Transcript A. Moreo:The High T c Superconductivity Puzzle

The High Tc Superconductivity
Puzzle.
Adriana Moreo
Dept. of Physics and ORNL
University of Tennessee,
Knoxville,
TN, USA.
Supported by NSF grant DMR-0706020.
Superconductivity Timeline
Heike Kammerlingh Onnes
discovers superconductivity
In Hg. Tc=4.2K
1908
What is Superconductivity?
• Resisitivity vanishes below Tc.
Hg
– Normal conductor: induced
current dissipates as heat in
seconds.
– Superconductor: induced
current last for years (decay
constant >109 years).
• No magnetic field in its interior:
Meissner effect.
– Normal conductor: perfect
conductor with R=0 is
penetrated by an external Hfield.
– Superconductor:
spontaneously generates
surface currents that opposes
the external H-field.
T>Tc
H
J
H
T<Tc
SC
PC
Superconductivity Timeline
Heike Kammerlingh Onnes
discovers superconductivity
In Hg. Tc=4.2K
1908
Bardeen,
Cooper, and
Schrieffer
develop BCS
theory.
1958
What causes SC in Hg?
BCS Theory
• Electrons form pairs.
• Electron-phonon
interaction is the
“glue”.
• Only electrons within
a shell around the FS
form pairs.
• Pairs are rotationally
invariant.

k


k , k ,
 c c
k
U
Coulomb repulsion
Normal State
-k
Cooper Pair
BCS Superconductors
• Metals.
• Quest towards
higher Tc not very
successful.
•Highest Tc =
23.2K in Nb3Ge
(1973).
Superconductivity Timeline
Heike Kammerlingh Onnes
discovers superconductivity
In Hg. Tc=4.2K
1908
Bardeen,
Cooper, and
Schrieffer
develop BCS
theory.
Bednorz and Muller
discover high Tc
Cuprates.
1958
1986
High Tc Cuprates
• Discovered in 1986 by
Bednordz and Muller.
• Tc~30K in La2-xBaxCuO4.
• Ceramics with CuO
planes.
• AF insulators for x=0.
• Tc= 90K in YBaCu3O7.
• Highest Tc~130K for
HgBa2Ca2Cu3O6d.
Cuprates: Unconventional SC
• The SC gap has
nodes.
• D-wave symmetry.
Models
• t-J model or Hubbard
model with large U
(strong Coulomb
repulsion).
• One orbital:dx2-y2
t
– AF for undoped.
– D-wave pairing trend.
– Correct FS shape.
J
Mechanism:
Magnetism friend or foe?
• Electron-Phonon?
– Tc is too high.
– E-ph too weak to
overcome strong
Coulomb repulsion.
• Magnetism?
– Does it provide the
“glue”?
– Or does it need to go
away to allow
pairing?
We still do not know the answer!
Superconductivity Timeline
Heike Kammerlingh Onnes
discovers superconductivity
In Hg. Tc=4.2K
1908
Bardeen,
Cooper, and
Schrieffer
develop BCS
theory.
Bednorz and Muller
discover high Tc
Cuprates.
1958
1986
2001
MgB2 is discovered
at BNL, NIST, and
University of Oslo.
Tc=39K
Superconductivity Timeline
Heike Kammerlingh Onnes
discovers superconductivity
In Hg. Tc=4.2K
1908
Bardeen,
Cooper, and
Schrieffer
develop BCS
theory.
Fe based
superconductors
are discovered in
Japan. Tc=56K.
Bednorz and Muller
discover high Tc
Cuprates.
1958
1986
2001
2007
MgB2 is discovered
At BNL, NIST, and
University of Oslo.
Tc=39K
F doped LaOFeAs
• Quaternary oxypnictides:
LnOMPn (Ln: La, Pr;
M:Mn, Fe, Co, Ni; Pn: P,
As).
• Fe –As planes.
• La-O planes.
• Fe form a square lattice.
• F replaces O and
introduces e- in Fe.
Parent compound
• Long range
magnetic
order.
• Metal.
• Order
parameter:
suggests small
to intermediate
U and J.
De la Cruz et al., Nature 453, 899 (2008). See also
McGuire et al., cond-mat:0804.0796; Dong et al.,
cond-mat:0803.3426 and others.
Theory
• Band Structure: 3d Fe
orbitals are important.
(LDA)
• dxz and dyz most
important close to eF.
(Korshunov et al., condmat:0804.1793).
• Metallic state.
• Possible itinerant
magnetic order.
Singh et al., cond-mat:
0803.0429; Xu et al., condmat:0803.1282; Giovannetti et
al., cond-mat: 0804.0866; and
several others.
Fermi Surface
LDA
• Two hole pockets at G point.
• Two electron pockets at M.
• dxz and dyz orbitals (with
some dxy hybridization).
ARPES
Liu et al.,
cond-mat:
0806.2147
NdFeAsO1-xFx
Singh et al., PRL100, 237003
(2008).
Numerical Simulations
(Daghofer et al., PRL101, 237004 (2008)).
• Relevant degrees of freedom need to be identified.
• Construct the minimal model.
• Exact diagonalization and Variational Cluster
Approximation (Daghofer) using a small cluster.
• Successful with the cuprates: found magnetic order
and correct pairing symmetry.
Minimal Model
• Consider the Fe-As
planes.
• Two d orbitals dxz and dyz
based on LDA and
experimental results.
• Consider electrons
hopping between Fe ions
via As bridge.
• Square Fe lattice.
• Interactions: Coulomb
and Hund.
a/ 2
a/ 2
 /a
2

a
2

a
Hoppings
H k  t1  (d i, x , d i  x , x ,  d i, y , d i  y , y ,  h.c.)
i ,
 t 2  (d i, y , d i  x , y ,  d i, x , d i  y , x ,  h.c.)
i ,
 t3  (d i, x , d i  x  y , x ,  d i, x , d i  x  y , x ,
i ,
 d i, y , d i  x  y , y ,  d i, y , d i  x  y , y ,  h.c.)
 t 4  (d i, x , d i  x  y , y ,  d i, y , d i  x  y , x ,  h.c.)
i ,
 t 4  (d i, x , d i  x  y , y ,  d i, y , d i  x  y , x ,  h.c.)
i ,
Obtain from Slater-Koster overlap integrals between Fe-d and As-p orbitals and
Fe-As-Fe hopping.
Fitted Hoppings
(from Raghu et al.)
•
•
•
•
t1=-1
t2=1.3
t3=-.85
t4=-.85
Coulomb interactions
H int
J
 U  ni , , ni , ,  (U ' ) ni , x ni , y
2 i
i ,
 2 J  Si , x .Si , y  J  (d
i
U '  U  2J

i , x ,
d

i , x ,
d i , y , d i , y ,  h.c.)
i
Largest cluster that can
be studied with Lanczos
techniques.
Numerical results: undoped limit
• U<1 for metal in
undoped case.
• If J=U/4, U<1 to
reproduce
experimental order
parameter in parent
compound.
• S(k) peaks at (0,) and
(,0).
• Similar results for fitted
hoppings.
Electron Doping
(Moreo et al., PRB79, 134502 (2009))
Spin singlet
A1g spacial
 (k )   (cosk x  cosk y )d

9

B2g orbital


k , , k ,  ,
d
Inter-orbital pairing with B2g symmetry
9 (k )   (cosk x  cosk y )d k, ,d k ,  ,

12 (k )1  (cosk x  cosk y )( d k, x ,d k , y ,  d k, y ,d k , x , )
Spin triplet
2 (k )   (cos k x  cosk y )d k, ,d k , ,

Intra-orbital with A1g symmetry
Latest Developments
• Mean Field Calculations Performed in
multiorbital Models.
• Three Orbital Model Presented.
• Symmetry Based Study of the possible pairing
operators in a full 5 orbital model.
• References:
–
–
–
–
–
Daghofer et al., PRL101, 237004 (2008).
Yu et al., PRB79, 104510(2009).
Moreo et al., PRB79, 134502 (2009).
Moreo et al., PRB80, 104507 (2009).
Daghofer et al, submitted to PRB (2009).
Conclussions
• Numerical Techniques provide Crucial guidance
in systems where electrons interact strongly.
• Magnetism and orbital order need to be studied
in order to understand the mechanism of SC.
• The knowledge and the techniques developed
from the study of SC can be applied to the study
of many other problems in materials.