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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. Supported by NSF grant DMR-1104386. Superconductivity Timeline Heike Kammerlingh Onnes discovers superconductivity in Hg. Tc=4.2K 1911 What is Superconductivity? Hg Resistivity vanishes at Tc. – Normal conductor: induced current rapidly dissipates as heat. – Superconductor: induced current last for years (decay constant >109 years). 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>Tc H J H T<Tc SC PC Superconductivity Timeline Heike Kammerlingh Onnes discovers superconductivity in Hg. Tc=4.2K 1911 Bardeen, Cooper, and Schrieffer develop BCS theory. 1958 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 , k , c c k U Coulomb repulsion Normal State -k Cooper Pair BCS Superconductors • Metals. • Quest towards higher Tc not very successful. Tc < 10 K for pure elements •Highest Tc = 23.2K in Nb3Ge (1973). Superconductivity Timeline Heike Kammerlingh Onnes discovers superconductivity in Hg. Tc=4.2K 1911 Bardeen, Cooper, and Schrieffer develop BCS theory. Bednorz and Muller discover high Tc Cuprates. 1958 1986 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. Cuprates: Unconventional SC • The SC gap has nodes. • D-wave symmetry. 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! Models • t-J model or Hubbard model with large U (strong Coulomb repulsion). • One orbital:dx2-y2 t – AF for undoped. – D-wave pairing trend. – Correct FS shape. J Superconductivity Timeline Heike Kammerlingh Onnes discovers superconductivity in Hg. Tc=4.2K 1911 Bardeen, Cooper, and Schrieffer develop BCS theory. Bednorz and Muller discover high Tc Cuprates. 1958 1986 Fe based superconductors are discovered in Japan. Tc=56K. 2007 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. 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). 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). 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). Is the Coulomb interaction strong or weak? Weak Coupling? •Itinerant electrons •Nested Fermi surface Strong Coupling? •Localized moments •Mott insulator Pairing Symmetry Experimental results: •Uniform gaps (ARPES) •Nodes (bulk methods) Theory: Spin Fluctuations + Coulomb: ARSH FeSe0.45Te0.55 •S+/-: Mazin et al., Kuroki et al. •S with accidental nodes. B. Zeng et al., Nat.Comm. 1, 112 (2010) ARPES Ba0.6K0.4Fe2As2 Nakayama et al., EPL85, 67002 (2009). No Nodes Nodes or deep minima (also consistent with d-wave B2g). 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) Minimal Model (two orbitals) • 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. Daghofer et al., PRL 101, 23704 (2008); A. M. et al., PRB79, 134502 (2009). Non-interacting. Parameters from Raghu et al. PRB (2008). Coulomb interactions H int J U ni , , ni , , (U ' ) ni , x ni , y 2 i i , 2 J Si , x .Si , y J (d i U ' U 2J i , x , d i , x , d i , y , d i , y , h.c.) i •Largest lattice that can be studied with Lanczos methods has 8 sites. • Incorporating symmetries: more than 5x106 states in the Hilbert space. Numerical results: undoped limit JH/U=0.125 Experimental magnetic structure is reproduced. 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). Mean Field Study of the Magnetic Order 1 d l, , d l ', ', ' (n cos ( q.rl ) m ) l ,l ' , ' , ' 2 R. Yu et al., PRB79, 104510 (2009). Diagonal in orbital space Fitted hoppings J=0 J=U/8 J=U/4 Uc1 2.2 2 2 Uc2 7.4 6.6 6 Uc1Uc2 • Two critical values of U: Uc1 and Uc2. • U<Uc1: paramagnetic metal • Uc1<U<Uc2: magnetic metal (band overlap) • U>Uc2: magnetic insulator. Gap develops with increasing U. MF estimation of parameter values MF on three-orbital model M. Daghofer et al., PRB 81, 014511 (2010). 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). Neutron scattering results (ORNL-UT) provide order parameter for several pnictides. (p,0) magnetic order parameter: comparing with neutrons, allow us to establish limits on Hubbard couplings U. 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. i : (cos k x cosk y )d k, , d k , , v : (cos k x cosk y )d k, ,d k , , viii : (cos k x cosk y ) 1 d k, ,d k , , A. Nicholson et al., PRL106, 217002 (2011). A. Nicholson et al., PRL106, 217002 (2011). Mean Field Gaps S+/- Hole pockets Nodal Electron pockets Hole pockets Electron pockets 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.