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