Experimental test of spin-fluctuation-mediated Cooper pairing models in copper oxide superconductors

The twenty-fifth anniversary of the discovery of high-temperature superconductivity is approaching without a clear and compelling theory of the mechanism underlying this phenomenon. Current research focuses on two fundamental questions: Does a Bardeen-Cooper-Schrieffer pairing scheme based on the retarded interaction between fermionic quasiparticles and low-energy bosons yield an adequate description of the mechanism of high-temperature superconductivity, or are high-energy, instantaneous interactions essential? If the dominant contribution arises from low-energy bosons, what are the relative contributions of lattice vibrations, which are known to mediate superconductivity in ordinary metals and alloys, and spin fluctuations, which are generated by strong Coulomb correlations in high-temperature superconductors?

In this project, we will combine two strategies that have been employed to quantify the strength of spin-fluctuation-mediated pairing interactions. The results will have important implications for our understanding of high temperature superconductivity.

The first approach aims to identify fingerprints of coupling to bosonic modes in the electronic spectral functions extracted from angle-resolved photoemission (ARPES), optical, or tunneling data. ARPES is a particularly powerful method to explore the cuprate high-temperature superconductors, because it yields the spectral function of fermionic quasiparticles as a function of both energy and momentum. Damascelli and his group have reported a comprehensive map of the Fermi surface of overdoped Tl2Ba2CuO6+ δ, which has remained the only cuprate compound where detailed agreement with the results of quantum oscillation measurements and with predictions of density functional theory has been demonstrated [1]. While Tl2Ba2CuO6+ δ has thus served as a key reference compound in the literature on high-temperature superconductors, detailed information about electronic self-energy anomalies due to the interaction with bosonic modes has thus far not been reported.

A second, complementary strategy aims to determine the energy- and momentum-dependent self-energy of the bosonic modes under investigation as potential mediators of the pairing interaction. A particularly powerful method is inelastic neutron scattering (INS), a technique that has been used extensively by Keimer’s group in order to characterize the spin fluctuation spectra of cuprate superconductors. Because of the weak INS cross section, however, this technique requires large single crystals and has thus far been largely limited to the systems YBa2Cu3O6+δ and La2-xSrxCuO4 where sufficiently large specimens can be prepared [2,3]. INS experiments on a mosaic of small optimally doped Tl2Ba2CuO6+ δ crystals have revealed spin fluctuations whose spectral weight is strongly renormalized in the superconducting state [4], in qualitative agreement with prior observations on YBa2Cu3O6+δ and La2-xSrxCuO4. However, these experiments have been limited to a small energy and momentum window, where the spin fluctuations are sufficiently intense.

Following up on recent pioneering experiments on undoped cuprates [5] and theoretical work [6], Keimer’s group has used resonant inelastic x-ray scattering (RIXS) in order to collect a much more comprehensive data set on spin fluctuations in YBa2Cu3O6+δ and Tl2Ba2CuO6+ δ, [7] which covers much of the Brillouin zone and doping levels ranging from undoped, Mott-insulating YBa2Cu3O6 all the way into the highly overdoped regime of Tl2Ba2CuO6+ δ. Surprisingly intense, well-defined spin fluctuations are present over the entire doping range, even in the highly overdoped regime. The combination of RIXS and INS data thus yields essentially complete information about the doping and temperature evolution of the spin fluctuations in two representative families of high-temperature superconductors.

Single crystals are a key ingredient in both of these experimental approaches. The UBC group of Bonn, Liang, and Hardy is well known for their synthesis of the highest-quality YBa2Cu3O6+δ crystals currently available worldwide, and they have recently succeeded in growing Tl2Ba2CuO6+ δ crystals of exceptionally high quality as well [8]. The ARPES and RIXS experiments mentioned above have been performed on Tl2Ba2CuO6+ δ crystals resulting from this synthesis effort.

The new collaboration between the UBC and Max Planck groups will thus allow a joint quantitative analysis of the energy- and momentum-resolved ARPES and INS/RIXS data on identical, high-quality single crystals of both YBa2Cu3O6+δ and Tl2Ba2CuO6+ δ. The theoretical framework for such an analysis has already been introduced by Keimer and collaborators [9], and applied to ARPES and INS data on underdoped YBa2Cu3O6.6. It turned out that both data sets could be fitted in a mean-field model with a single adjustable parameter, the coupling strength between spin fluctuations and fermionic quasiparticles, and that an Eliashberg analysis with this coupling strength yielded a reasonable (albeit too large) value of the superconducting transition temperature. However, the polar surface of YBa2Cu3O6+δ has limited the quality of the surface-sensitive ARPES results. Moreover, the Eliashberg theory is not rigorously justified for underdoped cuprates.

Under the proposed research project, we will therefore take a more comprehensive approach starting from highly overdoped Tl2Ba2CuO6+ δ, where Landau Fermi-liquid theory yields an adequate description of the fermiology, and the Eliashberg theory is expected to be adequate for the superconducting state. Initial RIXS and ARPES data are already available, and the framework for the theoretical analysis is in place. We will then extend this work to the optimally doped regime, which is accessible through both Tl2Ba2CuO6+ δ crystals with lower oxygen content, and through YBa2Cu3O7 crystals. Comparison of the data collected on both materials at the same doping level will reveal any materials-specific aspects generated, for instance, by the different sequences of CuO2 layers in the crystal structure.

We also intend to use this complementary approach to reinvestigate deeply underdoped YBa2Cu3O6.5. Damascelli’s group has recently performed pioneering ARPES experiments on YBa2Cu3O6+δ surfaces with accurately controlled doping levels, using an innovative scheme in which potassium donor atoms were deposited on the surface [10]. Accurate measurements on YBa2Cu3O6.5 are particularly important in view of the recent discovery of quantum oscillations in this compound [11], which suggest the applicability of Landau Fermi-liquid theory to underdoped high-temperature superconductors. Damascelli’s method now opens up the perspective of performing a detailed comparison between ARPES and quantum oscillation measurements on YBa2Cu3O6.5 samples with accurately controlled, homogeneous doping levels and oxygen superstructures, in a manner similar to the work on Tl2Ba2CuO6+ δ.

In summary, we expect that the joint analysis of fermionic and bosonic self-energies in the framework of the proposed research project will yield a comprehensive description of the spin fluctuation mediated pairing mechanism over a wide range of doping levels.


  1. M. Platé et al., Fermi Surface and Quasiparticle Excitations of Overdoped Tl2Ba2CuO6+ δ by ARPES. Phys. Rev. Lett. 95, 077001 (2005).
  2. V. Hinkov et al., Electronic Liquid Crystal State in the High-Temperature Superconductor YBa2Cu3O6.45. Science 319, 597 (2008).
  3. D. Haug et al., Neutron scattering study of the magnetic phase diagram of underdoped YBa2Cu3O6+x. New J. Phys. 12, 105006 (2010) and references therein.
  4. H. He et al., Magnetic Resonant Mode in the Single-Layer High-Temperature Superconductor Tl2Ba2CuO6+ δ. Science 295, 1045 (2002).
  5. L. Braicovich et al., Dispersion of Magnetic Excitations in the Cuprate La2CuO4 and CaCuO2 Compounds Measured Using Resonant x-Ray Scattering. Phys. Rev. Lett. 102, 167401 (2009).
  6. M.W. Haverkort, Theory of Resonant Inelastic X-Ray Scattering by Collective Magnetic Excitations. Phys. Rev. Lett. 105, 167404 (2010).
  7. M. Le Tacon et al., Intense paramagnon excitations in a large family of high-temperature superconductors. Nature Phys. (in press) and unpublished data.
  8. D.C. Peets et al., Encapsulated Single Crystal Growth and Annealing of the High-Temperature Superconductor Tl-2201, J. Cryst. Growth 312, 344 (2010).
  9. T. Dahm et al., Strength of the spin-fluctuation-mediated pairing interaction in a high-temperature superconductor. Nature Phys. 5, 217 (2009).
  10. M.A. Hossain et al., In-situ doping control of the surface of high-Tc cuprates. Nature Phys. 4, 527 (2008);
  11. D. Fournier et al., Loss of nodal quasiparticle integrity in underdoped YBCO. Nature Phys. 6, 905 (2010).
  12. D. LeBoeuf et al. Electron pockets in the Fermi surface of hole-doped high-Tc superconductors. Nature 450, 533 (2007).

Principal investigators

B. Keimer (MPI-FKF) b.keimer@fkf.mpg.de

A. Damascelli (UBC) damascelli@physics.ubc.ca

D. Bonn (UBC) bonn@physics.ubc.ca

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