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

with Lilia Boeri and Alexander Yaresko

Lecture 5, XV Training Course in the Physics of Strongly Correlated Systems, IASS Vietri sul Mare

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 a striped AFM state, with a small moment m ~

0.3 µB in LnOFeAs and ~ 0.9 µB in Ba1/2FeAs.

LaLaOOFeFeAAss

LaLaOO++

FeFeAsAs----

FeFeAAss

Fe 3dFe 3d66

Γ

MY

X

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.

XXYY ΓΓ==ΓΓ

YY

XX=M=M

XX

MM

d0

d6

Wannier orbitals

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 p and 5 Fe d Wannier orbitals by means of downfolding plus N-ization (NMTO).

xz,yz

xy

At k =(0,0) the Fe xy Blochwave is anti-bonding, i.e. the xy band has its top at Γ.

At k = (π, π) the Fe xz Blochwave is anti-bonding, i.e. the xz band has its top at M.

xz

x

z

-(-xz) xz

xy

+

-

x

y

xy xy xy

xy xy

Positions of the hole pockets in the large BZ:

The set of The set of 5 Fe d 5 Fe d Wannier Wannier orbitalsorbitals

The The set of set of 8 8 Fe d Fe d and and As p As p WanniWannier er orbitalorbitalss

XY = x2-y2

zz = 3z2-1

xz

x

(π,0) (π, π)k

0

+1

-1

-2

-3

Pure bands Hybridizations φ

0

0

π/4

XY

zzxz

x

eV

φ

XY/xz

XY/x

XY/zz

zz/x

xz/x

xz/zz

xy

z

yz

y

(π,0) (π, π)k

0

+1

-1

-2

-3

Pure bands Hybridizations

φ

00

0 -π/2

-π/4

xyz

yz

y

eV

φ

xy/yz

xy/y

xy/z

z/y

yz/y

yz/z

1/5 1/5 ××

e

e h

h

h

Non-hybridized Non-hybridized xy-z xy-z and and xz-yxz-y like bands near like bands near XX

Hybridized Hybridized xy-z xy-z and and xz-yxz-y like bands near like bands near XX

This This super-super-ellipsoidal ellipsoidal electron electron pocketpocket points points towards the towards the doubly doubly degenerate degenerate hole pockets hole pockets at at MM

1/5 1/5 ××

e

e h

h

h

The set of The set of 5 Fe d 5 Fe d Wannier Wannier orbitalsorbitals

The The set of set of 8 8 Fe d Fe d and and As p As p WanniWannier er orbitalorbitalss

ttxy,zxy,z = 0.52 = 0.52 eVeV

= 0.30 eV= 0.30 eV

Main effect of tetraheder Main effect of tetraheder elongationelongation

Γ ZX

The set of The set of 5 Fe d 5 Fe d Wannier Wannier orbitalsorbitals

ttxy,zxy,z = 0.52 = 0.52 eVeV

= 0.30 eV= 0.30 eV

Main effect of tetraheder Main effect of tetraheder elongationelongation

Γ ZX

Inter-layer coupling in BaFe2As2

of (M, kz-π/c) z/xy (grey dashed) with (Γ,kz) z/zz

As a first application of our As a first application of our pdpd model we have studied model we have studied

magnetism. Striped AFM order corresponds to a SDW with magnetism. Striped AFM order corresponds to a SDW with q q

= (0,= (0,ππ) = ) = YY..

SDW Hamiltonian

Exchange splitting

Magnetic moment

Self-consistency condition

I is the Stoner- or Hund's-rule exchange coupling constant for Fe

1) Start from PM bands

2) Fold in … 3) Couple with Δ…

4) Compute m(Δ)5) Solve 5) Solve mm((ΔΔ) = ) = ΔΔ/I/I

qq

xy

xy

xzyz

xzxy

ΔΔ = 0.18 = 0.18 eV m = eV m = 0.3 0.3 μμBB

zz/XY zz/XYzz/XY

xy /z

xy/z

yz /y

yz/yminorityminority majority majority polarization

ΔΔ = 2.2 = 2.2 eV m = eV m = 2.4 2.4 μμBB

(π,0) (π, π)k

0

+1

-1

-2

-3

φXY

zzeV

π/4

xz

x

φa

b

ak/ak+π

=bk/bk+π

ak/bk+π

=bk/ak

+π

Δ = 2.2 eV

0

-π/4

yz

y

φ

(π,0) (π, π)k

0

+1

-1

-2

-3

φ

-π/2

xy

z

eV

-π/4

Δ = 2.2 eV

h

e

x=e/Fe y=h/Fe

φ(t)=q·t

zz/XY

xz

x y

xy

xz

yz

xy/zx

z

XY/zz

XY/zz

XY

XY/zz

XY/zz

xy/z

XY/zzxy/z

XY/zz

XY/zz

zz/XY

xz

yzxy

XY/zz

xz

xz

x y

Δ = 1.1 eV

Para- and stripe antiferromagnetic hole bands

Double-counting corrected hole bands

ek(Δ) = εk(Δ) ++ ¼ pk(Δ)Δ

magnetic magnetic energy gainenergy gain

DELETE DASHED FERMI LEVEL

k-resolved magnetic energies for Δ=2.3 eV

LaOFeAs

Elongated minus Exp structureExp structure txy/z=0.52 eV Elongated structure: txy/z=0.30 eV

Exp structure: txy/z=0.52 eV Elongated structure: txy/z=0.30 eV