Andrea DamascelliDepartment of Physics & Astronomy

University of British ColumbiaVancouver, B.C.

Introduction to Angle-Resolved Photoelectron Spectroscopy

Group: Electronic Structure of Solids

S. WangB. Lau

S. HossainJ. MottersheadA. Damascelli

AMPEL BldgRoom 245

H.W. LiD.L. Feng

A. RiemannG. Sawatzky

Previous Collaborators ARPES at Stanford:

K.M. Shen, D.H. Lu, D.L. Feng, N.P. Armitage, F. Ronning, C. Kim, Z.-X. Shen

Band Structure Calculations (NRL, Washington): I.I. Mazin, D.J. Singh

Samples: Sr2RuO4

S. Nakatsuji, T. Kimura, Y. Tokura, Z.Q. Mao, Y. Maeno

Bi2Sr2CaCu2O8+

H. Eisaki, R. Yoshizaki, J.-i. Shimoyama, K. Kishio, G.D. Gu, S. Oh, A. Andrus, J. O’Donnell, J.N. Eckstein

YBa2Cu3O7-

D.A. Bonn, R. Liang, W.N. Hardy, A.I. Rykov, S. Tajima

Nd2-xCexCuO4

Y. Onose, Y. Taguchi, Y. Tokura; P.K. Mang, N. Kaneko, M. Greven

Ca2-xNaxCu2O2Cl2L.L. Miller, T. Sasagawa, Y. Kohsaka, H. Takagi

Outline

State-of-the-Art ARPES: the essentials

Conclusions and discussion

Sr2RuO4

IntroductionInteresting properties and open issues

Experimental resultsBulk & surface electronic structure

Electronic structure of complex systems

ARPES on Bi2Sr2CaCu2O8+

Strongly Correlated Electron Systems

Controlparameters

Bandwidth (U/W) Band filling

Dimensionality

Degrees offreedom

Charge / Spin Orbital Lattice

d - f open

shells materials

U<<WCharge fluctuations

U>>WSpin fluctuations

• Kondo• Mott-Hubbard• Heavy Fermions• Unconventional SC• Spin-charge order• Colossal MR

Nd2-xCexCuO4 La2-xSrxCuO4

0.3 0.2 0.10

100

200

300

SC

AFTem

pera

ture

(K

)

Dopant Concentration x0.0 0.1 0.2 0.3

SC

AF

Pseudogap

'Normal'M etal

I II IIIb IVb Vb VIb VIIb VIIIb Ib IIb III IV V VI VII 0

  Lanthanides*Actinides **

Ca2-xSrxRuO4

***

Ru Tc

H HeLi Be B C N O F NeNa Mg Al Si P S Cl Ar

Rb Sr Y Zr Nb Mo Rh Pd Ag Cd In Sn Sb Te I XeCs Ba La Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At RnFr Ra Rf Db Sg Bh Hs Mt

Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr

K Ca Sc Ti V Cr Fe Co Ni Cu Zn Ga Ge As Se Br Kr

Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

Mn

Ac

Strongly Correlated Electron Systems

Understand the macroscopic electronic properties

and the role of competing degrees of freedom

Study the low-energy electronic excitations

ARPESVelocity and direction of the electrons in the solid

Allowed electronic statesRepeated-zone scheme

Electrons in a 1D periodic potential

Wave functionsin a 1D lattice

EF

FirstBrillouin

zone

SecondBrillouinzone

SecondBrillouin

zone

1D chain of atoms

Allowed electronic statesRepeated-zone scheme

EF

Electrons in a 1D periodic potential

Many properties of a solids are determined by electrons near EF

(conductivity, magnetoresistance, superconductivity, magnetism)

Only a narrow energy slice around EF is relevant for these properties

(~kT=25 meV at room temperature).First

Brillouinzone

SecondBrillouinzone

SecondBrillouin

zone

A “Simple” Example : Metal Surfaces (Cu and Ag)Angle-Resolved Photoemission Spectroscopy

A “Simple” Example : Metal Surfaces (Cu and Ag)Angle-Resolved Photoemission Spectroscopy

A “Simple” Example : Metal Surfaces (Cu and Ag)Angle-Resolved Photoemission Spectroscopy

Ekin,,

Momentum Conservation

Ekin EB

Energy Conservation

p|| k|| Ekin

Angle-Resolved Photoemission Spectroscopy

kF

kF

Electrons in Reciprocal Space

Ekin,,

Momentum Conservation

Ekin EB

Energy Conservation

p|| k|| Ekin

Photoemission intensity: I(k,)=I0 |M(k,)|2f() A(k,

Single-particle spectral function

(k,) : the “self-energy” - captures the effects of interactions

Angle-Resolved Photoemission Spectroscopy

Angle-Resolved Photoemission Spectroscopy

Photoemission intensity: I(k,)=I0 |M(k,)|2f() A(k,

No RenormalizationInfinite lifetime

Non-interacting Fermi Liquid

Advantages and Limitations of ARPES

Advantages Limitations

• Direct information about electronic states!

• Straightforward comparison with theory - little or no modelling.

• High-resolution information about BOTH energy and momentum

• Surface-sensitive probe

• Sensitive to “many-body” effects

• Can be applied to small samples (100 m x 100 m x 10 nm)

• Not bulk sensitive

• Requires clean, atomically flat surfaces in ultra-high vacuum

• Cannot be studied as a function of pressure or magnetic field

ARPES: advantages and limitations

Mom

entu

m

Energy0.2°2-10now2°20-40pastE (meV)

Improved energy resolution Improved momentum resolution Improved data-acquisition efficiency

Parallel multi-angle recording

Angle-Resolved Photoemission Spectroscopy

Energy

SSRL Beamline 5 - 4 : NIM / Scienta System

20 10 0 -10

Au sampleh=22.7 eV

T=10 K

Totalresolution5.0 meV

Inten

sity

(a.u

.)

Binding Energy (meV)

NIMNIM // SCIENTA SystemSCIENTA System

0.2°2-10E (meV)

Total Resolution

5.0 meV

Sr2RuO4: basic propertiesMaeno et al., Nature 372, 532 (1994)

Sr2RuO4 : 2D Fermi Liquid (c/ab=850)

Ca2RuO4 : insulating Anti-FerroMagnet

SrRuO3 : metallic FerroMagnet

RuO2

SrO

SrO

2D perovskite

Lattice-magnetism interplayOrbital degrees of freedom

• Pairing mechanism ?• Order parameter ? • FM-AF fluctuations ?

Unconventionalsuperconductivity

Rice & Sigrist, JPCM 7, L643 (1995)

Nakatsuji & Maeno, PRL 84, 2666 (2000)

Ca2-xSrxRuO4

Low-Energy Electronic structure of Sr2RuO4

Band structure calculation: 3 t2g bands crossing EF

3 sheets of FS (hole-like) and (electron-like)

A. Liebsch et al, PRL 84, 1591 (2000)

eg

t2g

Ru4+ 4d 4

S=1x

yz

x

yz

x

yz

xz yz xy

I.I. Mazin et al, PRL 79, 733 (1997)M

M

X

D.J. Singh, PRB 52, 1358 (1995)

Fermi Surface of Sr2RuO4

M

M

X

0.1 0.0

X

Inte

nsity

(a.u

.)Binding Energy (eV)

ARPES : circa 1996

M

M

X

A. Damascelli et al., PRL 85, 5194 (2000)K.M. Shen et al., PRB 64, 180502R (2001)

ARPES : present day

0.2 0.0

X

Inte

nsity

(a.u.

)

Binding Energy (eV)

Fermi Surface Topology of Sr2RuO4

M

XM

Surface reconstruction of cleaved Sr2RuO4

Rotation of the RuO6 octahedra around the c axis

Soft phonon branch

Structural instabilityof Ca2-xSrxRuO4

Ca2-xSrxRuO4

R. Matzdorf et al., Science 289, 746 (2000)

bulksurface

Cleavageplane

O. Friedt et al., PRB 63, 174432 (2001)

Surface electronic structure of Sr2RuO4

EF mapping ±10 meV

Cold cleaveT=10 K

M

XM

100 0100 0Binding energy (meV)

How to gain unambiguous informationon the bulk electronic structure?

On samples cleaved at 180 K the surface-related features are

suppressed

Hot cleaveT=180 K

100 0100 0Binding energy (meV)

Bulk electronic structure of Sr2RuO4

200 100 0200 100 0Binding Energy (meV)

200 100 0Binding Energy (meV)

200 100 0

SB

T= 10 K h=28 eV

M

M

X

Sr2RuO4 cleaved at 180 K

M

XM

On samples cleaved at 180 K the surface-related features

are suppressed

X

I.I. Mazin et al., PRL 79, 733 (1997)

Thus, the ARPES - FS is consistent with de Haas-van

Alphen and LDA results

Dispersion of the bulk electronic bands

vF / vFband exp= 3.2

Experiment compares well with LDA+U calculationsA. Liebsch & A. Lichtenstein, PRL 84, 1591 (2000)

Superconductivity

2-electronbound state

-k

kCooper Pair

spin-singlet pairing

A. Chainani et al., PRL 85 (2000)

Superconductivity can onlybe seen on low energy scalesand needs high resolution!

“Classic Low-temperature” Superconductors

Metallic Density of States

Superconducting Density of States

High-Temperature Superconductors

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2Energy Relative to the Fermi Level (eV)

Bi2212 Tc = 78K

--- 20 K--- 85 K

A

B

Γ

Y

MA

B

M

Pho

toem

issi

on In

tens

ity

(π, 0)

“s-wave”

“d-wave”

A

A

B

B

Valla et al., Science 285, 2110 (1999)

Many Body effects in the Quasiparticle Dispersion

Mechanism for High-TC

Magnetic fluctuations ?Electron-phonon coupling ?

Lanzara et al., Nature 412, 510

Many Body effects in the Quasiparticle Dispersion

Mechanism for High-TC

Magnetic fluctuations ?Electron-phonon coupling ?

Electron Momentum

Bind

ing

Ener

gy

FS in unprecedented detail Fermi velocity and effective mass Investigate the issue of surface FM

Superconducting (d-wave) gap Many-body effects in the QP dispersion

ARPES results from Sr2RuO4

Feedback to microscopic modelsQuantify the spin/charge correlation

effects

A. Damascelli et al., PRL 85, 5194 (2000); PRL 87, 239702 (2001)K.M. Shen, A. Damascelli, et al., PRB 64, 180502(R) (2001)

Conclusions

A. Damascelli, Z. Hussain, and Z.-X Shen, Rev. Mod. Phys. 75, 473 (2003)For a review article see:

ARPES is a powerful tool for the study of theelectronic structure of complex materials