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Thomas C. Schulthess Computational Materials Sciences Computer Science and Mathematics Division

Fermion Glue in the Hubbard Model: New Insights into the Cuprate Pairing Mechanism with Advanced Computing. Thomas C. Schulthess Computational Materials Sciences Computer Science and Mathematics Division. t. U. t. Outline. Superconductivity. A model for high-temperature superconductors.

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Thomas C. Schulthess Computational Materials Sciences Computer Science and Mathematics Division

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  1. Fermion Glue in the Hubbard Model:New Insights into the Cuprate Pairing Mechanism with Advanced Computing Thomas C. Schulthess Computational Materials Sciences Computer Science and Mathematics Division

  2. t U t Outline Superconductivity A model for high-temperaturesuperconductors Non-super-conductive metal Resistance Superconductor Tc Temperature 0 K Algorithm andleadership computing 50 New scientific insights 40 3/2m 30 20 Vd 10 1/2d 0 -10 irr U = 8t; No = 4;(n) = 0.85 -20 -30 T/t 0.0 0.5 1.0 1.5 2.0 2.5 3.0

  3. LHe Power requirementsfor cooling versus temperaturein Kelvin LH2 LNe LN2 0 20 40 60 80 100 What is superconductivity? • A macroscopic quantum state with • Zero resistance • Perfect diamagnetism • Applications: • MAGLEV, MRI,power transmission, generators, motors • Only disadvantage: • Cooling necessary • Tc ≈ 150 K in HTSC • Ultimate goal: • Tc ≈ room temperature Non-super-conductive metal Resistance Superconductor Tc Temperature 0 K

  4. Discovered byBednorz and Müllerin 1986 High-temperature superconductors 140 HgBaCaCuO 1993 HgTlBaCuO 1995 TIBaCaCuO 1988 High temperaturenon-BCS BiSrCaCuO 1980 100 YBa2Cu3O7 19870 Liquid H2 T [K] 60 Low temperature BCS La2-xBaxCuO4 1986 MgB2 2001 NbC Nb=A1=Ge 20 Pb V3Si Nb3Ge Nb3Su LiquidHe NbN Hg Bednorzand Müller Nb 1940 1920 1960 1980 2000 • Highly anisotropic • SuperconductingCuO planes BCS Theory

  5. t U t 2-D Hubbard model ofhigh-temperature superconductors HTSC: 1023interacting electrons DCA/QMC:Map Hubbard model onto embedded cluster 2-D Hubbard modelfor CuO planes

  6. ➙dger or delay updating➙dgemm Algorithm and leadership computing: Fixed startup cost favors fewer,faster processors ➙ Cray X1E (N = 4480) (4480 x 32) Measurement➙cgemm G Sample QMC time Warm up G G G Warm up Warm up Warm up

  7. - + + - Superconductivity as a consequence of strong electronic correlations T. A. Maier, M. Jarrell, T. C. Schulthess, P. R. C. Kent, J. B. White, Systematic study of D-wave superconductivity in the 2D repulsive Hubbard model, Phys. Rev. Lett. 95, 237001 (2005).

  8. - + + - 50 U = 8t; No = 4; (n) = 0.85 3/2m 40 Vd 1/2d 30 Spin irr 20 Pairing 10 Fully irr. 0 -10 Charge -20 -30 0.0 0.5 1.0 1.5 2.0 2.5 3.0 T/t Magnetic origin of pairing interaction • Attractive pairing interaction between nearest neighbor singlets • Dynamics associated with antiferromagnetic spin fluctuation spectrum • Pairing interaction mediated by antiferromagnetic fluctuations T. A. Maier, M. S. Jarrell, and D. J. Scalapino, Structure of the pairing interaction in the two-dimensional Hubbard Model, Phys. Rev.Lett. 96, 047005 (2006). T. A. Maier, M. Jarrell, and D. J. Scalapino, Pairing interaction in the two-dimensional Hubbard model studied with a dynamic cluster quantum Monte Carlo approximation, Phys. Rev.B,74, 094513 (2006). T. A. Maier, M. Jarrell, and D. J. Scalapino, Spin susceptibility representation of the pairing interaction for the two-dimensional Hubbard model, Phys. Rev. B, 75, 134519 (2007).

  9. Spin susceptibility representationenables neutron scattering validation • Test simple spin fluctuation representationof pairing interaction and calculate Tc in Hubbard model • Future: Demonstrate validity of Hubbard model simulations • Measure spin susceptibility in neutron scattering experiments and calculate Tc Electron filling “Exact” QMC Ū fitted from pairing interaction T. A. Maier, A. Macridin, M. Jarrell and D. J. Scalapino, Systematic analysis of a spin susceptibility representation of the pairing interaction in the 2D Hubbard Model, Phys. Rev. B, in press (2007). Ū fitted from single-particle spectrum

  10. Summary/conclusions/outlook • Superconductivity: A macroscopic quantum effect • 2-D Hubbard model for strongly correlatedhigh-temperature superconducting cuprates • Dynamic cluster quantum Monte Carlo simulationson Cray X1E • Superconductivity as a result of strong correlations • Pairing mediated by antiferromagnetic spin fluctuations • Simple spin susceptibility representationof pairing interaction • Verification by neutron scattering experiments?

  11. Contacts • Thomas Maier • Computational Materials SciencesComputer Science and Mathematics Division • (865) 576-3597 • maierta@ornl.gov • Paul Kent Computational Materials SciencesComputer Science and Mathematics Division (865) 574-4845 • kentpr@ornl.gov • Thomas Schulthess • Computational Materials SciencesComputer Science and Mathematics Division • (865) 574-1942 • schulthesstc@ornl.gov 11 Schulthess_Superconductivity_SC07

  12. The team University of California University of Cincinnati Oak RidgeNational Lab • D. Scalapino • M. Jarrell • Paul Kent • Thomas Maier • Thomas Schulthess

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