1. A New Piece in The High T c Superconductivity Puzzle: Fe based Superconductors. Adriana Moreo Dept. of Physics and ORNL University of Tennessee, Knoxville, TN, USA. Supported by NSF grant DMR-1104386.

2. Superconductivity Timeline 1911 Heike Kammerlingh Onnes discovers superconductivity in Hg. T c =4.2K

3. What is Superconductivity? Resistivity vanishes at Tc. –Normal conductor: induced current rapidly dissipates as heat. –Superconductor: induced current last for years (decay constant >10 9 years). Hg

4. Superconductivity No magnetic field in its interior: Meissner effect. –Normal conductor: perfect conductor with R=0 is penetrated by an external H-field. –Superconductor: spontaneously generates surface currents that opposes the external H-field. T>T c T<T c H H SCPC J

5. Superconductivity Timeline 1911 Heike Kammerlingh Onnes discovers superconductivity in Hg. T c =4.2K 1958 Bardeen, Cooper, and Schrieffer develop BCS theory.

6. What causes SC in Hg? BCS Theory Electrons form pairs. Electron-phonon interaction is the “glue”. Only electrons within a thin shell around the FS form pairs. Pairs are rotationally invariant. k -k Cooper Pair Normal State U Coulomb repulsion

7. BCS Superconductors Metals. Quest towards higher T c not very successful. Highest T c = 23.2K in Nb 3 Ge (1973). T c < 10 K for pure elements

8. Superconductivity Timeline 19581911 Heike Kammerlingh Onnes discovers superconductivity in Hg. T c =4.2K Bardeen, Cooper, and Schrieffer develop BCS theory. 1986 Bednorz and Muller discover high T c Cuprates.

9. High T c Cuprates Discovered in 1986 by Bednordz and Muller. T c ~30K in La 2-x Ba x CuO 4. Ceramics with CuO 2 planes. AF insulators for x=0. T c ~ 90K in YBaCu 3 O 7. Highest T c ~130K for HgBa 2 Ca 2 Cu 3 O 6+d.

10. Cuprates: Unconventional SC The SC gap has nodes. D-wave symmetry.

11. Mechanism: Magnetism friend or foe? Electron-Phonon? –T c is too high. –E-ph too weak to overcome strong Coulomb repulsion. Magnetism? –Does it provide the “glue”? –Or does it need to go away to allow pairing? We still do not know the answer!

12. Models t-J model or Hubbard model with large U (strong Coulomb repulsion). One orbital:d x2-y2 –AF for undoped. –D-wave pairing trend. –Correct FS shape. t J

13. Superconductivity Timeline 19581911 Heike Kammerlingh Onnes discovers superconductivity in Hg. T c =4.2K Bardeen, Cooper, and Schrieffer develop BCS theory. 1986 Bednorz and Muller discover high T c Cuprates. 2007 Fe based superconductors are discovered in Japan. T c =56K.

14. F doped LaOFeAs Quaternary oxypnictides: LnOMPn (Ln: La, Pr; M:Mn, Fe, Co, Ni; Pn: P, As). Fe –As planes. La-O planes. Fe form a square lattice. F replaces O and introduces e- in Fe-As planes.

15. Parent compound Long range magnetic order. Bad metal. Order parameter: suggests small to intermediate U and J H. De la Cruz et al., Nature 453, 899 (2008).

16. Theory Band Structure: 3d Fe orbitals are important. (LDA) d xz and d yz most important close to  F. (Korshunov et al., PRB78, 140509(R) (2008)). Metallic state. Possible itinerant magnetic order. L. Boeri et al., PRL101, 026403 (2008).

17. Fermi Surface Two hole pockets at  point. Two electron pockets at M. d xz and d yz orbitals (with some d xy hybridization). M. Norman, Physics 1, 21(2008).

18. Is the Coulomb interaction strong or weak? Weak Coupling? Itinerant electrons Nested Fermi surface Strong Coupling? Localized moments Mott insulator

19. Pairing Symmetry ARSH FeSe 0.45 Te 0.55 B. Zeng et al., Nat.Comm. 1, 112 (2010) Nakayama et al., EPL85, 67002 (2009). ARPES Ba 0.6 K 0.4 Fe 2 As 2 No Nodes Nodes or deep minima (also consistent with d-wave B 2g ). Experimental results: Uniform gaps (ARPES) Nodes (bulk methods) Theory: Spin Fluctuations + Coulomb: S+/-: Mazin et al., Kuroki et al. S with accidental nodes.

20. Our Approach Construct microscopic models. Study their properties with: –Numerical Techniques: Lanczos. –Mean Field Compare results with experimental data: –Obtain parameter values. –Make predictions. Daghofer et al., PRL101, 237004 (2008)

21. Minimal Model (two orbitals) Consider the Fe-As layers. Keep d xz and d yz based on LDA and experimental results. Consider electrons hopping between Fe ions via As as a bridge. Square Fe lattice. Interactions: Coulomb and Hund (U,U ’,J H ). Only model that can be studied with unbiased numerical techniques. Non-interacting. Parameters from Raghu et al. PRB (2008). Daghofer et al., PRL 101, 23704 (2008); A. M. et al., PRB79, 134502 (2009).

22. Coulomb interactions Largest lattice that can be studied with Lanczos methods has 8 sites. Incorporating symmetries: more than 5x10 6 states in the Hilbert space.

23. Numerical results: undoped limit De la Cruz et al., Nature 453, 899 (2008). See also A. D. Christianson et al., PRL 103, 087002 (2009). J H /U=0.125 U=2.8 |t 1 | A. M. et al., PRB79, 134502 (2009). Experimental magnetic structure is reproduced.

24. Mean Field Study of the Magnetic Order Fitted hoppings J=0J=U/8J=U/4 U c1 2.222 U c2 7.46.66 Two critical values of U: U c1 and U c2. U<U c1 : paramagnetic metal U c1 <U<U c2 : magnetic metal (band overlap) U>U c2 : magnetic insulator. R. Yu et al., PRB79, 104510 (2009). Gap develops with increasing U. U c1 U c2 Diagonal in orbital space

25. MF estimation of parameter values Magnetic Bragg peak intensity for Ba(Fe0.96Co0.04)2As2 at x=0.04. A. D. Christianson et al., PRL 103, 087002 (2009). De la Cruz et al., Nature 453, 899 (2008). M. Daghofer et al., PRB 81, 014511 (2010). MF on three-orbital model ( ,0) magnetic order parameter: c omparing with neutrons, allow us to establish limits on Hubbard couplings U. Neutron scattering results (ORNL-UT) provide order parameter for several pnictides.

26. Dynamic Pairing Correlations Several pairing symmetries have large spectral weight close to the ground state (different from the cuprates where s-wave has weight at high energies). The non-trivial symmetry of the pairing operators arises from the orbital part rather than the spatial part of the operators. Raman measurements may be able to separate the orbital and spatial contributions. Sugai et al. PRB82, 140504(R) (2010) observe B 1g with operator viii in BaFe 1.84 Co 0.16 As 2. A. Nicholson et al., PRL106, 217002 (2011).

27. Mean Field Gaps S+/- Nodal Hole pockets Electron pockets Hole pockets Electron pockets A. Nicholson et al., PRL106, 217002 (2011).

28. Conclusions Numerical Simulations in two orbital model: –Magnetic metallic undoped regime for intermediate U and J values. – A 1g, B 2g, states compete. B 1g state is close. Mean Field calculations: –As a function of U there are three phases: 1) paramagnetic; 2) magnetic metallic; and 3) magnetic insulator. –The ground state in the magnetic metallic regime is magnetically ordered with spin stripes. –The same results are observed in realistic models with additional orbitals. The symmetry of the pairing operator in the pnictides changes with slight variations in the parameters. This may explain the diversity in experimental results. Preliminary results for hole doping indicate a similar behavior.