonal HgBa2CuO4+δ. Phys. Rev. X 10:021059. DOI:10.1103/PhysRevX.10.021059 |
| [13] | Kivelson S. A., Fradkin E. and Emery V. J. (1998). Electronic liquid–crystal phases of a doped Mott insulator. Nature 393:550−553. DOI:10.1038/31177 |
| [14] | Chang J., Niedermayer Ch., Gilardi R., et al. (2008). Tuning competing orders in La2−xSrxCuO4 cuprate superconductors by the application of an external magnetic field. Phys. Rev. B 78:104525. DOI:10.1103/PhysRevB.78.104525 |
| [15] | Wang Y. and Chubukov A. V. (2015). Enhancement of superconductivity at the onset of charge-density-wave order in a metal. Phys. Rev. B 92:125108. DOI:10.1103/PhysRevB.92.125108 |
| [16] | Arpaia R., Martinelli L., Sala M. M., et al. (2023). Signature of quantum criticality in cuprates by charge density fluctuations. Nat. Commun. 14:7198. DOI:10.1038/s41467-023-42961-5 |
| [17] | Davis J. C. S. and Lee D.-H. (2013). Concepts relating magnetic interactions, intertwined electronic orders, and strongly correlated superconductivity. Proc. Natl. Acad. Sci. USA 110:17623−17630. DOI:10.1073/pnas.1316512110 |
| [18] | Sachdev S. and La Placa R. (2013). Bond order in two-dimensional metals with antiferromagnetic exchange interactions. Phys. Rev. Lett. 111:027202. DOI:10.1103/PhysRevLett.111.027202 |
| [19] | Zheng B.-X., Chung C.-M., Corboz P., et al. (2017). Stripe order in the underdoped region of the two-dimensional Hubbard model. Science 358:1155−1160. DOI:10.1126/science.aam7127 |
| [20] | Huang E. W., Mendl C. B., Liu S., et al. (2017). Numerical evidence of fluctuating stripes in the normal state of high-Tc cuprate superconductors. Science 358:1161−1164. DOI:10.1126/science.aak9546 |
| [21] | Ament L. J. P., van Veenendaal M., Devereaux T. P., et al. (2011). Resonant inelastic x-ray scattering studies of elementary excitations. Rev. Mod. Phys. 83:705−767. DOI:10.1103/RevModPhys.83.705 |
| [22] | Li J., Nag A., Pelliciari J., et al. (2020). Multiorbital charge-density-wave excitations and concomitant phonon anomalies in Bi2Sr2LaCuO6+δ. Proc. Natl. Acad. Sci. USA 117:16219−16225. DOI:10.1073/pnas.2001755117 |
| [23] | Lin J. Q., Miao H., Mazzone D. G., et al. (2020). Strongly correlated charge density wave in La2−xSrxCuO4 evidenced by doping-dependent phonon anomaly. Phys. Rev. Lett. 124:207005. DOI:10.1103/PhysRevLett.124.207005 |
| [24] | Huang H. Y., Singh A., Mou C. Y., et al. (2021). Quantum fluctuations of charge order induce phonon softening in a superconducting cuprate. Phys. Rev. X 11:041038. DOI:10.1103/PhysRevX.11.041038 |
| [25] | Chaix L., Ghiringhelli G., Peng Y. Y., et al. (2017). Dispersive charge density wave excitations in Bi2Sr2CaCu2O8+δ. Nat. Phys. 13:952−956. DOI:10.1038/nphys4157 |
| [26] | Li Q., Huang H.-Y., Ren T., et al. (2023). Prevailing charge order in overdoped La2−xSrxCuO4 beyond the superconducting dome. Phys. Rev. Lett. 131:116002. DOI:10.1103/PhysRevLett.131.116002 |
| [27] | Peng Y. Y., Husain A. A., Mitrano M., et al. (2020). Enhanced electron-phonon coupling for charge-density-wave formation in La1.8-xEu0.2SrxCuO4+δ. Phys. Rev. Lett. 125:097002. DOI:10.1103/PhysRevLett.125.097002 |
| [28] | Martinelli L., Biało I., Hong X., et al. (2025). Decoupling of static and dynamic charge correlations revealed by uniaxial strain in a cuprate superconductor. Phys. Rev. B 112:L041124. DOI:10.1103/n834-dkyh |
| [29] | Wang Q., Horio M., von Arx K., et al. (2020). High-temperature charge-stripe correlations in La1.675Eu0.2Sr0.125CuO4. Phys. Rev. Lett. 124:187002. DOI:10.1103/PhysRevLett.124.187002 |
| [30] | Zhou K.-J., Walters A., Garcia-Fernandez M., et al. (2022). I21: An advanced high-resolution resonant inelastic X-ray scattering beamline at Diamond Light Source. J. Synchrotron Radiat. 29:563−580. DOI:10.1107/s1600577522000601 |
| [31] | Wang Q., von Arx K., Horio M., et al. (2021). Charge order lock-in by electron-phonon coupling in La1.675Eu0.2Sr0.125CuO4. Sci. Adv. 7:eabg7394. DOI:10.1126/sciadv.abg7394 |
| [32] | Shirane G., Shapiro S. M., and Tranquada J. M. (2002). Neutron scattering with a triple-axis spectrometer: Basic techniques. Cambridge University Press, Cambridge. DOI: 10.1017/CBO9780511534881 |
| [33] | Devereaux T. P., Shvaika A. M., Wu K., et al. (2016). Directly characterizing the relative strength and momentum dependence of electron-phonon coupling using resonant inelastic x-ray scattering. Phys. Rev. X 6:041019. DOI:10.1103/PhysRevX.6.041019 |
| [34] | Chen C. T., Sette F., Ma Y., et al. (1991). Electronic states in La2−xSrxCuO4+δ probed by soft-x-ray absorption. Phys. Rev. Lett. 66:104−107. DOI:10.1103/PhysRevLett.66.104 |
| [35] | Lee S., Huang E. W., Johnson T. A., et al. (2022). Generic character of charge and spin density waves in superconducting cuprates. Proc. Natl. Acad. Sci. USA 119:e2119429119. DOI:10.1073/pnas.2119429119 |
| [36] | Wang Q., von Arx K., Mazzone D. G., et al. (2022). Uniaxial pressure induced stripe order rotation in La1.88Sr0.12CuO4. Nat. Commun. 13:1795. DOI:10.1038/s41467-022-29465-4 |
| [37] | Miao H., Lorenzana J., Seibold G., et al. (2017). High-temperature charge density wave correlations in La1.875Ba0.125CuO4 without spin–charge locking. Proc. Natl. Acad. Sci. USA 114:12430−12435. DOI:10.1073/pnas.1708549114 |
| [38] | Miao H., Fumagalli R., Rossi M., et al. (2019). Formation of incommensurate charge density waves in cuprates. Phys. Rev. X 9:031042. DOI:10.1103/PhysRevX.9.031042 |
| [39] | Choi J., Wang Q., Jöhr S., et al. (2022). Unveiling unequivocal charge stripe order in a prototypical cuprate superconductor. Phys. Rev. Lett. 128:207002. DOI:10.1103/PhysRevLett.128.207002 |
| [40] | Christensen N. B., Chang J., Larsen J., et al. (2014). Bulk charge stripe order competing with superconductivity in La2−xSrxCuO4 (x = 0.12). arXiv: 1404.3192. DOI: 10.48550/arXiv.1404.3192 |
| [41] | Pintschovius L., Pyka N., Reichardt W., et al. (1991). Lattice dynamical studies of HTSC materials. Physica C: Superconductivity 185-189:156−161. DOI:10.1016/0921-4534(91)91965-7 |
| [42] | McQueeney R. J., Petrov Y., Egami T., et al. (1999). Anomalous dispersion of LO phonons in La1.85Sr0.15CuO4 at low temperatures. Phys. Rev. Lett. 82:628. DOI:10.1103/PhysRevLett.82.628 |
| [43] | McQueeney R. J., Sarrao J. L., Pagliuso P. G., et al. (2001). Mixed lattice and electronic states in high-temperature superconductors. Phys. Rev. Lett. 87:077001. DOI:10.1103/PhysRevLett.87.077001 |
| [44] | Park S. R., Fukuda T., Hamann A., et al. (2014). Evidence for a charge collective mode associated with superconductivity in copper oxides from neutron and x-ray scattering measurements of La2−xSrxCuO4. Phys. Rev. B 89:020506. DOI:10.1103/PhysRevB.89.020506 |
| [45] | Fukuda T., Mizuki J., Ikeuchi K., et al. (2005). Doping dependence of softening in the bond-stretching phonon mode of La2−xSrxCuO4 (0 ≤ x ≤ 0.29). Phys. Rev. B 71:060501. DOI:10.1103/PhysRevB.71.060501 |
| [46] | Giustino F., Cohen M. L. and Louie S. G. (2008). Small phonon contribution to the photoemission kink in the copper oxide superconductors. Nature 452:975−978. DOI:10.1038/nature06874 |
| [47] | Zhou X. J., Shi J., Yoshida T., et al. (2005). Multiple bosonic mode coupling in the electron self-energy of (La2−xSrx)CuO4. Phys. Rev. Lett. 95:117001. DOI:10.1103/PhysRevLett.95.117001 |
| [48] | Arpaia R., Caprara S., Fumagalli R., et al. (2019). Dynamical charge density fluctuations pervading the phase diagram of a Cu-based high-Tc superconductor. Science 365:906−910. DOI:10.1126/science.aav1315 |
| [49] | Lee W. S., Zhou K.-J., Hepting M., et al. (2021). Spectroscopic fingerprint of charge order melting driven by quantum fluctuations in a cuprate. Nat. Phys. 17:53−57. DOI:10.1038/s41567-020-0993-7 |
| [50] | Coldea R., Hayden S. M., Aeppli G., et al. (2001). Spin waves and electronic interactions in La2CuO4. Phys. Rev. Lett. 86:5377−5380. DOI:10.1103/PhysRevLett.86.5377 |
| [51] | Kivelson S. A., Bindloss I. P., Fradkin E., et al. (2003). How to detect fluctuating stripes in the high-temperature superconductors. Rev. Mod. Phys. 75:1201. DOI:10.1103/RevModPhys.75.1201 |
| [52] | Li W., Zhang Y., Deng P., et al. (2017). Stripes developed at the strong limit of nematicity in FeSe film. Nat. Phys. 13:957−961. DOI:10.1038/nphys4186 |
| [53] | Chen Z., Li D., Lu Z., et al. (2023). Charge order driven by multiple-Q spin fluctuations in heavily electron-doped iron selenide superconductors. Nat. Commun. 14:2023. DOI:10.1038/s41467-023-37792-3 |
| [54] | Bu K., Zhang W., Fei Y., et al. (2021). Observation of an electronic order along [110] direction in FeSe. Nat. Commun. 12:1385. DOI:10.1038/s41467-021-21318-w |
| [55] | Sun H., Huo M., Hu X., et al. (2023). Signatures of superconductivity near 80 K in a nickelate under high pressure. Nature 621:493−498. DOI:10.1038/s41586-023-06408-7 |
| [56] | Zhang J., Phelan D., Botana A. S., et al. (2020). Intertwined density waves in a metallic nickelate. Nat. Commun. 11:6003. DOI:10.1038/s41467-020-19836-0 |
| Hong X., Yan Y., Martinelli L., et al. (2026). Unveiling the nature of collective charge excitations in a cuprate superconductor. The Innovation Physics 1:100011. https://doi.org/10.59717/j.tip.2026.100011 |
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Crystal structure, phonon modes, XAS, and RIXS intensity map
Spectral fits of the low-energy RIXS excitations
Momentum dependence of the 50- and 70-meV modes
Temperature dependence of charge order and its fluctuations
RIXS intensity and constant-energy cuts at 21 K
Temperature-difference analysis of the inelastic RIXS intensity
Charge-excitation spectral weight and simulation