Strong Coupling Perspective on LaO1-xFxFeAs

1. Modeling of LaO1-xFxFeAs from the Strong Coupling Perspective: the Magnetic Order and Pairing Channels. Adriana Moreo Dept. of Physics and ORNL University of Tennessee, Knoxville, TN, USA. Collaborators: M.Daghofer, J. Riera., E. Arrigoni, D. Scalapino and E. Dagotto. Supportedby NSF grants DMR-0706020.

2. 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. F doped LaOFeAs

3. Experimental Properties • Tc up to 28K (above 50K replacing La by other rare earths). Chen et al., cond-mat:0803.0128 • Bad metal or semiconductor in undoped regime. • Anomalous specific heat. Suggest nodes in SC state. • Anomaly in resistivity at 150K. Dong et al., cond-mat: 0803.3426

4. Parent compound • Long range magnetic order. • Small order parameter: suggests small or intermediate U and J. De la Cruz et al., cond-mat: 0804.0795. See also McGuire et al., cond-mat:0804.0796; Dong et al., cond-mat:0803.3426 and others.

5. Doped compound • No magnetic order (neutrons, NMR, Mossbauer). • Nodal Gap (specific heat,NMR) or large ungapped regions (integrated PES). • Two gaps (NMR). • Unconventional mechanism, singlet pairing (mSR, NMR). • Hole doping also occurs. (La1-xSrxOFeAs). La1-xSrxOFeAs Wen et al., cond-mat:0803.3021.

6. Theory • Band Structure: 3d Fe orbitals are important. (LDA) • dxz and dyz most important close to eF. (Korshunov et al., cond-mat:0804.1793). • Metallic state. • Possible itinerant magnetic order. Singh et al., cond-mat: 0803.0429; Xu et al., cond-mat:0803.1282; Giovannetti et al., cond-mat: 0804.0866.

7. Fermi Surface LDA • Two hole pockets at G point. • Two electron pockets at M. • dxz and dyz orbitals (with some dxy hybridization). ARPES Liu et al., cond-mat: 0806.2147 NdFeAsO1-xFx Singh et al., cond-mat: 0803.0429

8. Interactions: strong or weak electronic correlations? • X-ray spectra: weak correlation (Kurmaev et al., cond.-mat.: 0805.0668). • DMFT : strong correlation (Haule et al., cond-mat: 0803.1279). • RPA: U~3, J=0 (Raghu et al., cond.-mat: 0804.1113). • RPA and mean field calculations including Coulomb and Hund interactions are predicting the expected magnetic order and all possible variations of the order parameter.

9. Numerical Simulations (Daghofer et al., cond-mat:0805.0148). • Relevant degrees of freedom need to be identified. • Construct the minimal model. • Exact diagonalization in a small cluster. • Very successful with the cuprates: found magnetic order and correct pairing symmetry.

10. Minimum Model • Consider the Fe-As planes. • Two d orbitals dxz and dyz based on LDA and experimental results. • Consider electrons hopping between Fe ions through a double exchange process Fe-As-Fe. Square Fe lattice. • Interactions: Coulomb and Hund.

11. Hoppings Obtain from Slate-Koster overlap integrals between Fe-d and As-p orbitals and Fe-As-Fe double exchange hopping.

12. Hoppings pds=1 pdp=-0.2 ddp=-pdp ddd=0.1pdp The hoppings are obtained in terms of the lattice parameters and the pd overlap Integrals.

13. Interaction

14. Numerical Results: no doping • U<1 for metal in undoped case. • If J=U/4, U<1 to reproduce experimental order parameter in parent compound. • S(k) peaks at (0,p) and (p,0).

15. Electron Doping Spin singlet J=U/4 Spin triplet

16. Symmetry of the Pairing Operator According to D4h point group See Y. Wan and Q-H Wang, cond-mat:0805.0923. Sixteen possible pairing operators.

17. Gap Symmetry

18. Band Structure gap Y M singlet X G triplet node Fermi Surface

19. Two Gaps • Experimental indications of two gaps. • Experiments indicate “d-wave” gap. Y. Wang et al., cond-mat: 0806.1986; K. Matano et al., cond-mat: 0806.0249; F. Hunte et al., cond-mat:0804.0485.

20. Singlet (from numerical simulations) • No gap on e- pockets. • Nodes on h-pockets. • Two gaps. • “d-wave”

21. Conclusions • U and J have to be small or intermediate. • The above does not mean “weak coupling” since the ground state in the undoped case appears to be a magnetically highly correlated state. • In the region of parameter space explored the favored singlet pairing state has “d-wave” symmetry. • Hole FS develop gaps with nodes. No gaps on electron FS. • The spin singlet pairing operator that we obtained does not disagree with any of the experimental results currently available.

22. U=1., J=0.25, pdp=-0.5 Symmetry breaking for (0,p) U=0.5, J=0.125, pdp=-0.2