xy

winkwellmadeΠολεοδομικά Έργα

15 Νοε 2013 (πριν από 3 χρόνια και 11 μήνες)

80 εμφανίσεις

Explaining the

band 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

(d
6
) was discovered early in
2008. Within a few months,
T
c

was increased from 26 K in LaOFeAs to
55 K in SmOFeAs. In addition to the LnOFeAs compounds, A
½
FeAs,
and Fe
1+x
Se 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
µ
B

in LnOFeAs and ~ 0.9
µ
B

in Ba
1/2
FeAs.

La
O
Fe
As

La
O
+

Fe
As
--

Fe
As

Fe 3d
6

Γ

M

Y

X

Published

band

structures

are

complicated
.

Even

without

magnetism

they

have

2
x
5

d

bands

and

2
x
3

p

bands

in

the

Fe
2
As
2

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

2
D

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
.

X

Y

Γ
=
Γ

Y

X
=M

X

M

d
0

d
6

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 5
Fe d Wannier
orbitals


The set
of 8
Fe d
and
As p
Wannier
orbitals


-3
-2
-1
0
1
1
2
3
k
-3
-2
-1
0
1
1
2
3
k
-2
-1
0
1
2
1
2
3
k
-3
-2
-1
0
1
1
2
3
k
XY =

x
2
-
y
2

zz = 3z
2
-
1

xz

x

(
π
,0)

(
π
,
π
)

k

0

+1

-
1

-
2

-
3

Pure bands

Hybridizations

φ

0

0

π
/4

XY

zz

xz

x

eV

φ

XY
/
xz

XY
/
x

XY
/
zz

zz
/
x

xz
/
x

xz
/
zz

-3
-2
-1
0
1
1
2
3
k
-2
-1
0
1
2
1
2
3
k
xy

z

yz

y

-3
-2
-1
0
1
0
1
2
3
k
-3
-2
-1
0
1
0
1
2
3
k
(
π
,0)

(
π
,
π
)

k

0

+1

-
1

-
2

-
3

Pure bands

Hybridizations

φ

0

0

0

-
π
/2

-
π
/4

xy

z

yz

y

eV

φ

xy
/
yz

xy
/
y

xy
/
z

z
/
y

yz
/
y

yz
/
z

1/5
×

e

e

h

h

h


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 pocket

points towards
the doubly
degenerate hole
pockets at
M


1/5
×

e

e

h

h

h

The set of 5
Fe d Wannier
orbitals


The set
of 8
Fe d
and
As p
Wannier
orbitals


t
xy,z



= 0.52 eV


= 0.30 eV

Main effect of tetraheder elongation

Γ

Z

X

The set of 5
Fe d Wannier
orbitals


t
xy,z



= 0.52 eV


= 0.30 eV

Main effect of tetraheder elongation

Γ

Z

X

-1
0
1
2
E
1
2
3
k
Inter
-
layer coupling in BaFe
2
As
2

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


As a first application of our
pd

model we have studied

magnetism.
Striped AFM order corresponds to a SDW with
q
= (0,
π
) =
Y
.

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
m
(
Δ
) =
Δ
/I

q

xy

xy

xz

yz

xz

xy

Δ

= 0.18 eV
m = 0.3
μ
B

zz/XY

zz/XY

zz/XY

xy /z

xy/z

yz /y

yz/y

minority

majority
polarization

Δ

= 2.2 eV
m = 2.4
μ
B

-3
-2
-1
0
1
1
2
3
k
-3
-2
-1
0
1
1
2
3
k
(
π
,0)

(
π
,
π
)

k

0

+1

-
1

-
2

-
3

φ

XY

zz

eV

-3
-2
-1
0
1
1
2
3
k
π
/4

xz

x

φ

a

b

-3
-2
-1
0
1
1
2
3
k
a
k
/a
k+
π

=b
k
/b
k+
π

a
k
/b
k+
π

=b
k
/a
k+
π

Δ

= 2.2 eV

-1
0
1
1
2
3
k
-3
-2
-1
0
1
0
1
2
3
k
-3
-2
-1
0
1
0
1
2
3
k
-3
-2
-1
0
1
0
1
2
3
k
0

-
π
/4

yz

y

φ

(
π
,0)

(
π
,
π
)

k

0

+1

-
1

-
2

-
3

φ

-
π
/2

xy

z

eV

-
π
/4

-3
-2
-1
0
1
0
1
2
3
k
Δ

= 2.2 eV

h

e

x=e/Fe

y=h/Fe

φ
(
t
)=
q∙t

xz

xy

yz

xy/z

XY/zz

XY/zz

XY

XY/zz

XY/zz

xy/z

XY/zz

xy/z

XY/zz

xz

yz

xy

XY/zz

Δ

= 1.1 eV

Para
-

and stripe

antiferromagnetic
hole bands

Double
-
counting corrected hole bands

e
k
(
Δ
)

=
ε
k
(
Δ
)
+

¼ p
k
(
Δ
)
Δ

magnetic
energy gain

DELETE DASHED FERMI LEVEL

k
-
resolved magnetic
energies for
Δ
=2.3 eV

LaOFeAs

Elongated minus Exp structure

Exp structure
t
xy/z
=0.52 eV

Elongated structure:
t
xy/z
=0.30
eV

Exp structure:
t
xy/z
=0.52 eV

Elongated structure:
t
xy/z
=0.30
eV