Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Anisotropic electron damping and energy gap in Bi2Sr2CaCu2O8+δ

Jiemin Li1,*, Yanhong Gu1, Takemi Yamada2, Zebin Wu3, Genda Gu3, Tonica Valla3,4, Ilya Drozdov3, Ivan Božović3, Mark P. M. Dean3 et al.

Takami Tohyama5,†, Jonathan Pelliciari1,‡, and Valentina Bisogni1,§

  • *Contact author: jli1@bnl.gov
  • †Contact author: tohyama@rs.tus.ac.jp
  • ‡Contact author: pelliciari@bnl.gov
  • §Contact author: bisogni@bnl.gov

Phys. Rev. Research 7, 023319 – Published 27 June, 2025

DOI: https://doi.org/10.1103/k32g-pknp

Abstract

The many-body electron-electron interaction in cuprates causes broadening of the electronic bands in k space, leading to a deviation from the standard Fermi liquid. While a k-dependent anisotropic electronic scattering (k-DAES) has been assessed by photoemission, its fingerprint in Q space has been scarcely considered. Here, we explore the Q-dependent electron dynamics in optimally doped Bi2Sr2CaCu2O8+δ through the evolution of low-energy charge excitations as measured by resonant inelastic x-ray scattering (RIXS). In the normal state, the RIXS spectra display a continuum of excitations down to 0 meV, while the superconducting state features a spectral weight suppression below 80 meV without any enhancement at higher energies. To interpret the energy and Q evolution of our data, we introduce a phenomenological expression of the charge susceptibility by including the k-DAES. We show that only the charge susceptibility with k-DAES captures the RIXS data, highlighting the importance of k-DAES when describing the Q dependence of charge excitations from 0 to a few eV scale. Furthermore, we also find that the inclusion of k-DAES is essential when quantitative parameters such as the electronic energy gap are extracted from RIXS data.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (70)

  1. J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Theory of superconductivity, Phys. Rev. 108, 1175 (1957).
  2. J. G. Bednorz and K. A. Müller, Possible high Tc superconductivity in the Ba-La-Cu-O system, Z. Phys. B 64, 189 (1986).
  3. J. Nagamatsu, N. Nakagawa, T. Muranaka, Y. Zenitani, and J. Akimitsu, Superconductivity at 39 K in magnesium diboride, Nature (London) 410, 63 (2001).
  4. B. Keimer, S. A. Kivelson, M. R. Norman, S. Uchida, and J. Zaanen, From quantum matter to high-temperature superconductivity in copper oxides, Nature (London) 518, 179 (2015).
  5. G. A. Thomas, J. Orenstein, D. H. Rapkine, M. Capizzi, A. J. Millis, R. N. Bhatt, L. F. Schneemeyer, and J. V. Waszczak, Ba2YCu3O7−δ: Electrodynamics of crystals with high reflectivity, Phys. Rev. Lett. 61, 1313 (1988).
  6. R. T. Collins, Z. Schlesinger, F. Holtzberg, P. Chaudhari, and C. Feild, Reflectivity and conductivity of YBa2Cu3O7, Phys. Rev. B 39, 6571 (1989).
  7. I. Božović, J. H. Kim, J. S. Harris, and W. Y. Lee, Optical study of plasmons in Tl2Ba2Ca2Cu3O10, Phys. Rev. B 43, 1169 (1991).
  8. S. L. Cooper, A. L. Kotz, M. A. Karlow, M. V. Klein, W. C. Lee, J. Giapintzakis, and D. M. Ginsberg, Development of the optical conductivity with doping in single-domain YBa2Cu3O6+x, Phys. Rev. B 45, 2549 (1992).
  9. E. Abrahams and C. M. Varma, What angle-resolved photoemission experiments tell about the microscopic theory for high-temperature superconductors, Proc. Natl. Acad. Sci. USA 97, 5714 (2000).
  10. D. A. Bonn, P. Dosanjh, R. Liang, and W. N. Hardy, Evidence for rapid suppression of quasiparticle scattering below Tc in YBa2Cu3O7−δ, Phys. Rev. Lett. 68, 2390 (1992).
  11. C. T. Rieck, W. A. Little, J. Ruvalds, and A. Virosztek, Infrared and microwave spectra of an energy gap in high-temperature superconductors, Phys. Rev. B 51, 3772 (1995).
  12. C. M. Varma, P. B. Littlewood, S. Schmitt-Rink, E. Abrahams, and A. E. Ruckenstein, Phenomenology of the normal state of Cu-O high-temperature superconductors, Phys. Rev. Lett. 63, 1996 (1989).
  13. M. Abdel-Jawad, M. P. Kennett, L. Balicas, A. Carrington, A. P. Mackenzie, R. H. McKenzie, and N. E. Hussey, Anisotropic scattering and anomalous normal-state transport in a high-temperature superconductor, Nat. Phys. 2, 821 (2006).
  14. Y. Fang, G. Grissonnanche, A. Legros, S. Verret, F. Laliberté, C. Collignon, A. Ataei, M. Dion, J. Zhou, D. Graf, M. J. Lawler, P. A. Goddard, L. Taillefer, and B. J. Ramshaw, Fermi surface transformation at the pseudogap critical point of a cuprate superconductor, Nat. Phys. 18, 558 (2022).
  15. T. Valla, A. V. Fedorov, P. D. Johnson, B. O. Wells, S. L. Hulbert, Q. Li, G. D. Gu, and N. Koshizuka, Evidence for quantum critical behavior in the optimally doped cuprate Bi2Sr2CaCu2O8+δ, Science 285, 2110 (1999).
  16. T. Valla, A. V. Fedorov, P. D. Johnson, Q. Li, G. D. Gu, and N. Koshizuka, Temperature dependent scattering rates at the fermi surface of optimally doped Bi2Sr2CaCu2O8+δ, Phys. Rev. Lett. 85, 828 (2000).
  17. A. Kaminski, H. M. Fretwell, M. R. Norman, M. Randeria, S. Rosenkranz, U. Chatterjee, J. C. Campuzano, J. Mesot, T. Sato, T. Takahashi, T. Terashima, M. Takano, K. Kadowaki, Z. Z. Li, and H. Raffy, Momentum anisotropy of the scattering rate in cuprate superconductors, Phys. Rev. B 71, 014517 (2005).
  18. J. Chang, M. Mansson, S. Pailhes, T. Claesson, O. J. Lipscombe, S. M. Hayden, L. Patthey, O. Tjernberg, and J. Mesot, Anisotropic breakdown of Fermi liquid quasiparticle excitations in overdoped La2−xSrxCuO4, Nat. Commun. 4, 2559 (2013).
  19. C. M. Varma and E. Abrahams, Effective lorentz force due to small-angle impurity scattering: Magnetotransport in high- Tc Superconductors, Phys. Rev. Lett. 86, 4652 (2001).
  20. M. R. Norman, Anisotropic exchange and superconductivity in UPt3, Phys. Rev. B 41, 170 (1990).
  21. A. J. Millis, Nearly antiferromagnetic Fermi liquids: An analytic eliashberg approach, Phys. Rev. B 45, 13047 (1992).
  22. T. Dahm, P. J. Hirschfeld, D. J. Scalapino, and L. Zhu, Nodal quasiparticle lifetimes in cuprate superconductors, Phys. Rev. B 72, 214512 (2005).
  23. M. Mitrano, A. A. Husain, S. Vig, A. Kogar, M. S. Rak, S. I. Rubeck, J. Schmalian, B. Uchoa, J. Schneeloch, R. Zhong, G. D. Gu, and P. Abbamonte, Anomalous density fluctuations in a strange metal, Proc. Natl. Acad. Sci. USA 115, 5392 (2018).
  24. A. A. Husain, M. Mitrano, M. S. Rak, S. Rubeck, B. Uchoa, K. March, C. Dwyer, J. Schneeloch, R. Zhong, G. D. Gu, and P. Abbamonte, Crossover of charge fluctuations across the strange metal phase diagram, Phys. Rev. X 9, 041062 (2019).
  25. L. J. P. Ament, M. van Veenendaal, T. P. Devereaux, J. P. Hill, and J. van den Brink, Resonant inelastic x-ray scattering studies of elementary excitations, Rev. Mod. Phys. 83, 705 (2011).
  26. M. Mitrano, S. Johnston, Y.-J. Kim, and M. P. M. Dean, Exploring quantum materials with resonant inelastic x-ray scattering, Phys. Rev. X 14, 040501 (2024).
  27. P. Marra, S. Sykora, K. Wohlfeld, and J. van den Brink, Resonant inelastic x-ray scattering as a probe of the phase and excitations of the order parameter of superconductors, Phys. Rev. Lett. 110, 117005 (2013).
  28. H. Suzuki, M. Minola, Y. Lu, Y. Peng, R. Fumagalli, E. Lefrançois, T. Loew, J. Porras, K. Kummer, D. Betto, S. Ishida, H. Eisaki, C. Hu, X. Zhou, M. W. Haverkort, N. B. Brookes, L. Braicovich, G. Ghiringhelli, M. Le Tacon, and B. Keimer, Probing the energy gap of high-temperature cuprate superconductors by resonant inelastic x-ray scattering, npj Quantum Mater. 3, 65 (2018).
  29. G. Merzoni, L. Martinelli, L. Braicovich, N. B. Brookes, F. Lombardi, F. Rosa, R. Arpaia, M. Moretti Sala, and G. Ghiringhelli, Charge response function probed by resonant inelastic x-ray scattering: Signature of electronic gaps of YBa2Cu3O7−δ, Phys. Rev. B 109, 184506 (2024).
  30. C. Jia, K. Wohlfeld, Y. Wang, B. Moritz, and T. P. Devereaux, Using RIXS to uncover elementary charge and spin excitations, Phys. Rev. X 6, 021020 (2016).
  31. M. R. Norman, M. Randeria, H. Ding, and J. C. Campuzano, Phenomenological models for the gap anisotropy of Bi2Sr2CaCu2O8 as measured by angle-resolved photoemission spectroscopy, Phys. Rev. B 52, 615 (1995).
  32. W. S. Lee, I. M. Vishik, K. Tanaka, D. H. Lu, T. Sasagawa, N. Nagaosa, T. P. Devereaux, Z. Hussain, and Z.-X. Shen, Abrupt onset of a second energy gap at the superconducting transition of underdoped Bi2212, Nature (London) 450, 81 (2007).
  33. T. Kondo, R. Khasanov, T. Takeuchi, J. Schmalian, and A. Kaminski, Competition between the pseudogap and superconductivity in the high-Tc copper oxides, Nature (London) 457, 296 (2009).
  34. T. Valla, I. K. Drozdov, and G. D. Gu, Disappearance of superconductivity due to vanishing coupling in the overdoped Bi2Sr2CaCu2O8+δ, Nat. Commun. 11, 569 (2020).
  35. I. M. Vishik, E. A. Nowadnick, W. S. Lee, Z. X. Shen, B. Moritz, T. P. Devereaux, K. Tanaka, T. Sasagawa, and T. Fujii, A momentum-dependent perspective on quasiparticle interference in Bi2Sr2CaCu2O8, Nat. Phys. 5, 718 (2009).
  36. I. M. Vishik, M. Hashimoto, R.-H. He, W.-S. Lee, F. Schmitt, D. Lu, R. G. Moore, C. Zhang, W. Meevasana, T. Sasagawa, S. Uchida, K. Fujita, S. Ishida, M. Ishikado, Y. Yoshida, H. Eisaki, Z. Hussain, T. P. Devereaux, and Z.-X. Shen, Phase competition in trisected superconducting dome, Proc. Natl. Acad. Sci. USA 109, 18332 (2012).
  37. S. Onari, H. Kontani, and M. Sato, Structure of neutron-scattering peaks in both s++-wave and s±-wave states of an iron pnictide superconductor, Phys. Rev. B 81, 060504 (2010).
  38. M. Hashimoto, I. M. Vishik, R.-H. He, T. P. Devereaux, and Z.-X. Shen, Energy gaps in high-transition-temperature cuprate superconductors, Nat. Phys. 10, 483 (2014).
  39. J. Wen, Z. Xu, G. Xu, M. Hücker, J. Tranquada, and G. Gu, Large Bi-2212 single crystal growth by the floating-zone technique, J. Cryst. Growth 310, 1401 (2008).
  40. I. K. Drozdov, I. Pletikosić, C.-K. Kim, K. Fujita, G. D. Gu, J. C. S. Davis, P. D. Johnson, I. Božović, and T. Valla, Phase diagram of Bi2Sr2CaCu2O8+δ revisited, Nat. Commun. 9, 5210 (2018).
  41. J. Dvorak, I. Jarrige, V. Bisogni, S. Coburn, and W. Leonhardt, Towards 10 meV resolution: The design of an ultrahigh resolution soft X-ray RIXS spectrometer, Rev. Sci. Instrum. 87, 115109 (2016).
  42. 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 Bi2Sr2CaCu2O8+δ, Nat. Phys. 13, 952 (2017).
  43. M. Minola, G. Dellea, H. Gretarsson, Y. Y. Peng, Y. Lu, J. Porras, T. Loew, F. Yakhou, N. B. Brookes, Y. B. Huang, J. Pelliciari, T. Schmitt, G. Ghiringhelli, B. Keimer, L. Braicovich, and M. Le Tacon, Collective nature of spin excitations in superconducting cuprates probed by resonant inelastic x-ray scattering, Phys. Rev. Lett. 114, 217003 (2015).
  44. M. P. M. Dean, A. J. A. James, R. S. Springell, X. Liu, C. Monney, K. J. Zhou, R. M. Konik, J. S. Wen, Z. J. Xu, G. D. Gu, V. N. Strocov, T. Schmitt, and J. P. Hill, High-energy magnetic excitations in the cuprate superconductor Bi2Sr2CaCu2O8+δ: Towards a unified description of its electronic and magnetic degrees of freedom, Phys. Rev. Lett. 110, 147001 (2013).
  45. M. P. M. Dean, A. J. A. James, A. C. Walters, V. Bisogni, I. Jarrige, M. Hücker, E. Giannini, M. Fujita, J. Pelliciari, Y. B. Huang, R. M. Konik, T. Schmitt, and J. P. Hill, Itinerant effects and enhanced magnetic interactions in bi-based multilayer cuprates, Phys. Rev. B 90, 220506 (2014).
  46. M. Dean, Insights into the high temperature superconducting cuprates from resonant inelastic x-ray scattering, J. Magn. Magn. Mater. 376, 3 (2015).
  47. 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 Bi2Sr2LaCuO6+δ, Proc. Natl. Acad. Sci. USA 117, 16219 (2020).
  48. 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).
  49. H. C. Robarts, M. Barthélemy, K. Kummer, M. García-Fernández, J. Li, A. Nag, A. C. Walters, K. J. Zhou, and S. M. Hayden, Anisotropic damping and wave vector dependent susceptibility of the spin fluctuations in La2−xSrxCuO4 studied by resonant inelastic x-ray scattering, Phys. Rev. B 100, 214510 (2019).
  50. M. Hepting, L. Chaix, E. W. Huang, R. Fumagalli, Y. Y. Peng, B. Moritz, K. Kummer, N. B. Brookes, W. C. Lee, M. Hashimoto, T. Sarkar, J.-F. He, C. R. Rotundu, Y. S. Lee, R. L. Greene, L. Braicovich, G. Ghiringhelli, Z. X. Shen, T. P. Devereaux, and W. S. Lee, Three-dimensional collective charge excitations in electron-doped copper oxide superconductors, Nature (London) 563, 374 (2018).
  51. A. Nag, M. Zhu, M. Bejas, J. Li, H. C. Robarts, H. Yamase, A. N. Petsch, D. Song, H. Eisaki, A. C. Walters, M. García-Fernández, A. Greco, S. M. Hayden, and K.-J. Zhou, Detection of acoustic plasmons in hole-doped lanthanum and bismuth cuprate superconductors using resonant inelastic x-ray scattering, Phys. Rev. Lett. 125, 257002 (2020).
  52. A. Nag, L. Zinni, J. Choi, J. Li, S. Tu, A. C. Walters, S. Agrestini, S. M. Hayden, M. Bejas, Z. Lin, H. Yamase, K. Jin, M. García-Fernández, J. Fink, A. Greco, and K.-J. Zhou, Impact of electron correlations on two-particle charge response in electron- and hole-doped cuprates, Phys. Rev. Res. 6, 043184 (2024).
  53. K. Scott, E. Kisiel, T. J. Boyle, R. Basak, G. Jargot, S. Das, S. Agrestini, M. Garcia-Fernandez, J. Choi, J. Pelliciari, J. Li, Y.-D. Chuang, R. Zhong, J. A. Schneeloch, G. Gu, F. Légaré, A. F. Kemper, K.-J. Zhou, V. Bisogni, S. Blanco-Canosa et al., Low-energy quasi-circular electron correlations with charge order wavelength in Ba2Sr2CaCu2O8+δ, Sci. Adv. 9, eadg3710 (2023).
  54. A. Greco, H. Yamase, and M. Bejas, Plasmon excitations in layered high-Tc cuprates, Phys. Rev. B 94, 075139 (2016).
  55. A. Greco, H. Yamase, and M. Bejas, Origin of high-energy charge excitations observed by resonant inelastic X-ray scattering in cuprate superconductors, Commun. Phys. 2, 3 (2019).
  56. Y. Zhu, M. Liao, Q. Zhang, H.-Y. Xie, F. Meng, Y. Liu, Z. Bai, S. Ji, J. Zhang, K. Jiang, R. Zhong, J. Schneeloch, G. Gu, L. Gu, X. Ma, D. Zhang, and Q.-K. Xue, Presence of s-wave pairing in josephson junctions made of twisted ultrathin Bi2Sr2CaCu2O8+x Flakes, Phys. Rev. X 11, 031011 (2021).
  57. O. Can, T. Tummuru, R. P. Day, I. Elfimov, A. Damascelli, and M. Franz, High-temperature topological superconductivity in twisted double-layer copper oxides, Nature (London) 17, 519 (2021).
  58. L. Ju, T. Ren, Z. Li, Z. Liu, C. Shi, Y. Liu, S. Hong, J. Wu, H. Tian, Y. Zhou, and Y. Xie, Emergence of high-temperature superconductivity at the interface of two Mott insulators, Phys. Rev. B 105, 024516 (2022).
  59. S. Y. F. Zhao, X. Cui, P. A. Volkov, H. Yoo, S. Lee, J. A. Gardener, A. J. Akey, R. Engelke, Y. Ronen, R. Zhong, G. Gu, S. Plugge, T. Tummuru, M. Kim, M. Franz, J. H. Pixley, N. Poccia, and P. Kim, Time-reversal symmetry breaking superconductivity between twisted cuprate superconductors, Science 382, 1422 (2023).
  60. D. Li, K. Lee, B. Y. Wang, M. Osada, S. Crossley, H. R. Lee, Y. Cui, Y. Hikita, and H. Y. Hwang, Superconductivity in an infinite-layer nickelate, Nature (London) 572, 624 (2019).
  61. H. Lu, M. Rossi, A. Nag, M. Osada, D. F. Li, K. Lee, B. Y. Wang, M. Garcia-Fernandez, S. Agrestini, Z. X. Shen, E. M. Been, B. Moritz, T. P. Devereaux, J. Zaanen, H. Y. Hwang, K.-J. Zhou, and W. S. Lee, Magnetic excitations in infinite-layer nickelates, Science 373, 213 (2021).
  62. M. Hepting, M. P. M. Dean, and W.-S. Lee, Soft x-ray spectroscopy of low-valence nickelates, Front. Phys. 9, 808683 (2021).
  63. S. Fan, H. LaBollita, Q. Gao, N. Khan, Y. Gu, T. Kim, J. Li, V. Bhartiya, Y. Li, W. Sun, J. Yang, S. Yan, A. Barbour, X. Zhou, A. Cano, F. Bernardini, Y. Nie, Z. Zhu, V. Bisogni, C. Mazzoli et al., Capping effects on spin and charge excitations in parent and superconducting Nd1−xSrxNiO2, Phys. Rev. Lett. 133, 206501 (2024).
  64. J. A. Sobota, Y. He, and Z.-X. Shen, Angle-resolved photoemission studies of quantum materials, Rev. Mod. Phys. 93, 025006 (2021).
  65. Z. Schlesinger, R. T. Collins, F. Holtzberg, C. Feild, S. H. Blanton, U. Welp, G. W. Crabtree, Y. Fang, and J. Z. Liu, Superconducting energy gap and normal-state conductivity of a single-domain YBa2Cu3O7 crystal, Phys. Rev. Lett. 65, 801 (1990).
  66. P. V. Bogdanov, A. Lanzara, X. J. Zhou, W. L. Yang, H. Eisaki, Z. Hussain, and Z. X. Shen, Anomalous momentum dependence of the quasiparticle scattering rate in overdoped Bi2Sr2CaCu2O8, Phys. Rev. Lett. 89, 167002 (2002).
  67. T. Yoshida, M. Hashimoto, I. M. Vishik, Z.-X. Shen, and A. Fujimori, Pseudogap, superconducting gap, and fermi arc in high-Tc cuprates revealed by angle-resolved photoemission spectroscopy, J. Phys. Soc. Jpn. 81, 011006 (2012).
  68. X. He, X. Xu, X. Shi, and I. Božović, Optimization of La2−xSrxCuO4 Single crystal film growth via molecular beam epitaxy, Condens. Matter 8, 13 (2023).
  69. C. T. Chen, L. H. Tjeng, J. Kwo, H. L. Kao, P. Rudolf, F. Sette, and R. M. Fleming, Out-of-plane orbital characters of intrinsic and doped holes in La2−xSrxCuO4, Phys. Rev. Lett. 68, 2543 (1992).
  70. Q. Li, H.-Y. Huang, T. Ren, E. Weschke, L. Ju, C. Zou, S. Zhang, Q. Qiu, J. Liu, S. Ding, A. Singh, O. Prokhnenko, D.-J. Huang, I. Esterlis, Y. Wang, Y. Xie, and Y. Peng, Prevailing charge order in overdoped La2−xSrxCuO4 beyond the superconducting dome, Phys. Rev. Lett. 131, 116002 (2023).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation