A New Piece in The High T c Superconductivity Puzzle: Fe based Superconductors.

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

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

3. What is Superconductivity? Resistivity vanishes at Tc. • Normal conductor: induced current rapidly dissipates as heat. • Superconductor: induced current last for years (decay constant >109 years). Hg

4. T>Tc H H J T<Tc SC PC 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.

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

6. k -k 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. U Coulomb repulsion Normal State Cooper Pair

7. BCS Superconductors • Metals. • Quest towards higher Tc not very successful. Tc < 10 K for pure elements • Highest Tc = 23.2K in Nb3Ge (1973).

8. Heike Kammerlingh Onnes discovers superconductivity in Hg. Tc=4.2K Bednorz and Muller discover high Tc Cuprates. 1986 Bardeen, Cooper, and Schrieffer develop BCS theory. Superconductivity Timeline 1911 1958

9. High Tc Cuprates • Discovered in 1986 by Bednordz and Muller. • Tc~30K in La2-xBaxCuO4. • Ceramics with CuO2 planes. • AF insulators for x=0. • Tc~ 90K in YBaCu3O7. • Highest Tc~130K for HgBa2Ca2Cu3O6+d.

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

11. Mechanism: Magnetism friend or foe? • Electron-Phonon? • Tc 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:dx2-y2 • AF for undoped. • D-wave pairing trend. • Correct FS shape. t J

13. Fe based superconductors are discovered in Japan. Tc=56K. Heike Kammerlingh Onnes discovers superconductivity in Hg. Tc=4.2K Bednorz and Muller discover high Tc Cuprates. 2007 1986 Bardeen, Cooper, and Schrieffer develop BCS theory. Superconductivity Timeline 1911 1958

14. 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. F doped LaOFeAs

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

16. Theory • Band Structure: 3d Fe orbitals are important. (LDA) • dxz and dyz most important close to eF. (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 G point. • Two electron pockets at M. • dxz and dyz orbitals (with some dxy 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 • Experimental results: • Uniform gaps (ARPES) • Nodes (bulk methods) • Theory: • Spin Fluctuations + Coulomb: • S+/-: Mazin et al., Kuroki et al. • S with accidental nodes. ARSH FeSe0.45Te0.55 B. Zeng et al., Nat.Comm. 1, 112 (2010) Nodes or deep minima (also consistent with d-wave B2g). ARPES Ba0.6K0.4Fe2As2 Nakayama et al., EPL85, 67002 (2009). No 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) Daghofer et al., PRL 101, 23704 (2008); A. M. et al., PRB79, 134502 (2009). • Consider the Fe-As layers. • Keep dxz and dyz 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’,JH). • Only model that can be studied with unbiased numerical techniques. Non-interacting. Parameters from Raghu et al. PRB (2008).

22. Coulomb interactions • Largest lattice that can be studied with Lanczos methods has 8 sites. • Incorporating symmetries: more than 5x106 states in the Hilbert space.

23. Experimental magnetic structure is reproduced. Numerical results: undoped limit JH/U=0.125 U=2.8 |t1| De la Cruz et al., Nature 453, 899 (2008). See also A. D. Christianson et al., PRL 103, 087002 (2009). A. M. et al., PRB79, 134502 (2009).

24. Mean Field Study of the Magnetic Order R. Yu et al., PRB79, 104510 (2009). • Two critical values of U: Uc1 and Uc2. • U<Uc1: paramagnetic metal • Uc1<U<Uc2: magnetic metal (band overlap) • U>Uc2: magnetic insulator. Diagonal in orbital space Gap develops with increasing U. Uc1Uc2

25. MF on three-orbital model M. Daghofer et al., PRB 81, 014511 (2010). (p,0) magnetic order parameter: comparing with neutrons, allow us to establish limits on Hubbard couplings U. MF estimation of parameter values De la Cruz et al., Nature 453, 899 (2008). Magnetic Bragg peak intensity for Ba(Fe0.96Co0.04)2As2 at x=0.04. A. D. Christianson et al., PRL 103, 087002 (2009). 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 B1g with operator viii in BaFe1.84Co0.16As2. A. Nicholson et al., PRL106, 217002 (2011).

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

28. Conclusions • Numerical Simulations in two orbital model: • Magnetic metallic undoped regime for intermediate U and J values. • A1g, B2g, states compete. B1g 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.