-
Photoemission Spectroscopy (2)Strongly correlated electron systems
Teppei YoshidaGraduate School of Human and Environmental Studies,
Kyoto University
Cheiron school2013 Principle of photoemission spectroscopy
Physicalpropertiesofmaterial
Metal
Fermi levelBand gap
Semiconductor
ElectronicstructureneartheFermilevel
Photoemissionspectra
SrTiO3
Takizawa et al., PRB 09
Electronic structure from molecular orbital to solid state band
T.Takahashi
Energy
Atomicorbital
Atomicorbital
Energy
Atom
SmallMolecule Large
MoleculeSolid
DensityofStates
bandMolecularorbitalAtomic
orbital
Bondingorbital
Antibondingorbital
-
Electronic structure Band dispersion and Fermi surface
Quantumnumber:wavenumberkMomentumhk
kFFermilevel
E=h2k2/2m
kF
T.Takahashi
k k k
Metal Insulator Semimetal
kF
Energy
Energy
Angleresolvedphotoemissionspectroscopy(ARPES)
Takahashi groupARPES calender 2006
Electron analyzerBand dispersion and Fermi surface
Momentum
Ene
rgy
k
E
Fermi level
Metal Insulator
k
E
Detector
slit
sample
photon
Principle of ARPES
Solid
Vacuum
k//
P//
Surface
p
k
Energy conservation
Ekin= - EB+h -
sin)(2
sin2
B
kin//
hEmmEk
Momentum conservationparallel to the surface
sin2 kin//////
mEpkp
X
Y
Zhv
e-
-
Spring8
Dimension of Fermi surface1D 2D 3D
Energy conservation
Momentum conservation Parallel to surface
Ekin= - EB+h -
sin)(2sin2B
kin//
hEmmEkh
sin2 kin//////
mEpkp
h
)cos(2 2kin VEmk h
V: Inner potential
h
ky
kx
kz
Solid
Vacuum
k//
P//
Surface
p
k
Three-dimensional Fermi surface mapping
ElectronAnalyzer
T.Takahashi
Multi-axis manipulator
-
Advanced Light Source BL 10.0.1Golden Gate Bridge
Advanced Light Source
ALS BL10.0.01 EDC and MDC
EDC (energy distribution curve)MDC (momentum distribution curve)
Spectral weight mapping
IntensityatFermilevel
Fermi surface and band dispersion
-
HiSOR BL9
http://www.hsrc.hiroshimau.ac.jp/english/bl9.htm
VeryHighresolutionphotoemissionspectroscopy
ShingroupMachineFromHP
http://shin.issp.utokyo.ac.jp/souchi/3gouki/
ShinGroupISSP,UniversityofTokyo
Worldrecordofenergyresolution
Probing depth
Mea
n fre
e pa
th (
)
Kinetic energy (eV)
SX
HX
VUV
Low energy
Energyresolution
-
Photon Factory
Tsukuba,Japan
KEK(Highenergy)
Tsukuba,Japan
KEK,PFinformationFromHP
PF BL-28A
ALS BL-10
experimental end station
HiSOR BL- 9A
SSRL BL 5-4
HP
Whatissuperconductivity?
Copper
Superconductor
Zeroresistance nothermalloss
Misner Effects
Discoveryofsuperconductivity
LiquidHe1908
Kamerlingh Onnes
DiscoveryofsuperconductivityinHg 1911
Nobelprizein1913Tc=4.2K
-
BCS (Bardeen,Cooper,Schrieffer)theoryElectronPhononinteraction
Electronsmakepairsmediatedbylatticevibrations(phonon)
Cooperpairs
NobelPrizein1972BCStheory1957
HighTc cuprate superconductor
J.G.BednorzandK.A.Mller, Z. Phys. B64 (1986)189
Discoveryofironbasedsuperconductors(2008)
Hightransitiontemperaturenexttothecuprates family
H.Hosono Y.Kamihara
LaFeAsO
HistoryofsuperconductivityCuprate supercondutors
Discovery of high-Tc cuprates1986)
Discovery of iron-based supercondutor 2008
J. G. Bednorz,A. K. Muller
H. Hosono
Conventional superconductors
Iron-basedsuperconducto
year
Tran
sitio
n te
mpe
ratu
re ,
T c(K
)
-
HighTc cuprate superconductors
SC
MottinsulatorAF
0 0.1 0.2 0.3
200
300
100Tc
Pseudo gap
T*
Metal(Fermi liquid)
T(K
)Phase diagram CuO2 plane Crystal structure
Hole concentration, x
OCu
Bi
Sr
CaBi2Sr2CaCu2O8+Bi2212Tc,max=95Kc=30.7
Bi2Sr2Ca2Cu3O10+Bi2223Tc,max=110Kc=37.1
Bi2Sr2CuO6+Bi2201Tc,max=34Kc=24.6
CuO2Planes
Tc of multilayer cuprates
Single-, double-, and triple layer cuprates
A. Iyo et al, JPSJ06
CuO2Tc
IP, Bi2223
SC gap
Node
Antinoded-
BCS theory BCS theory
Superconductinggap (T)
Tc
Tc
Densityofstates
-
Observation of SC gap by ARPES
http://www.hsrc.hiroshimau.ac.jp/temperature.htm
Observation of SC gap by ARPES
http://arpes.phys.tohoku.ac.jp/contents/study/CuO.html
Fermi surface and band dispersions in high-Tc cuprates Band structure and Fermi surface of high-Tc cuprates (Overdoped sample)
H. Sakakibara et al., PRL 09
Theory
ARPES
T. Yoshida et al., PRB 01
La2CuO4
d-
0
T(K
)
EF
Fermisurface
-
k-k
"Cooper Pair"
PreformedCooperpairs?
Pseudogap issue
Dingetal.
Bi2212
Tc=85K
GapopeningaboveTc !?
d-
0 0.1 0.2 0.3
200
300
100Tc
T*
T(K
)
Evolution of Fermi surface
Howthepsedogap andmetallicstatesareformedfromMottinsulator?
Large Fermi surfaceSmall Fermi surface
(,)
(0,0) (,0)
Mott insulator Pseudogap state MetalFermi liquid
d-
0 0.1 0.2 0.3
200
300
100Tc
T*
T(K
)
, x
La2-xSrxCuO4
Fermiarc
LHB
Metallic band
T. Yoshida et al. PRL. 03.
LHB
Fermi surface mapping QP band dispersions LSCO x=0.03
truncated Fermi surfaceFermi arc)
QP band structure in node direction Origin of metallic conductivity
Relation between SC gap and pseudogap ?
(0,0) (,0)
()
d-
0 0.1 0.2 0.3
200
300
100Tc
T*T
(K)
Pseudogap andFermiarc
T. Yoshida et al. PRB. 06.
, x
-
FormationofquasiparticlebandLSCO
Y. Kohsaka et al., JPSJ 03.T. Yoshida et al., PRL 03.
There are two kinds of evolution process of QP structure.
Ca2xNaxCuO2Cl2 (Na-CCOC)
In-gap states Band topMott insulator
Anisotropic SC gap in Bi2212
Holenumber
Leeetal.,Nature2007
Bi2212
Band dispersion and Fermi surfaces of Bi2223
OP
IP
OPOverdoped
Underdoped
Overdoped
S. Ideta et al., PRL 10
Tc=110K
d-wave superconducting gap
node
Ideta etal.,PRL
-
Superconducting gaps of Bi2223
Deviation from simple d-wave.
IP: underdopedOP:overdoped
Simple d-wave
T.Satoetal.,PRL01.
0IP ~ 60meV
*IP ~ 80 meV
0OP ~40 meV
IP
OP
OP
IP
OPOverdoped
Underdoped
Overdoped
S. Ideta et al., PRL 10
Tc=110K
Stronglycorrelatedelectronsystem
Mottinsulator
U: W:
MetalFermi liquid
(Nearly) free electrons
Localized electrons
HighTc cuprate superconductor Correlated electronsThere are three kinds of electrons.
1) Band electronsNearly free electrons can move between atoms.
2) Localized electronsElectrons localized near atom sites due to correlation.
3)Correlated electronsThese electrons can move between atomsbut their movements are not so easyas in band electrons.
cf. Prof. Nagaosa at Univ. Tokyo
-
band electronsU / WDOS
X.Y. Zhang, M.J. Rozenberg and G. Kotliar, PRL 93.
Correlation effects on DOS
Electroncorrelation
Metal
Insulatorlocalized electrons
correlated electrons
Correlation effects in ARPES spectra
Band electrons
Localized electrons
Correlated electrons
interaction
Movable electrons
SrVO3
Correlated electron system SrVO3
T.Yoshidaetal.,PRB10.
M.Takizawaetal.,PRB09.
Bulk Thin film
Localized electrons
Kink structure in quasi particle
Iwasawa etal.,Sci.Rep.3,1930(2012).JSSRRJournal
Eel:electronelectroninteractionEbl:electronbosoninteraction
:Selfenergy
Band electrons
Correlated electrons
Band electrons
Correlated electrons
-
Coherent band part
U / W
U
W
DOS
X.Y. Zhang, M.J. Rozenberg and G. Kotliar, PRL 93.
Mass enhancement due to electron correlation
SrVO3(3d1)
MassrenormalizationnearMItransition
A. Sekiyama et al. PRL04.
PES spectra
Energy (eV)
Inte
nsity
(arb
. uni
ts)
Incoherent part
SrVO3
Correlated electron system SrVO3
S. Aizaki, T. Y. et al. PRL 12.
A. Lanzara et al. Nature 2001
HighTc cupratesSrVO3
kink ~ 60meVElectron-phononinteraction?
Electron-phonon interactionBand dispersion
T. Valla et al. PRL83, 2085 (1999)
ARPES
Mo(110)D
Ashcroft,MerminSolidStatePhysics
Electron-phonon interaction
Hengsberger et al. 83, 592 (1999)
ARPES
Be(0001)
Ashcroft,MerminSolidStatePhysics
-
Model of Self-energy
(el-ph)(elel(el-imp
F
Debye
F()~n1Debye model
F
ph
F()~( o)
Einstein model
el-ph
0
''2 )(Im dFphel
Quasi-particle structure of high-Tc cuprates
A. Lanzara et al. Nature 2001
kink in band dispersionshave been observed.
Electron-phononinteraction ?
Be(0001)
Y
Bi2212 T