1. Presented by 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. 2 Schulthess_Superconductivity_SC07 Superconductivity A model for high-temperature superconductors Algorithm and leadership computing New scientific insights tt U Outline 0.02.53.02.01.51.00.5 50 40 30 20 10 0 -10 -20 -30 T/t U = 8t; N o = 4;(n) = 0.85 VdVd 3/2  m 1/2  d  irr Superconductor Non-super- conductive metal 0 K TcTemperature Resistance

3. 3 Schulthess_Superconductivity_SC07 What is superconductivity?  A macroscopic quantum state with  Zero resistance  Perfect diamagnetism  Applications:  MAGLEV, MRI, power transmission, generators, motors  Only disadvantage:  Cooling necessary  T c ≈ 150 K in HTSC  Ultimate goal:  T c ≈ room temperature Superconductor Non-super- conductive metal 0 K TcTc Temperature Resistance 020406080100 LHe LH 2 LNe LN 2 Power requirements for cooling versus temperature in Kelvin

4. 4 Schulthess_Superconductivity_SC07 Discovered by Bednorz and Müller in 1986  Highly anisotropic  Superconducting CuO planes High-temperature superconductors Liquid He 140 100 60 20 T [K] 192019601980 1940 2000 TIBaCaCuO 1988 HgBaCaCuO 1993 BiSrCaCuO 1980 La 2-x Ba x CuO 4 1986 Nb=A1=Ge Nb 3 Ge MgB 2 2001 Nb 3 Su NbN Nb Hg Pb NbC V 3 Si YBa 2 Cu 3 O 7 19870 High temperature non-BCS Low temperature BCS Bednorz and Müller BCS Theory Liquid H 2 HgTlBaCuO 1995

5. 5 Schulthess_Superconductivity_SC07 HTSC: 10 23 interacting electrons 2-D Hubbard model for CuO planes DCA/QMC: Map Hubbard model onto embedded cluster 2-D Hubbard model of high-temperature superconductors t t U

6. 6 Schulthess_Superconductivity_SC07 G Warm up SampleQMC time ➙ dger or delay updating ➙ dgemm (N = 4480) (4480 x 32) Measurement ➙ cgemm Warm up G G G Algorithm and leadership computing: Fixed startup cost favors fewer, faster processors ➙ Cray X1E

7. 7 Schulthess_Superconductivity_SC07 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). Superconductivity as a consequence of strong electronic correlations NcNcNcNc ZdZdZdZd TcTcTcTc 4A 4A00.056 8A 8A1-0.006 12A 12A20.016 16B 16B20.015 16A 16A30.025 20A40.022 24A40.020 26A40.023 + + - -

8. 8 Schulthess_Superconductivity_SC07 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).  Attractive pairing interaction between nearest neighbor singlets  Dynamics associated with antiferromagnetic spin fluctuation spectrum  Pairing interaction mediated by antiferromagnetic fluctuations Pairing Fully irr. 50 40 30 20 10 0 -10 -20 -30 0.02.53.02.01.51.00.5 T/t U = 8t; N o = 4; (n) = 0.85 Spin Charge VdVd 3/2  m 1/2  d  irr + + - - Magnetic origin of pairing interaction

9. 9 Schulthess_Superconductivity_SC07  Test simple spin fluctuation representation of pairing interaction and calculate T c in Hubbard model  Future: Demonstrate validity of Hubbard model simulations  Measure spin susceptibility in neutron scattering experiments and calculate T c Spin susceptibility representation enables neutron scattering validation 0.950.900.85 T c0 0.0800.0740.067 T c0 (1) 0.100 (25%) 0.087 (18%) 0.074 (10%) T c0 (2) 0.108 (35%) 0.084 (14%) 0.064 (4%) “Exact” QMC Ū fitted from pairing interaction Ū fitted from single-particle spectrum Electron filling 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).

10. 10 Schulthess_Superconductivity_SC07 Summary/conclusions/outlook  Superconductivity: A macroscopic quantum effect  2-D Hubbard model for strongly correlated high-temperature superconducting cuprates  Dynamic cluster quantum Monte Carlo simulations on Cray X1E  Superconductivity as a result of strong correlations  Pairing mediated by antiferromagnetic spin fluctuations  Simple spin susceptibility representation of pairing interaction  Verification by neutron scattering experiments?

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

12. 12 Schulthess_Superconductivity_SC07 The team M. Jarrell University of Cincinnati D. Scalapino University of California Paul Kent Thomas Maier Thomas Schulthess Oak Ridge National Lab