Explaining the band structure and itinerant magnetism of the new iron- arsenide superconductors

1. Lecture 5, XV Training Course in the Physics of Strongly Correlated Systems, IASS Vietri sul Mare Explaining the band structure and itinerant magnetism of the new iron-arsenide superconductors with Lilia Boeri and Alexander Yaresko

2. Superconductivity in F-doped iron pnictides (d6) was discovered early in 2008. Within a few months, Tc was increased from 26 K in LaOFeAs to 55 K in SmOFeAs. In addition to the LnOFeAs compounds, A½FeAs, and Fe1+xSe superconducting compounds have been found. The superconductivity seems to be unconventional (s+/-, d, s+id) since the calculated electron-phonon interaction is weak (Boeri: λ~0.2) and the parent compound displays a transition to astriped AFM state,with a small moment m ~ 0.3 µB in LnOFeAs and ~ 0.9 µB in Ba1/2FeAs.

3. LaOFeAs Fe 3d6 FeAs LaO+ Y M FeAs-- Γ X

4. M Y xz,yz X X Y xy Γ=Γ X=M d6 Wannier orbitals d0 Published band structures are complicated. Even without magnetism they have 2x5 d bands and 2x3 p bands in the Fe2As2 translational cell. We simplify them by using the space group generated by a primitive translation of the square lattice followed by mirroring in the Fe plane. This reduces the formula unit to FeAs and makes the 2D Brillouin zone identical to the one used for the cuprate superconductors. Below we show the unfolding (red) of the LAPW bands (black) and Fermi surface. We have derived a generally applicable (e.g. for studies of magnetism and superconductivity) and accurate tight-binding (TB) model describing the LDA single-particle wavefunctions of the bands near the Fermi level in terms of the 3 As pand5 Fe dWannier orbitals by means of downfolding plus N-ization (NMTO).

6. + - xy xy xy y x xy xy xy z x -(-xz) xz xz Positions of the hole pockets in the large BZ: At k =(0,0) the Fe xy Blochwave is anti-bonding, i.e. the xyband has its top at Γ. At k = (π, π) the Fe xz Blochwave is anti-bonding, i.e. the xzband has its top at M.

9. The set of 5 Fe d Wannier orbitals

10. The set of 8 Fe d and As p Wannier orbitals

15. +1 Pure bands Hybridizations φ π/4 φ XY XY =x2-y2 XY/x 0 0 xz xz zz = 3z2-1 zz eV zz/x -1 XY/zz XY/xz 0 xz/zz -2 xz/x -3 x x (π,0) (π, π) k

19. +1 Pure bands Hybridizations 0 0 0 φ φ xy -π/4 xy/y xy/yz -1 yz yz -π/2 eV 0 yz/z -2 z xy z/y z yz/y y y -3 xy/z (π,0) (π, π) k

21. h e h 1/5 × h e

22. Non-hybridized xy-z and xz-y like bands near X Hybridized xy-z and xz-y like bands near X This super-ellipsoidal electron pocketpoints towards the doubly degenerate hole pockets at M

23. h e h 1/5 × h e

27. The set of 5 Fe d Wannier orbitals

28. The set of 8 Fe d and As p Wannier orbitals

30. Main effect of tetraheder elongation txy,z = 0.52 eV = 0.30 eV

31. X Z Γ

32. The set of 5 Fe d Wannier orbitals

33. Main effect of tetraheder elongation txy,z = 0.52 eV = 0.30 eV

40. X Z Γ

41. Inter-layer coupling in BaFe2As2 of (M, kz-π/c) z/xy (grey dashed) with (Γ,kz) z/zz

44. As a first application of our pd model we have studiedmagnetism. Striped AFM order corresponds to a SDW with q = (0,π) = Y. Exchange splitting SDW Hamiltonian Iis the Stoner- or Hund's-rule exchange coupling constant for Fe Self-consistency condition Magnetic moment q 3) Couple with Δ… 2) Fold in … 4) Compute m(Δ) 5) Solve m(Δ) = Δ/I 1) Start from PM bands

46. xy/z zz/XY zz/XY yz /y zz/XY xy yz/y xy /z xy xz xz yz xy Δ = 2.2 eV m = 2.4 μB Δ = 0.18 eV m = 0.3 μB minoritymajority polarization

48. Δ = 2.2 eV +1 ak/ak+π=bk/bk+π φ π/4 φ XY a 0 xz zz eV -1 ak/bk+π=bk/ak+π b -2 -3 x (π,0) k (π, π)

50. Δ = 2.2 eV +1 0 0 φ -π/4 -π/4 xy -1 φ yz -π/2 eV -2 z y -3 (π,0) k (π, π)