Download A New Piece in The High T c Superconductivity Puzzle: Fe

A New Piece in The High Tc
Superconductivity Puzzle: Fe based
Superconductors.
Adriana Moreo
Dept. of Physics and ORNL
University of Tennessee,
Knoxville, TN, USA.
Supported by NSF grant DMR-1104386.
Superconductivity Timeline
Heike Kammerlingh Onnes
discovers superconductivity
in Hg. Tc=4.2K
1911
What is Superconductivity?
Hg
Resistivity vanishes
at Tc.
– Normal conductor:
induced current
rapidly dissipates
as heat.
– Superconductor:
induced current last
for years (decay
constant >109 years).
Superconductivity
• No magnetic field in
its interior: Meissner
effect.
– Normal conductor:
perfect conductor
with R=0 is
penetrated by an
external H-field.
– 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
1911
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
thin 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.
Tc < 10 K
for pure elements
•Highest Tc = 23.2K in
Nb3Ge (1973).
Superconductivity Timeline
Heike Kammerlingh Onnes
discovers superconductivity
in Hg. Tc=4.2K
1911
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 CuO2 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.
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!
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
Superconductivity Timeline
Heike Kammerlingh Onnes
discovers superconductivity
in Hg. Tc=4.2K
1911
Bardeen,
Cooper, and
Schrieffer
develop BCS
theory.
Bednorz and Muller
discover high Tc
Cuprates.
1958
1986
Fe based
superconductors
are discovered in
Japan. Tc=56K.
2007
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-As planes.
Parent compound
• Long range
magnetic order.
• Bad metal.
• Order
parameter:
suggests small to
intermediate U
and JH.
De la Cruz et al., Nature 453, 899 (2008).
Theory
• Band Structure: 3d Fe
orbitals are important.
(LDA)
• dxz and dyz most
important close to eF.
(Korshunov et al., PRB78,
140509(R) (2008)).
• Metallic state.
• Possible itinerant
magnetic order.
L. Boeri et al., PRL101,
026403 (2008).
Fermi Surface
• Two hole pockets at G point.
• Two electron pockets at M.
• dxz and dyz orbitals (with
some dxy hybridization).
M. Norman, Physics 1, 21(2008).
Is the Coulomb interaction
strong or weak?
Weak Coupling?
•Itinerant electrons
•Nested Fermi surface
Strong Coupling?
•Localized moments
•Mott insulator
Pairing Symmetry
Experimental results:
•Uniform gaps (ARPES)
•Nodes (bulk methods)
Theory:
Spin Fluctuations +
Coulomb:
ARSH FeSe0.45Te0.55
•S+/-: Mazin et al.,
Kuroki et al.
•S with accidental
nodes.
B. Zeng et al., Nat.Comm. 1, 112 (2010)
ARPES Ba0.6K0.4Fe2As2
Nakayama et al., EPL85, 67002 (2009).
No Nodes
Nodes or deep
minima (also
consistent with
d-wave B2g).
Our Approach
• Construct microscopic models.
• Study their properties with:
– Numerical Techniques: Lanczos.
– Mean Field
• Compare results with experimental data:
– Obtain parameter values.
– Make predictions.
Daghofer et al., PRL101, 237004 (2008)
Minimal Model (two orbitals)
• Consider the Fe-As layers.
• Keep dxz and dyz based on
LDA and experimental
results.
• Consider electrons hopping
between Fe ions via As as a
bridge.
• Square Fe lattice.
• Interactions: Coulomb and
Hund (U,U’,JH).
• Only model that can be
studied with unbiased
numerical techniques.
Daghofer et al., PRL 101,
23704 (2008); A. M. et al.,
PRB79, 134502 (2009).
Non-interacting.
Parameters from
Raghu et al. PRB
(2008).
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 lattice that can be
studied with Lanczos
methods has 8 sites.
• Incorporating symmetries:
more than 5x106 states in
the Hilbert space.
Numerical results: undoped limit
JH/U=0.125
Experimental magnetic
structure is reproduced.
U=2.8 |t1|
De la Cruz et al., Nature 453, 899 (2008). See also
A. D. Christianson et al., PRL 103, 087002 (2009).
A. M. et al.,
PRB79, 134502 (2009).
Mean Field Study of the Magnetic Order
1
d l, , d l ', ', '  (n  cos ( q.rl ) m )  l ,l ' , ' , '
2
R. Yu et al.,
PRB79, 104510 (2009).
Diagonal in orbital space
Fitted
hoppings
J=0
J=U/8
J=U/4
Uc1
2.2
2
2
Uc2
7.4
6.6
6
Uc1Uc2
• Two critical values of
U: Uc1 and Uc2.
• U<Uc1: paramagnetic
metal
• Uc1<U<Uc2: magnetic
metal (band overlap)
• U>Uc2: magnetic
insulator.
Gap develops with increasing U.
MF estimation of parameter values
MF on three-orbital model
M. Daghofer et al., PRB 81, 014511 (2010).
Magnetic Bragg peak intensity for
Ba(Fe0.96Co0.04)2As2 at x=0.04.
A. D. Christianson et al., PRL 103,
087002 (2009).
De la Cruz et al., Nature
453, 899 (2008).
Neutron scattering results
(ORNL-UT) provide order
parameter for several
pnictides.
(p,0) magnetic order
parameter: comparing with
neutrons, allow us to establish
limits on Hubbard couplings U.
Dynamic Pairing Correlations
•Several pairing symmetries have
large spectral weight close to the
ground state (different from the
cuprates where s-wave has weight
at high energies).
• The non-trivial symmetry of the
pairing operators arises from the
orbital part rather than the
spatial part of the operators.
•Raman measurements may be able
to separate the orbital and spatial
contributions. Sugai et al. PRB82,
140504(R) (2010) observe B1g with
operator viii in BaFe1.84Co0.16As2.
i :  (cos k x  cosk y )d k, , d k , ,

v :  (cos k x  cosk y )d k, ,d k ,  ,

viii :  (cos k x  cosk y ) 1 d k, ,d k , ,


A. Nicholson et al., PRL106, 217002 (2011).
A. Nicholson et al., PRL106, 217002 (2011).
Mean Field Gaps
S+/-
Hole pockets
Nodal
Electron pockets
Hole pockets
Electron pockets
Conclusions
• Numerical Simulations in two orbital model:
– Magnetic metallic undoped regime for intermediate U and J
values.
– A1g, B2g, states compete. B1g state is close.
• Mean Field calculations:
– As a function of U there are three phases: 1) paramagnetic;
2) magnetic metallic; and 3) magnetic insulator.
– The ground state in the magnetic metallic regime is
magnetically ordered with spin stripes.
– The same results are observed in realistic models with
additional orbitals.
• The symmetry of the pairing operator in the pnictides
changes with slight variations in the parameters. This
may explain the diversity in experimental results.
• Preliminary results for hole doping indicate a similar
behavior.