Vladimir Cvetković
Zlatko Te
š
anovi
ć
Department of Physics, UC Riverside
Riverside, CA, May 6, 2009
Valley density

wave (VDW)
and Superconductivity
in Iron

Pnictides
Institute for Quantum Matter
Department of Physics and Astronomy
Johns Hopkins University
Europhys. Lett.
85
, 37002 (2009)
arXiv.org:0808.3742
Valentin Stanev
Three Ages of
Superconductivity
Are we almost there (room temperature SC)?
Superconductivity eras
1
Prehistoric eras
time
pnictides
conventional (BCS)
cuprates
iron age
bronze age
stone age
Early days of the iron
superconductivity
17 papers on arXiv in a single day (July 2008)
2
LaFeAsO
1

x
F
x
La
1

x
Sr
x
FeAsO
SmFeAsO
1

x
F
x
CeFeAsO
1

x
F
x
PrFeAsO
1

x
F
x
NdFeAsO
1

x
F
x
GdFeAsO
1

x
F
x
SmFeAsO
1

x
F
x
SmFeAsO
1

x
GdFeAsO
1

x
Gd
1

x
Th
x
FeAsO
DyFeAsO
1

x
F
x
TbFeAsO
1

x
F
x
Tb
1

x
Th
x
FeAsO
Ba
1

x
K
x
Fe
2
As
2
Sr
1

x
K
x
Fe
2
As
2
Eu
1

x
La
x
Fe
2
As
2
Ca
1

x
Na
x
Fe
2
As
2
Eu
1

x
K
x
Fe
2
As
2
Li
1

x
FeAs
a

FeSe
1

x
BaNi
2
P
2
LaO
1

x
NiBi
LaOFeP
LaO
1

x
F
x
FeP
LaONiP
a

FeSe
SrNi
2
As
2
BaCo
x
Fe
2

x
As
2
SrCo
x
Fe
2

x
As
2
BaNi
x
Fe
2

x
As
2
FeSe
0.5
Te
0.5
2008
T
c
(K)
courtesy of J. Hoffman
Structure
Universal properties
of iron

pnictides
Magnetic order (
C. de la Cruz,
et.al., Nature
453
, 899 (2008)
)
Phase diagram (
H Chen etal,
EPL
85
, 17006 (2008)
)
Comparison between
Cuprates and Pnictides
Pnictides are correlated, but not as much correlated as cuprates.
Cuprates
5
3d electrons from Cu (9)
and p electrons from O
Layered materials,
extremely anisotropic
Layered materials,
moderately anisotropic
Rare earth and other `dirt’
between relevant (Cu) layers
Rare earth and other `dirt’ between
relevant (Fe) layers (not in 11)
3d electrons from Fe (6) and
p electrons from P/As
AF in parent compound
and SC in proximity
Only one 3d orbital at Fermi level
All 3d orbitals at Fermi level
AF in parent compound
and SC in proximity
Insulating parent compound
Metallic parent compound
One hole

half filled
Four holes

not near half filled
AFM is due to the local correlations
Itinerant AFM
Pnictides
The particular crystal structure of pnictides reduces the role of J
H
.
In transition metals (3d) Hund’s rule (minimization of Coulomb repuslion)
leads to the highest possibe magnetic moment.
If Hund’s rule had won, iron pnictides would have had S = 2.
6
Hund’s
rule defeated
Instead, the tetrahedral (As) environment brings all the 3d orbitals close to
the Fermi level. Large overlap with As orbitals promotes iron itinerancy.
Example: Mn in cubic (Mn2+) and tetragonal (here Mn3+) environment.
7
Band structure and
t
ight
binding model
Two orbital model (
S. Raghu, et al, Phys. Rev. B 77, 220503R (2008)
) reconstructs
only the FS’s shape
FS’s topology implied by this model (
Y. Ran, et al., arXiv:0805.3553
)
d
xz
d
yz
Band structure from LDA (
S. Lebegue, Phys. Rev. B 75, 035110 (2007); I.I. Mazin, et al.,
Phys. Rev. Lett. 101, 057003 (2008)
) and experiments (
C. Liu, et al., arXiv:0806.2147
)
We consider an effective 2D model with 5 Fe + 3 As orbitals
8
`Minimal’ tight binding model
d
xz
odd parity
even parity
The importance of Fe 3d
–
As 4p
hybridization:
Without pnictide atoms many hopping
processes would vanish by symmetry.
These symmetries are violated by
pnictide puckering.
d
yz
d
xy
d
xx

yy
d
2zz

xx

yy
Energy levels and nearest neighbor hoppings
9
T
ight

binding Hamiltonian
Parameters, band structure, and FSs:
Hole and electron pockets (valleys) are separated by vector
M
= (
p
,
p
).
Semiconductor
Semimetal
10
m
d
c
Semiconductors turned
semimetals (turned SC)
Multiband SC, SDW,
CDW, ODW, etc.
The master instability in pnictides is a valley
density wave (VDW) at vector
M
.
Due to the multiband nature of the problem, VDW
is SDW, CDW, ODW, or a combination thereof.
e
d
e
c
Experimentally observed
magnetic/structural trans.
We claim: All these orders are a particular `orientation’ of Valley
Density Wave (hence SDW, CDW, ODW, or a mixture).
Collinear magnetic order (nearly) accompanied by a structural transition at
T
c
~140K (
C de la Cruz, etal, Nature
453
, 899 (2008); H Chen etal, EPL
85
, 17006 (2008)
).
Magnetic transition
Structural transition
Metallic resistivity
11
Effective Hamiltonian
near the Fermi level
Kinetic part
Interaction (density

density and Hund)
Two hole (
G
) and two particle (M) bands
M
12
Simple vertices:
Density
Spin
13
Types of scattering
Intraband (repulsion)
Interband
Mixed spinless
Mixed Josephson
General vertices
where
is Wannier functions overlap.
Proximity to a symmetry
Particle hole transformation
Fermi surfaces are similar
Highly symmetric point in the Hamiltonian
U(8)
SU(2)
sp
xU(1)
ch
U(8) spinor
14
M
Gradual symmetry reduction
U(8)
[SU(2)
sp
xU(1)
ch
]
4
SU(2)
sp
xU(1)
ch
U(4)
(h)
xU(4)
(e)
15
[SU(2)
sp
xU(1)
ch
]
4
SU(2)
sp
xU(1)
ch
U(4)
(h)
xU(4)
(e)
[SU(2)
orb
xU(1)
ch
]
2
xSU(2)
sp
[SU(2)
orb
]
2
xSU(2)
sp
xU(1)
ch
Gradual symmetry reduction
U(8)
U(4)
(h)
xU(4)
(e)
15
Flavorless model
(Valley Density Wave)
U(2)
U(1)xU(1)
U(1)
ch
Ground state is fSC (VDW)
Ground state is fFFLO:
U(1)xU(1)
M
U(2) spinor
Ginsburg

Landau action (Gorkov)
16
The symmetry of the order parameter is
s
’, and
there is only one SC gap (interband Cooper pairs)
Decoupling the Josephson term G2 into two
SC order parameters
Flavorless
model
(Superconductivity)
17
There is only one gap in 1111 (
T.Y. Chen, et al. Nature 453, 1224 (2008)
)
122 seems to have 2 gaps (possibly due to a larger FS mismatch).
The interaction terms (intraband repulsive +
Josephson mixed):
Substantially different than an intraband SC (realized when U < 0).
Proximity to the VDW is crucial. Without it G2*<U*, and we have no SC.
RG flow equations (G
1
= 0):
RG flow for the couplings
In order for the s’ SC to appear, G
2
must overcome intraband repulsion.
18
Bare values
but
where
w
C1
and
w
C2
are inter and intraband energy scales.
At the same time, the perfect nesting must be avoided (hence the dopping).
U(4)
(h)
xU(4)
(e)
[SU(2)
orb
xU(1)
ch
]
2
xSU(2)
sp
[SU(2)
orb
]
2
xSU(2)
sp
xU(1)
ch
[SU(2)
sp
xU(1)
ch
]
4
SU(2)
sp
xU(1)
ch
U(4)
(h)
xU(4)
(e)
Restoring the
flavors
U(8)
19
Flavorful
VDW
20
VDW order parameter is a matrix:
GL action at U(4)xU(4) is
Theorem: Let
S
be an (VDW) action invariant under group
G
. The action
of each group element on holes and particles is represented by
unitary matrices U
(h)
(g) and U
(e)
(g) respectively. If
D
is a ground state for
this action, so is matrix .
s
2
is a spin Pauli matrix
due to the p

h transformation.
The ground state:
Any maximally paired state minimizes the S
GL
. We need additional terms
to break the degeneracy.
U(4)
(h)
xU(4)
(e)
[SU(2)
orb
xU(1)
ch
]
2
xSU(2)
sp
[SU(2)
orb
]
2
xSU(2)
sp
xU(1)
ch
[SU(2)
sp
xU(1)
ch
]
4
SU(2)
sp
xU(1)
ch
U(4)
(h)
xU(4)
(e)
Restoring the
flavors
U(8)
21
Spin content of VDW
22
G
1
acts only on spin

singlet pairs
Singlet pairing occurs first (when cooling) followed closely by triplet
pairing. These are structural/magnetic transitions observed in pnictides.
G
2
can be decoupled into direct and exchange channel
CDW/ODW:
The unitarity of
D
enforces SODW order to be predetermined by the
CDW (singlet) phase ODW.
SDW/SODW:
Spin singlet order parameter
U(4)
(h)
xU(4)
(e)
[SU(2)
orb
xU(1)
ch
]
2
xSU(2)
sp
[SU(2)
orb
]
2
xSU(2)
sp
xU(1)
ch
[SU(2)
sp
xU(1)
ch
]
4
SU(2)
sp
xU(1)
ch
U(4)
(h)
xU(4)
(e)
Restoring the
flavors
U(8)
metallic VDW (fFFLO)
23
Conclusions
•
New family of high

Tc superconductors
•
Magnetic/structural transition and metallic resistivity
•
Phase diagram similar to cuprates (AF, SC), but this
is misleading (no Mott limit)
•
Minimal model (at least 4 orbitals)
•
The leading instability is VDW
•
Details determined by G
1
and G
2

CDW and SDW
•
G
2
necessary for the superconductivity (s’), which is multi

and inter

band
•
Orbital density wave (ODW) predicted
24
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