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Evolution of the electronic excitation spectrum with strongly diminishing hole density in superconducting Bi2Sr2CaCu2O8+δ

Nature Physics volume 4, pages 319–326 (2008)Cite this article

Abstract

Coulomb interactions between the carriers may provide the mechanism for enhanced unconventional superconductivity in the copper oxides. However, they simultaneously cause inelastic quasiparticle scattering that can destroy it. Understanding the evolution of this balance with doping is crucial because it is responsible for the rapidly diminishing critical temperature as the hole density p is reduced towards the Mott insulating state. Here, we use tunnelling spectroscopy to measure the T→0 spectrum of electronic excitations N(E) over a wide range of hole density p in superconducting Bi2Sr2CaCu2O8+δ. We introduce a parameterization for N(E) based on a particle–hole symmetric anisotropic energy gap Δ(k)=Δ1(cos(kx)−cos(ky))/2 plus an inelastic scattering rate that varies linearly with energy Γ2(E)=α E. We demonstrate that this form of N(E) enables successful fitting of differential tunnelling conductance spectra throughout much of the Bi2Sr2CaCu2O8+δ phase diagram. We find that Δ1 values rise with falling p along the familiar trajectory of excitations to the ‘pseudogap’ energy, whereas the energy-dependent inelastic scattering rate Γ2(E)=α E seems to be an intrinsic property of the electronic structure and rises steeply for p<16%. Such diverging inelastic scattering may play a key role in suppression of superconductivity in the copper oxides as the Mott insulating state is approached.

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Figure 1: Theoretical effect of Γ2=α E inelastic scattering on the density of states N(E).
Figure 2: Fits of equation (2) N(E) to the average g(V) spectrum for each gap magnitude.
Figure 3: Correlations between spatial arrangements of Δpp, Δ1, α and Γ2* versus hole density p.
Figure 4: Doping dependence of spatial arrangements of Δ1(r) normalized by mean value of Δ1.
Figure 5: Spatial arrangements of kink energy Δ0(r) that separates homogeneous from heterogeneous electronic structure.
Figure 6: Local and global relationships between α and Δ1 plus ‘phase diagram’ of 〈Δ1〉, 〈Δ0〉 and 〈Γ2*〉.

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Acknowledgements

We acknowledge and thank D. Dessau, E. W. Hudson, P. Johnson, D. H. Lee, P. A. Lee, A. P. Mackenzie, A. Millis, M. Norman, N. P. Ong, M. Randeria, D. J. Scalapino, K. Shen, T. Timusk, Y. Uemura and T. Valla for helpful conversations and communications. This work is supported by NSF through the Cornell Center for Material Research, by the Cornell Theory Center, by Brookhaven National Laboratory under Contract No. DE-AC02-98CH1886 with the US Department of Energy, by US Department of Energy Awards DE-FG02-06ER46306 and DE-FG02-05ER46236, by the US Office of Naval Research and by Grant-in-Aid for Scientific Research from the Ministry of Science and Education (Japan) and the 21st-Century COE Program for JSPS. Fellowship support is acknowledged by K.F. from I2CAM.

Author information

Authors and Affiliations

  1. Department of Physics, LASSP, Cornell University, Ithaca, New York 14850, USA

    J. W. Alldredge, Jinho Lee, M. Wang, K. Fujita, Y. Kohsaka, C. Taylor & J. C. Davis

  2. School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews KY16 9SS, Scotland

    Jinho Lee

  3. Department of Physics, University of Colorado, Boulder, Colorado 8030, USA

    K. McElroy

  4. Magnetic Materials Laboratory, RIKEN, Wako 351-0198, Japan

    Y. Kohsaka

  5. NI-AIST, 1-1-1 Central 2, Umezono, Tsukuba, Ibaraki 305-8568, Japan

    H. Eisaki

  6. Department of Physics, University of Tokyo, Tokyo 113-8656, Japan

    S. Uchida

  7. Department of Physics, University of Florida, Gainesville, Florida 32611, USA

    P. J. Hirschfeld

  8. CMP&MS Department, Brookhaven National Laboratory, Upton, New York 11973, USA

    J. C. Davis

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  1. J. W. Alldredge
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Alldredge, J., Lee, J., McElroy, K. et al. Evolution of the electronic excitation spectrum with strongly diminishing hole density in superconducting Bi2Sr2CaCu2O8+δ. Nature Phys 4, 319–326 (2008). https://doi.org/10.1038/nphys917

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