Strongly correlated electron systems(superconductors)
andNeutron scattering-view from a neutron instrumental scientistJ-PARC Center, JAEA
Masatoshi AraiJ-PARC / Materials Life Science Facility(the world class neutron/muon facility)

Importance of the dimensionality of the electron system
1D Fermi Surface

Band gap at lattice periodicity

2D Fermi Surface

Band gap at electron periodicity at EF

Periodicity of electron systemcreates Fermi surface nesting
and gap formation

2kF

System’s energy decreases !

2!(0) = 3.5k BTPMF
It is the same as BCS

2electrons in a unit cell -> insulator

Density response function(polarization susceptibility)f k +Q " f k1! (Q ) = #V k Ek " Ek "Q
1DSingularity strength is dominated by thesize of the nesting surface at EF
For 1D system! (Q ) =Q + 2k F
2mln
" h 2Q Q # 2k F! (2k F ) =DF 1.14 EB
lnNk BTIn case for 1D,
Peierls transition always occurs( metal- insulator transition )2D
3D
Kohn anomaly at 2KF
in the phonon dispersion
3D
2D
1DAnomaly at 2kF for electron system ⇒ CDWCorrelated electron system
and Hubbard model
Charge density: constantTransfer integral: tOn site Coulomb: Uspin density wave: AF! S (Q ) =g µ B ! (Q )1
1 " U ! (Q )2Spin susceptibility has a anomaly at a finite T
There is always a temperature where Uc (Q)/2=1, because of the character of c (Q)⇒ 2-kF-SDW is created if there is U (electron correlation) under nesting

condition.

Strong correlation creates AF insulator
AF ZB
If U>4t; strong correlation-kFkF
2kF
4kF

Half filling (Ne=Nu)
Antiferromagnetic correlation(SDW formation with a spin gap)
Mott insulator

Another explanation;"k =2!
aN uOccupation at a k is one not two.
Hence, 4kF-CDW occurs(TTF-TCNQ, 2KF-CDW + 4KF-CDW)

Superconductivity and Antiferromagnetism
Most of superconductors, recently discovered, have 2D-nature in the electron states.

Temperature

Oxide-HTC, Hf-compound, SrRuO, Organic SC (BEDT-TTF etc), Fe-pnictide
Oxide-HTC: stripe, 1/8 problem
very high U(OSC)~10eV
Organic SC: SDW, CDW
medium U~ U(OSC)/10Fe-pnictide: SDWAFSC
Charge concentration,Pressure, etc

Theoretical views for those superconductivity
depends on each cases.
However, there seems to be an universal view for them
(Generic, Robust concept ?)SC symmetry depends on SC gap nature.
exchange of electron-pair has asymmetric natureincluding wave function and spin part.
Cooper pair symmetry;s, d; singlet pairp; triplet pair

2D - SDW from LaFeAsO
TS=155K
TN=140K

2D nature in theelectronic statesTsTN
LaFeAsO1-xFx Tc~26K Kamihara, Hosono et al.
J. Am. Chem. Soc. 130, 3296 (2008).

SDW,AFAF
magnorder

2D-Fermi surface
Γ；hole like cylinder,M; electron like cylinder
Tc
2D - Fermi surface nesting
2D-SDW, SC
5-orbitals ( d(Z -R ), d(XZ), d(YZ), d(X -Y ), d(XY) )of 3d states have contribution
It is not a Mott insulator (U~1eV)
2electron concentration
R. Klingeler, et al., cond-mat
2008

222D.J. Singh and M.H. Du, Phys. Rev. Lett. 100, 237003(2008).

2/8

Structural Phase transition at 155K
(Tetragonal -> Monoclinic)
and3D-Anti-Ferromagnetic Long range order below 140K

MonoclinicTetragonal(Cruz et al. Nature 2008)

TS=155K

AF mag. peaks

TN=140K(AF points; (101)M, (103)M, (121)M )Inelastic Neutron Scatteringfrom a powder sample (LaFeAsO)(one of the most important role of neutrons)

T- dependence
S(Q=1.0~1.3 Å, E=7.5~9 meV)

240 K

140 K~TN7K

140K-7K

S(|Q|,E) (Ei=30 meV)

Spin gap formation

excitation from 2D-SDW
2D-SDW: Warren function
c*b*
hw=7.5-9meV(p,3p)(3p,3p)(p,p)
G Q(3p,p)a*

3D - AF long range order zone centers
Static 3D-AF order and2D-SDW in the inelastic region.
Existence of 2D-SDW

Nesting and unconventional S-wave SC
Formation of SDW by a nesting
Kuroki, Aoki, PRL 2008

BaFe2As2(Tc=0K), Spin wave excitation ?
7K

Similar experiments were rushedalmost in the same time on the same
instrument, MERLIN in ISIS.
Our Exp. date; 10 July
Christianson; 14 July
Ewings; after two above.

Ewings et al., cond-mat Aug. 2008
Ba0.6K0.4Fe2As2 (Tc=38K), Resonance peak in the SC states
7KChristianson et al. cond-mat July 2008

Crystal structure of YBa2Cu3O6+x

Oxide High Tc superconductor

Cu, spin 1/2

2D SC layer

Resemblance in the optical conductivity

Strong U(~8eV);strongly correlated electron system(half filling system)⇒ Mott insulator
2D electron system( 3d(X2-Y2), spin=1/2,charge transfer to the oxygen 2ps )2D magnetic system
2D phonon system

Bi2Sr2CaCu2O8+dElect. doping

01000

2000

3000

AFSC

Ba1-xKxFe2As2

N.L.Wang

Hole dopingby courtesy of UchidaSC

Incommensurate peaks in the oxide HTC-SC
Stripe: SDW (2kF) & CDW(4kF) ?

Incommensurability & Tc
Yamada et al. PRL

Periodicity of spin(d) and charge(2d)charge 2d = 0.25

Stripe (SDW)

4kF-CDW orders first(resemblance in TTF-TCNQ)

spin d = 0.12

SDW

J. M. Tranquada et.al. Nature 375 (1995)

La1.6-xNd0.4SrxCuO4

Common feature in the magnetic excitationin the oxide high Tc superconductors
La2-xBaxCO4(x=1/8)

YBa2Cu3O6.6

Hourglass shape in themagnetic excitation
additional
spin excitation

55meV
53meV

47meV
45meVresonanceexcitation

40meV
38meV
37meV

Qy

36meV
35meV

Incommensurate
spin excitation

Energy[meV]

51meV

Qx
Yokoo et al. J.Neutron Research
Tranquada et al. NatureHayden et al. NatureAnomalous Magnetic Excitation
Stripe Scenario& spin wave ?

Hourglass feature in
the Magnetic Excitation(2D-SDW ?)Imc can be obtained fromthe Fermi Surface characterby RPA (electron statetopology)

Norman PRB 2000

d~0.125

LSCO

Common for LSCO, YBCO etc
Nesting vector ←Tranquoda, Nature

Yakovenko 1995

Brinckmann and Lee, PRL 1999

Summary and guess1) Strongly correlated electron system (SCES) gives various exotic
physical properties.
2) Low dimensionality and the Fermi surface topology is important.
3) The discovery of the Fe-pnictide is very important for itself, but also
stimulating reconsideration of physics of Oxide HTCSC.
4) It seems that electron-electron correlation (nesting) has animportance.
5) Studying dynamics of materials, by means of Neutron, X-ray, ARPES,
Muon, is very important to understand the intrinsic mechanism of physicalproperties of SCES.
6) IMSS has those tools in hand, and hence the formation of theCondensed Matter Research Center is very timely to extend andenhance the activity of IMSS.
7) J-PARC can have an important role for it.

J-PARC neutron facility will
provide excellent opportunities tostudy strongly correlated electronsystems.

ENDmc/)n(p2000
Ty4t.
i0s@ns 1500
em/t
2nI1000
nortu 500
eN

4SEASONS & AMATERAS will come on line soon.

0BL01
@18m

0102030

Time (ms)The first neutrons
on May 30.

40

END