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

2. 2 Schulthess_Superconductivity_0611 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_0611 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_0611 Discovered by Bednorz and Müller in 1986  Highly anisotropic  Superconducting CuO - planes Liquid He 140 100 60 20 T [K] 192019601980 1940 2000 TIBaCaCuO 1988 HgBaCaCuO 1993 HgTlBaCuO 1995 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 High-temperature superconductors Liquid H 2

5. 5 Schulthess_Superconductivity_0611 HTSC: 10 23 interacting electrons 2D Hubbard model for CuO planes DCA/QMC: Map Hubbard model onto embedded cluster 2D Hubbard model of high-temperature superconductors t t U

6. 6 Schulthess_Superconductivity_0611 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_0611 (TAM et al., PRL ‘05) 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_0611 = = + + Γ pp Γ ph + + Γ Γ Γ Γ Λ irr Pairing interaction Mechanism (Pfitzner and Wölfle, PRB 1989; Esirgen and Bickers, PRB 1998) Fully irreducible S = 0 S = 1 Calulate with DCA/QMC (Maier et al., PRL 2006) + + - - Pairing interaction: A matter of perspective

9. 9 Schulthess_Superconductivity_0611 Maier et al., PRL 2006 Maier et al., PRB 2006 Maier et al., in preparation  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

10. 10 Schulthess_Superconductivity_0611 Summary/Conclusions/Outlook  Superconductivity: A macroscopic quantum effect  2D 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_0611 Contacts Thomas Maier Oak Ridge National Laboratory (865) 576-3597 maierta@ornl.gov 11 Schulthess_Superconductivity_0611 Paul Kent Oak Ridge National Laboratory (865) 574-4845 kentpr@ornl.gov Thomas Schulthess Oak Ridge National Laboratory (865) 574-4344 schulthesstc@ornl.gov

12. 12 Schulthess_Superconductivity_0611 The Team M. Jarrell University of Cincinnati D. Scalapino University of California Paul Kent Thomas Maier Thomas Schulthess Oak Ridge National Lab