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Quasiparticle scattering interference in the renormalized Hubbard model

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Abstract

In this paper, we study the quasiparticle scattering interference phenomenon in the presence of a single impurity within the renormalized Hubbard model. By calculating the energy and momentum dependence of the Fourier-transformed local density of states in the full Brillouin zone, we can qualitatively describe the main features of the quasiparticle scattering interference phenomenon in cuprate superconductors using a single point-like impurity. In particular, we show that with increasing energy, the position of the peak along the nodal ([0, 0] → [π, π]) direction moves steadily to a large momentum region, while the position of the peak along the antinodal ([0, 0] → [π, 0]) direction moves toward the center of the Brillouin zone.

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References

  1. A. V. Balatsky, I. Vekhter, and J.-X. Zhu, Impurity-induced states in conventional and unconventional superconductors, Rev. Mod. Phys. 78(2), 373 (2006)

    Article  ADS  Google Scholar 

  2. O. Fischer, M. Kugler, I. Maggio-Aprile, C. Berthod, and C. Renner, Scanning tunneling spectroscopy of high-temperature superconductors, Rev. Mod. Phys. 79(1), 353 (2007)

    Article  ADS  Google Scholar 

  3. T. Hanaguri, Y. Kohsaka, J. C. Davis, C. Lupien, I. Yamada, M. Azuma, M. Takano, K. Ohishi, M. Ono, and H. Takagi, Quasiparticle interference and superconducting gap in Ca2−x NaxCuO2Cl2, Nature Physics 3(12), 865 (2007)

    Article  ADS  Google Scholar 

  4. 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+δ, Nature Physics 5(10), 718 (2009)

    Article  ADS  Google Scholar 

  5. J. E. Hoffman, K. McElroy, D.-H. Lee, K. M. Lang, H. Eisaki, S. Uchida, and J. C. Davis, Imaging quasiparticle interference in Bi2Sr2CaCu2O8+δ, Science 297(5584), 1148 (2002)

    Article  ADS  Google Scholar 

  6. K. McElroy, R. W. Simmonds, J. E. Hoffman, 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 422(6932), 592 (2003)

    Article  ADS  Google Scholar 

  7. Q.-H. Wang and D.-H. Lee, Quasiparticle scattering interference in high-temperature superconductors, Phys. Rev. B 67(2), 020511 (2003)

    Article  ADS  Google Scholar 

  8. D. Zhang and C. S. Ting, Energy-dependent modulations in the local density of states of the cuprate superconductors, Phys. Rev. B 67(10), 100506 (2003)

    Article  ADS  Google Scholar 

  9. L.-Y. Zhu, W. A. Atkinson, and P. J. Hirschfeld, Power spectrum of many impurities in a d-wave superconductor, Phys. Rev. B 69(6), 060503 (2004)

    Article  ADS  Google Scholar 

  10. T. S. Nunner, W. Chen, B. M. Andersen, A. Melikyan, and P. J. Hirschfeld, Fourier transform spectroscopy of d-wave quasiparticles in the presence of atomic scale pairing disorder, Phys. Rev. B 73(10), 104511 (2006)

    Article  ADS  Google Scholar 

  11. B. Liu, X. Yan, and F. Yuan, Electron correlation and impurity-induced quasiparticle resonance states in cuprate superconductors, Journal of the Physical Society of Japan 82(10), 114713 (2013)

    Article  ADS  Google Scholar 

  12. B. Liu, X. Yan, and F. Yuan, Quasiparticle resonance states induced by a nonmagnetic impurity in Gossamer superconductors, Solid State Communications 177, 123 (2014)

    Article  ADS  Google Scholar 

  13. Z. P. Huang, X. X. Wan, and F. Yuan, Local density of states around two nonmagnetic impurities in cuprate superconductors, Front. Phys. 6(3), 309 (2011)

    Article  Google Scholar 

  14. S. P. Feng, Kinetic energy driven superconductivity in doped cuprates, Phys. Rev. B 68(18), 184501 (2003)

    Article  ADS  Google Scholar 

  15. S. P. Feng, T. X. Ma, and H. M. Guo, Magnetic nature of superconductivity in doped cuprates, Physica C 436(1), 14 (2006)

    Article  ADS  Google Scholar 

  16. Z. Wang, B. Liu, and S. P. Feng, Extinction of quasiparticle scattering interference in cuprate superconductors, Phys. Lett. A 374(30), 3084 (2010)

    Article  ADS  MATH  Google Scholar 

  17. M. A. Kastner, R. J. Birgeneau, G. Shirane, and Y. Endoh, Magnetic, transport, and optical properties of monolayer copper oxides, Rev. Mod. Phys. 70(3), 897 (1998)

    Article  ADS  Google Scholar 

  18. C. C. Tsuei and J. R. Kirtley, Pairing symmetry in cuprate superconductors, Rev. Mod. Phys. 72(4), 969 (2000)

    Article  ADS  Google Scholar 

  19. H. Ding, M. R. Norman, J. C. Campuzano, M. Randeria, A. F. Bellman, T. Yokoya, T. Takahashi, T. Mochiku, and K. Kadowaki, Angle-resolved photoemission spectroscopy study of the superconducting gap anisotropy in Bi2Sr2CaCu2O8+x , Phys. Rev. B 54(14), R9678 (1996)

    Article  ADS  Google Scholar 

  20. J. L. Talion, C. Bernhard, H. Shaked, R. L. Hitterman, and J. D. Jorgensen, Generic superconducting phase behavior in high-T c cuprates: T c variation with hole concentration in YBa2Cu3O7-δ, Phys. Rev. B 51(18), 12911 (1995)

    Article  ADS  Google Scholar 

  21. T. Timusk and B. Statt, The pseudogap in high-temperature superconductors: An experimental survey, Rep. Prog. Phys. 62(1), 61 (1999)

    Article  ADS  Google Scholar 

  22. S. Hüfner, M. A. Hossain, A. Damascelli, and G. A. Sawatzky, Two gaps make a high-temperature superconductor? Rep. Prog. Phys. 71(6), 062501 (2008)

    Article  ADS  Google Scholar 

  23. P. W. Anderson, The resonating valence bond state in La2CuO4 and superconductivity, Science 235(4793), 1196 (1987)

    Article  ADS  Google Scholar 

  24. G. Baskaran, Z. Zou, and P. W. Anderson, The resonating valence bond state and high-T c superconductivity — A mean field theory, Solid State Communications 63(11), 973 (1987)

    Article  ADS  Google Scholar 

  25. F. C. Zhang, C. Gros, T. M. Rice, and H. Shiba, A renormalised Hamiltonian approach to a resonant valence bond wavefunction, Supercond. Sci. Technol. 1(1), 36 (1988)

    Article  ADS  Google Scholar 

  26. P. W. Anderson, P. A. Lee, M. Randeria, T. M. Rice, N. Trivedi, and F. C. Zhang, The physics behind high-temperature superconducting cuprates: The “plain vanilla” version of RVB, J. Phys.: Condens. Matter 16(24), R755 (2004)

    Google Scholar 

  27. F. C. Zhang and T. M. Rice, Effective Hamiltonian for the superconducting Cu oxides, Phys. Rev. B 37(7), 3759 (1988)

    Article  ADS  Google Scholar 

  28. F. C. Zhang, Gossamer superconductor, Mott insulator, and resonating valence bond state in correlated electron systems, Phys. Rev. Lett. 90(20), 207002 (2003)

    Article  ADS  Google Scholar 

  29. J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Theory of superconductivity, Phys. Rev. 108(5), 1175 (1957)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  30. J. R. Schrieffer, Theory of superconductivity, San Francisco: Addison-Wesley, 1964

    MATH  Google Scholar 

  31. P. A. Lee and X.-G. Wen, Unusual superconducting state of underdoped cuprates, Phys. Rev. Lett. 78(21), 4111 (1997)

    Article  ADS  Google Scholar 

  32. Mark S. Hybertsen, E. B. Stechel, W. M. C. Foulkes, and M. Schlüter, Model for low-energy electronic states probed by X-ray absorption in high-T c cuprates, Phys. Rev. B 45(17), 10032 (1992)

    Article  ADS  Google Scholar 

  33. A. Damascelli, Z. Hussain, and Z.-X. Shen, Angle-resolved photoemission studies of the cuprate superconductors, Rev. Mod. Phys. 75(2), 473 (2003)

    Article  ADS  Google Scholar 

  34. Kai-Yu Yang, C. T. Shih, C. P. Chou, S. M. Huang, T. K. Lee, T. Xiang, and F. C. Zhang, Low-energy physical properties of high-T c superconducting Cu oxides: A comparison between the resonating valence bond and experiments, Phys. Rev. B 73(22), 224513 (2006)

    Article  ADS  Google Scholar 

  35. H. Ding, J. R. Engelbrecht, Z. Wang, J. C. Campuzano, S.-C. Wang, H.-B. Yang, R. Rogan, T. Takahashi, K. Kadowaki, and D. G. Hinks, Coherent quasiparticle weight and its connection to high-T c superconductivity from angle-resolved photoemission, Phys. Rev. Lett. 87(22), 227001 (2001)

    Article  ADS  Google Scholar 

  36. T. Yoshida, X. J. Zhou, T. Sasagawa, W. L. Yang, P. V. Bogdanov, A. Lanzara, Z. Hussain, T. Mizokawa, A. Fujimori, H. Eisaki, Z.-X. Shen, T. Kakeshita, and S. Uchida, Metallic behavior of lightly doped La2−x SrxCuO4 with a fermi surface forming an arc, Phys. Rev. Lett. 91(2), 027001 (2003)

    Article  ADS  Google Scholar 

  37. A. C. Durst and P. A. Lee, Impurity-induced quasiparticle transport and universal-limit Wiedemann-Franz violation in d-wave superconductors, Phys. Rev. B 62(2), 1270 (2000)

    Article  ADS  Google Scholar 

  38. U. Chatterjee, M. Shi, A. Kaminski, A. Kanigel, H. M. Fretwell, K. Terashima, T. Takahashi, S. Rosenkranz, Z. Z. Li, H. Raffy, A. Santander-Syro, K. Kadowaki, M. R. Norman, M. Randeria, and J. C. Campuzano, Nondispersive Fermi arcs and the absence of charge ordering in the pseudogap phase of Bi2Sr2CaCu2O8+δ, Phys. Rev. Lett. 96(10), 107006 (2006)

    Article  ADS  Google Scholar 

  39. U. Chatterjee, M. Shi, A. Kaminski, A. Kanigel, H. M. Fretwell, K. Terashima, T. Takahashi, S. Rosenkranz, Z. Z. Li, H. Raffy, A. Santander-Syro, K. Kadowaki, M. Randeria, M. R. Norman, and J. C. Campuzano, Anomalous dispersion in the autocorrelation of angle-resolved photoemission spectra of high-temperature Bi2Sr2CaCu2O8+δ superconductors, Phys. Rev. B 76(1), 012504 (2007)

    Article  ADS  Google Scholar 

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Correspondence to Feng Yuan.

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Wang, SH., Zhao, HS. & Yuan, F. Quasiparticle scattering interference in the renormalized Hubbard model. Front. Phys. 10, 109–115 (2015). https://doi.org/10.1007/s11467-014-0446-9

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