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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