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Two-lifetime model for the cuprates revisited

František Herman, Lucia Gelenekyová, Hana Havranová, and Richard Hlubina

  • Department of Experimental Physics, Comenius University, Mlynská Dolina F2, 842 48 Bratislava, Slovakia

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Phys. Rev. B 114, 134512 – Published 16 September, 2026

DOI: https://doi.org/10.1103/zzhc-2n9f

Abstract

Several models of the strange-metal state of the cuprate superconductors postulate the existence of strong inelastic forward scattering of the electrons, but direct evidence of such scattering is missing. Here we show that angle-resolved photoemission spectroscopy (ARPES) provides a unique tool that can address this issue. We propose a two-lifetime phenomenological model of the superconducting state of the cuprates, and we show that it explains several salient low-energy features of the measured ARPES spectra. The model enables discrimination between forward- and large-angle scattering and, in addition, gives access to the magnitude of the gap function away from the Fermi surface.

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References (45)

  1. 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).
  2. C. M. Varma, Colloquium: Linear in temperature resistivity and associated mysteries including high temperature superconductivity, Rev. Mod. Phys. 92, 031001 (2020).
  3. P. W. Anderson, The Theory of High Temperature Superconductivity (Princeton University Press, Princeton, NJ, 1996).
  4. P. A. Lee and N. Nagaosa, Gauge theory of the normal state of high-Tc superconductors, Phys. Rev. B 46, 5621 (1992).
  5. A. A. Abrikosov, Weakly screened Coulomb interaction and properties of HTSC's, Physica C 222, 191 (1994).
  6. M. L. Kulić and R. Zeyher, Influence of strong electron correlations on the electron-phonon coupling in high-Tc oxides, Phys. Rev. B 49, 4395(R) (1994).
  7. M. Grilli and C. Castellani, Electron-phonon interactions in the presence of strong correlations, Phys. Rev. B 50, 16880 (1994).
  8. E. Cappelluti and L. Pietronero, Nonadiabatic superconductivity: The role of van Hove singularities, Phys. Rev. B 53, 932 (1996).
  9. C. M. Varma, Theory of the pseudogap state of the cuprates, Phys. Rev. B 73, 155113 (2006).
  10. X. Wang and E. Berg, Scattering mechanisms and electrical transport near an Ising nematic quantum critical point, Phys. Rev. B 99, 235136 (2019).
  11. P. W. Phillips, L. Yeo, and E. W. Huang, Exact theory for superconductivity in a doped Mott insulator, Nat. Phys. 16, 1175 (2020).
  12. S. Kukreja, D. M. Willerton, and S.-S. Lee, Classification of non-Fermi liquids and universal superconducting fluctuations, arXiv:2601.21047.
  13. A. J. Millis, S. Sachdev, and C. M. Varma, Inelastic scattering and pair breaking in anisotropic and isotropic superconductors, Phys. Rev. B 37, 4975 (1988).
  14. P. W. Anderson, Theory of dirty superconductors, J. Phys. Chem. Solids 11, 26 (1959).
  15. E. Abrahams and C. Varma, What angle-resolved photoemission experiments tell about the microscopic theory for high-temperature superconductors, Proc. Natl. Acad. Sci. USA 97, 5714 (2000).
  16. F. Herman and R. Hlubina, Microscopic interpretation of the Dynes formula for the tunneling density of states, Phys. Rev. B 94, 144508 (2016).
  17. R. C. Dynes, V. Narayanamurti, and J. P. Garno, Direct measurement of quasiparticle-lifetime broadening in a strong-coupled superconductor, Phys. Rev. Lett. 41, 1509 (1978).
  18. F. Herman and R. Hlubina, Consistent two-lifetime model for spectral functions of superconductors, Phys. Rev. B 95, 094514 (2017).
  19. T. J. Reber, N. C. Plumb, Z. Sun, Y. Cao, Q. Wang, K. McElroy, H. Iwasawa, M. Arita, J. S. Wen, Z. J. Xu, G. Gu, Y. Yoshida, H. Eisaki, Y. Aiura, and D. S. Dessau, The origin and non-quasiparticle nature of Fermi arcs in Bi2Sr2CaCu2O8+δ, Nat. Phys. 8, 606 (2012).
  20. G. Levy de Castro, C. Berthod, A. Piriou, E. Giannini, and Ø. Fischer, Preeminent role of the Van Hove singularity in the strong-coupling analysis of scanning tunneling spectroscopy for two-dimensional cuprate superconductors, Phys. Rev. Lett. 101, 267004 (2008).
  21. T. Kondo, W. Malaeb, Y. Ishida, T. Sasagawa, H. Sakamoto, T. Takeuchi, T. Tohyama, and S. Shin, Point nodes persisting far beyond Tc in Bi2212, Nat. Commun. 6, 7699 (2015).
  22. M. R. Norman, M. Randeria, H. Ding, and J. C. Campuzano, Phenomenology of the low-energy spectral function in high-Tc superconductors, Phys. Rev. B 57, R11093(R) (1998).
  23. S.-D. Chen, M. Hashimoto, Y. He, D. Song, J.-F. He, Y.-F. Li, S. Ishida, H. Eisaki, J. Zaanen, T. P. Devereaux, D.-H. Lee, D.-H. Lu, and Z.-X. Shen, Unconventional spectral signature of Tc in a pure d-wave superconductor, Nature (London) 601, 562 (2022).
  24. T. J. Reber, S. Parham, N. C. Plumb, Y. Cao, H. Li, Z. Sun, Q. Wang, H. Iwasawa, M. Arita, J. S. Wen, Z. J. Xu, G. D. Gu, Y. Yoshida, H. Eisaki, G. B. Arnold, and D. S. Dessau, Pairing, pair-breaking, and their roles in setting the Tc of cuprate high temperature superconductors, arXiv:1508.06252.
  25. S. Ye, M. Xu, H. Yan, Z.-X. Li, C. Zou, X. Li, Y. Chen, X. Zhou, D.-H. Lee, and Y. Wang, Emergent normal fluid in the superconducting ground state of overdoped cuprates, Nat. Commun. 15, 4939 (2024).
  26. N. K. Shah, J. Zhao, and U. Chatterjee, Particle-hole symmetry in the pseudogap phase of moderately underdoped cuprate high temperature superconductors evidenced from joint density of states analysis, arXiv:2509.12568.
  27. J. M. Bok, J. J. Bae, H.-Y. Choi, C. M. Varma, W. Zhang, J. He, Y. Zhang, L. Yu, and X. J. Zhou, Quantitative determination of pairing interactions for high-temperature superconductivity in cuprates, Sci. Adv. 2, e1501329 (2016).
  28. H. Li, X. Zhou, S. Parham, T. J. Reber, H. Berger, G. B. Arnold, and D. S. Dessau, Coherent organization of electronic correlations as a mechanism to enhance and stabilize high-TC cuprate superconductivity, Nat. Commun. 9, 26 (2018).
  29. H. Yan, J. M. Bok, J. He, W. Zhang, Q. Gao, X. Luo, Y. Cai, Y. Peng, J. Meng, C. Li, H. Chen, C. Song, C. Yin, T. Miao, Y. Chen, G. Gu, C. Lin, F. Zhang, F. Yang, S. Zhang, et al., Ubiquitous coexisting electron-mode couplings in high-temperature cuprate superconductors, Proc. Natl. Acad. Sci. USA 120, e2219491120 (2023).
  30. T. J. Reber, X. Zhou, N. C. Plumb, S. Parham, J. A. Waugh, Y. Cao, Z. Sun, H. Li, Q. Wang, J. S. Wen, Z. J. Xu, G. Gu, Y. Yoshida, H. Eisaki, G. B. Arnold, and D. S. Dessau, A unified form of low-energy nodal electronic interactions in hole-doped cuprate superconductors, Nat. Commun. 10, 5737 (2019).
  31. A. Škrlec and R. Hlubina, Temperature dependence of the quasiparticle weight in metals with local self-energy, Phys. Rev. B 110, 155136 (2024).
  32. 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).
  33. 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).
  34. M. R. Norman, A. Kanigel, M. Randeria, U. Chatterjee, and J. C. Campuzano, Modeling the Fermi arc in underdoped cuprates, Phys. Rev. B 76, 174501 (2007).
  35. A. V. Chubukov, M. R. Norman, A. J. Millis, and E. Abrahams, Gapless pairing and the Fermi arc in the cuprates, Phys. Rev. B 76, 180501(R) (2007).
  36. R. S. Markiewicz, Bridging k and q space in the cuprates: Comparing angle-resolved photoemission and STM results, Phys. Rev. B 69, 214517 (2004).
  37. E.-A. Kim and M. J. Lawler, Interference of nematic quantum critical quasiparticles: A route to the octet model, Phys. Rev. B 81, 132501 (2010).
  38. L. Zhu, P. J. Hirschfeld, and D. J. Scalapino, Elastic forward scattering in the cuprate superconducting state, Phys. Rev. B 70, 214503 (2004).
  39. H. Hobou, S. Ishida, K. Fujita, M. Ishikado, K. M. Kojima, H. Eisaki, and S. Uchida, Enhancement of the superconducting critical temperature in Bi2Sr2CaCu2O8+δ by controlling disorder outside CuO2 planes, Phys. Rev. B 79, 064507 (2009).
  40. N. R. Lee-Hone, V. Mishra, D. M. Broun, and P. J. Hirschfeld, Optical conductivity of overdoped cuprate superconductors: Application to La2−xSrxCuO4, Phys. Rev. B 98, 054506 (2018).
  41. S. Graser, P. J. Hirschfeld, and D. J. Scalapino, Local quasiparticle lifetimes in a d-wave superconductor, Phys. Rev. B 77, 184504 (2008).
  42. More precisely speaking, the inelastic part of Γs(T) in a singlet superconductor is a measure of the sum of forward and 2kF scattering.
  43. R. J. Elliott, J. A. Krumhansl, and P. L. Leath, The theory and properties of randomly disordered crystals and related physical systems, Rev. Mod. Phys. 46, 465 (1974).
  44. I. M. Vishik, W. S. Lee, F. Schmitt, B. Moritz, T. Sasagawa, S. Uchida, K. Fujita, S. Ishida, C. Zhang, T. P. Devereaux, and Z. X. Shen, Doping-dependent nodal Fermi velocity of the high-temperature superconductor Bi2Sr2CaCu2O8+δ revealed using high-resolution angle-resolved photoemission spectroscopy, Phys. Rev. Lett. 104, 207002 (2010).
  45. K. McElroy, R. W. Simmonds, J. E. Hoffmann, D.-H. Lee, J. Orenstein, H. Eisaki, S. Uchida, and J. C. Davis, Relating atomic-scale electronic phenomena to wave-like quasiparticle states in superconducting Bi2Sr2CaCu2O8+δ, Nature (London) 422, 592 (2003).

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Phys. Rev. B 114, 134512– Published 16 September, 2026
  • Received 10 January 2026
  • Revised 4 August 2026
  • Accepted 1 September 2026
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