Principle of photoemission spectroscopy

Cheiron school 2013

Photoemission Spectroscopy (2)Strongly correlated electron systems

Physical propertiesof material

Teppei Yoshida
Graduate School of Human and Environmental Studies,
Kyoto University

Electronic structure near the Fermi level
Metal

Electronic structurefrom molecular orbital to solid state band

Semiconductor

Anti‐bondingorbital

Fermi level

SrTiO3

Photoemission
spectraAtomicorbitalAtomicorbitalBonding
orbital

Molecular
orbitalband

EnergyAtomicorbitalEnergyBand gap

AtomSmallSolidMolecule Large
Density of States
Molecule「光電子固体物性」 T. Takahashi
Takizawa et al., PRB ‘09

Electronic structureBand dispersion and Fermi surface
Insulator

Semimetal

EnergyEnergyMetalkF

kFFermilevelkkkkF

Quantum number: wave number k
Momentum hk

E= h2k2/2m「光電子固体物性」 T. Takahashi

Angle‐resolved photoemission
spectroscopy (ARPES)Electron analyzer
Band dispersion and Fermi surface

Principle of ARPESP//

Zp hv

Vacuume-slit
EnergyX

Takahashi group
ARPES calender 2006kk//

試料

Energy conservation
Insulator ESurface

Yphotonsample

SolidkDetector

Metal E

電子エネルギー分析器

Ekin= - EB+h -Momentum conservation（parallel to the surface）

p//  k//p//  2mEkin sinkFermi levelMomentum

k //  2mEkin sin

 2m(EB  h  ) sinDimension of Fermi surface

1D

2D

3D

Three-dimensional Fermi surface mapping
P//

Energy conservationp Vacuum

Ekin= - EB+h -

Momentum conservation （Parallel tosurface）

SolidSurfacep//  hk//p//  2mEkin sinkk//kzhkx
関山明ほか Spring‐8 最近の研究からElectron Analyzer「光電子固体物性」 T. Takahashi

kyhk //  2mEkin sin
 2m(EB  h  ) sin
hk   2m( Ekin cos   V )2

V: Innerpotential

Multi-axis manipulator

ALS BL10.0.01

Golden Gate Bridge

Advanced Light Source BL 10.0.1

EDC and MDC

Advanced Light Source

EDC (energy distribution curve)
MDC (momentum distribution curve)

Spectral weight mapping

Fermi surface and band dispersion

Intensity at Fermi level東北大 高橋研

東大 長谷川研HiSOR BL9Very High resolution photoemission spectroscopy
Shin groupMachine
From HP
World record ofenergy resolution

http://www.hsrc.hiroshima‐u.ac.jp/english/bl9.htm

Shin Group
ISSP, University of Tokyo
http://shin.issp.u‐tokyo.ac.jp/souchi/3gouki/

Probing depth
Escape depth of photoelectrons
Mean free path (Å)

SXHXSX•Energy resolution < 100meV•Quick mapping in momentum
space

VUV

Low energy

Kinetic energy (eV)VUV -> surface sensitive

Low energy photons（SOR, laser）•Resolution < 5meV
•It takes a time to map in
momentum space.

Hiroshima Synchrotron （HiSOR）

ＡＲＰＥＳ experimental end station

Photon Factory

高エネ研フォトンファクトリーPF BL-28AKEK (High energy …)

広島大学放射光センター
HiSOR BL- 9A

Tsukuba, Japan
Tsukuba, Japan

スタンフォード大学放射光研究所
SSRL BL 5-4

KEK, PF information
From HP

励起光エネルギー可変
直線偏光、円偏光

バークレー国立研究所
ALS BL-10

What is superconductivity?
CopperSuperconductor

Zero resistance→ no thermal loss

Discovery of superconductivity
Liquid He（1908）

Discovery of superconductivity
in Hg （1911）

住友電工のHPよりMisner Effects
Kamerlingh Onnes
Nobel prize in 1913
Tc=4.2 KBCS (Bardeen, Cooper, Schrieffer ) theory

High‐Tc cuprate superconductor

Electron‐Phonon interaction

Nobel Prize in 1972

BCS theory 1957
Cooper pairs

J. G. Bednorz and K. A. Müller, Z. Phys. B64 (1986) 189
Electrons make pairs mediated by lattice vibrations (phonon)

Discovery of iron‐based superconductors (2008)

History of superconductivity
Transition temperature , Tc (K)Discovery of high-Tc cuprates（1986)

LaFeAsO

J. G. Bednorz,
A. K. Muller

Discovery of iron-based
supercondutor （2008）

Iron-based
superconducto

H. Hosono

Conventional
superconductors

H. Hosono

Y. Kamihara

High transition temperature next
to the cuprates family

Cuprate supercondutorsyear

High‐Tc cuprate superconductors
Phase diagramCuO2 planeSingle-, double-, and triple layer cuprates
Tc of multilayercuprates

Crystal structure

A. Iyo et al, JPSJ’06

300

T(K)

Metal(Fermi liquid)
200

T*100

Pseudogap

銅Tc

CuO2Planes

酸素Bi

SC0Mott
insulator
（AF）

0.1
0.2
Hole
concentration, xO
Cu
Sr

0.3
Bi2Sr2CuO6+δ
Bi2201 Tc,max=34 K
c=24.6Å

Bi2Sr2CaCu2O8+δ
Bi2212 Tc,max=95 K
c=30.7Å

Ca

Bi2Sr2Ca2Cu3O10+δ
Bi2223 Tc,max=110 K
c=37.1ÅCuO2面の枚数とTcの間に相関がある。

BCS theory

BCS theory
Density of statesd-波 超伝導ギャップ
AntinodeSuperconducting gap (T)Tc

SC gapIP, Bi2223
NodeTcObservation of SC gap by ARPES

Observation of SC gap by ARPES

http://www.hsrc.hiroshima‐u.ac.jp/temperature.htm

http://arpes.phys.tohoku.ac.jp/contents/study/CuO.html

Band structure and Fermi surface of high-Tc cuprates (Overdoped sample)

Fermi surface and band dispersions in high-Tc cuprates

TheoryLa2CuO4

Fermi surface

EF
バンド分散
H. Sakakibara et al., PRL ‘09

ARPES

フェルミ面

金属（フェルミ液体）

T(K)

バンド分散

擬ギャップ

d-波 超伝導0T. Yoshida et al., PRB ‘01

Evolution of “Fermi surface”

Pseudogap issue

Mott insulator
k-k

Preformed
Cooper pairs?

Pseudogap stateMetal（Fermi liquid）(,)Bi2212
Tc=85 K？

"Cooper Pair"

Gap opening above Tc !?

(0,0)

(,0)

300

Small Fermi surface Large Fermi surface
300

La2-xSrxCuO4200

金属（フェルミ液体）

T*
100

擬ギャップ

T(K)

T(K)

金属
（フェルミ液体）Tcd-波 超伝導0モット絶縁体（反強磁性）

0.1

200

擬ギャップ

1000.20.30

QP band dispersions LSCO x=0.03
Metallicband300

LHB(,0)200

T*T(K)

LHB

Relation between
SC gap andpseudogap ?

0.3

Pseudogap and Fermi arc()“truncated Fermi surface”（Fermi arc)

0.10.2
ホールドープ量, x

モット絶縁体（反強磁性）

Fermi arc

(0,0)

Tc

d-波 超伝導
Ding et al.

Fermi surface mapping

How the psedogap andmetallic states are formed
from Mott insulator ?

T*金属（フェルミ液体）
100

擬ギャップ

00.1

T. Yoshida et al. PRL. ’03.

QP band structure in node direction⇒ Origin of metallic conductivityTcd-波 超伝導モット絶縁体（反強磁性）

0.20.3

ホールドープ量, xT. Yoshida et al. PRB. ’06.

Formation of quasi‐particle band
LSCO

Anisotropic SC gap in Bi2212
Bi2212Ca2–xNaxCuO2Cl2 (Na-CCOC)

Hole number

Y. Kohsaka et al., JPSJ ’03.

T. Yoshida et al., PRL ’03.

Mott insulator
In-gap states

Band top

There are two kinds of evolution process of QP structure.

Lee et al., Nature 2007

Band dispersion and Fermi surfaces of Bi2223

d-wave superconducting gap

Overdoped

OP

Underdoped

IP

OverdopedOP
node
S. Ideta et al.,PRL ‘10

Tc=110K
Ideta et al., PRL

Strongly correlated electron system

Superconducting gaps of Bi2223
*IP ~80 meV

Deviation fromsimple d-wave.

0IP ~60meVIP

0OP ~40 meVOP

T. Satoet al.,
PRL ’01.

Mott insulator
Overdoped

OP

Underdoped

IP

Overdoped

OP(Nearly)
free electrons

原子核電子

Localized electrons

S. Ideta et al.,PRL ‘10

温度

Tc=110K

High‐Tc cuprate superconductor

U: 電子間クーロン反発
W: バンド幅（電子の動きやすさ）

新奇物性の発現

Simple d-wave

IP: underdoped
OP:overdoped

Metal（Fermi liquid）

金属
モット
絶縁体

高温超伝導
巨大磁気抵抗

圧力
磁場
ドーピング

Correlated electrons
There are three kinds of “electrons”.
1) Band electrons
Nearly free electrons can move between atoms.
2) Localized electrons
Electrons localized near atom sites due to correlation.
3)Correlated electrons
These electrons can move between atoms
but their movements are not so easy
as in band electrons.
cf. Prof. Nagaosa at Univ. Tokyo

Correlation effects in ARPES spectra

Correlation effects on DOSDOS

U/Wband electrons

Band electrons

Metalinteraction
Correlated electrons

Localized electrons
correlated electrons

Electroncorrelation

localized electrons

Insulator

X.Y. Zhang, M.J. Rozenberg and G. Kotliar, PRL ’93.

Correlated electron system SrVO3
Bulk

Kink structure in quasi particle

Movable electrons

Thin film

Correlated electrons

エネルギー

Correlated electrons

SrVO3
運動量

Localized electrons

T. Yoshida et al.,
PRB ’10.

M. Takizawa et al.,
PRB ’09.

Band electrons

Eel: electron‐electron interaction
Ebl: electron‐boson interaction

Band electrons

: Self‐energy
Iwasawa et al., Sci. Rep. 3, 1930 (2012).
JSSRR Journal

Mass enhancement due to electron correlation
DOS

Correlated electron system SrVO3
SrVO3

PES spectra

High‐Tc cuprates

Coherent band part

Incoherent part

エネルギー

W

Intensity (arb. units)

U/W

Energy (eV)A. Sekiyama et al. PRL‘04.

A. Lanzara et al. Nature 2001

SrVO3運動量U

SrVO3(3d1)

X.Y. Zhang, M.J. Rozenberg and G. Kotliar, PRL ’93.

kink ~ 60meVElectron-phonon
interaction?

Mass renormalization nearMI transition

S. Aizaki, T. Y. et al. PRL ’12.

Electron-phonon interaction

Electron-phonon interaction
Band dispersion

ARPES

ARPES
D

Be(0001)

Mo(110)T. Valla et al.
PRL83, 2085
(1999)

電子‐格子相互作用

Ashcroft, Mermin“Solid State Physics”

Ashcroft, Mermin“Solid State Physics”
Hengsberger et al. 83, 592 (1999)

Model of Self-energy

Quasi-particle structure of high-Tc cuprates

(el-ph)(elel(el-imp
Einstein model“kink” in band dispersions
have been observed.

Im  el  ph        2 F ( ' ) d  'F() ~ ( ‐ o)Electron-phonon
interaction ?

0F



phDebye modelFF() ~ n‐1

Debyeel-phA. Lanzara et al. Nature 2001

Quasi-particle structure of high-Tc cuprates“Dip” structure in spectra.
A. Lanzara et al.,Nature 412, 510 (2001)

Be(0001)

Bi2212 T<Tc

Origin of kink:

Spin fluctuations?

Y

Electron-phonon interaction?
UD

optOD

T. Sato et al. PRL 03’