1. AFM correlation and the pairing mechanism in the iron pnictides and the (overdoped) cuprates Fa Wang (Berkeley) Hui Zhai (Berkeley) Ying Ran (Berkeley) A. Vishwanath (Berkeley) Collaborators Fa Wang et al, PRL 102, 047005 (2009) Fa Wang, Hui Zhai & DHL, EPL 85, 37005 (2009) Hui Zhai, Fa Wang & DHL, Phy. Rev. B (in press) Fa WangHui Zhai

2. Heavy fermion compounds, e.g., CeCoIn 5, CeRhIn 5, YbPd 2 Sn, CePd 2 Si 2, CeIn 3 Mathur et al, Nature, 394, 39 (‘98) Systems with superconductivity near antiferromagnetic order Organic Compounds, e.g.,  -(BETS) 2 FeBr 4,  -(BEDT-TTF) 2 Cu[N(CN) 2 ]Br BEDNORZ, MULLER, Z. PHYSIK B-COND MAT 64 189 (86). M.K. WU et al PHYS. REV. LETT. 58 908 (87).

3. The Question Does the AFM correlation have anything to do with the pairing mechanism in these materials? Let’s focus on the iron pnictides and the cuprates.

4. Method: Functional Renormalization Group (FRG) There is a lack of an ideal `ab initio' method for (strongly) correlated systems. FRG: Unbiased, applicable to infinite system, but lacks a small parameter (such as the  in 4-  ) to justify it rigorously. Exact diagonalization, Quantum Monte-Carlo,DMFT, Mean-field, Variational method, LDA, each has its own limitation.

5. Results for the (overdoped) Cuprates Approach from the overdoped side

6. k1k1 k3k3 k2k2 k4k4

8. Pairing mechanism Dual scattering processes ! A B

9. AFM driven correlations Note that SDW correlation grow over a very wide energy scale. It is not due to nesting.

10. FRG results for the iron pnictides Recent FRG results C. Platt, C. Honerkamp, W. Hanke, arXiv: 0903.1963

11. FeAs trilayer

12. k1k1 k3k3 k2k2 k4k4 k1+k2=k3+k4k1+k2=k3+k4 2 x 10 6 scattering vortices have to be re-evalueated at each step of RG

13. Order parameter has opposite sign on electron and hole FS. The gap function has large variations. Large variation of the order parameter around some FS. I. I. Mazin, et al. PRL 101, 057003 (2008) (LDA) K. Kuroki et al PRL 101, 087004 (2008). (LDA) Z.J. Yao et al, New J. Phys. 11, 025009 (2009) (FLEX) K. Seo et al, PRL 101, 206404 (2008). (Exchange model)

14. Gap variation The degree of gap anisotropy depends on microscopic parameters. It originates from the orbital dependence of pairing. It should be considered when fitting NMR and heat transport measurements.

15. Subleading pairing channels

16. SDW and orbital current order

17. Two types of Pomeranchuk instability This is a band version of “orbital ordering”. Expect this type of distortion to couple strongly with AFM. Give rise to Lattice distortion. Brings in magnetic anisotropy in the AFM ordered state.

18. Pairing Mechanism Dual scattering processes ! A B

19. AFM driven correlations SC AFM Current order PI AF correlation grow over a very wide energy range hence it is not due to nesting. However whether the AFM will be surpassed by SC does depend on how well the FS are nested.

20. Gap function Pnictide Ladder RG results

21. Conclusion

22. Thank You !

23. k1k1 k3k3 k2k2 k4k4 k1+k2=k3+k4k1+k2=k3+k4