Valley density-wave (VDW)

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15 Νοε 2013 (πριν από 3 χρόνια και 8 μήνες)

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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