Physica Scripta T109, 61 (2004). Probing the Electronic Structure of Complex Systems by State-of-the-Art ARPES

Andrea Damascelli Department of Physics & Astronomy University of British Columbia Vancouver, B.C.

Optics Photoemission

• photon in – photon out • photon in – electron out • electric dipole transition • electric dipole transition • particle-hole excitations • electron removal excitations • collective modes • collective modes? (phonons, magnons, plasmons) only as dressing of quasiparticles • number of particles is conserved • number of particles not conserved

Electron transition Electron removal

Particle-hole excitations Single-particle excitations of the N-particle system of the (N-1)-particle system Optics Gruninger (1999)

Absorption coefficient in a semiconductor

Courtesy of

NiO is a charge transfer insulator Courtesy of O – 2p

Jan Kunes

Ni – 3d(eg)

NiO is a charge transfer insulator Einstein's Annus Mirabilis: 1905

• The Brownian motion "On the motion of small particles suspended in liquids atrest required by the molecular-kinetic theory of heat.“ Annalen der Physik, 17 (1905), pp. 549-560.

1921 • The photoelectric effect "On a heuristic viewpoint concerning the production and transformation of light" Annalen der Physik, 17 (1905), pp. 132-148.

• The special theory of relativity "On the electrodynamics of moving bodies“ Annalen der Physik, 17 (1905), pp. 891-921

• Mass-energy Equivalency E=mc2 "Does the inertia of a body depend on its energy?“ Annalen der Physik, 18 (1905), pp. 639-41. UBC – 2005

Andrea Damascelli The Photoelectric Effect: Intro

Emission of an electron due to the absorption of light

UBC – 2005

Andrea Damascelli The Photoelectric Effect: Intro

Emission of an electron due to the absorption of light

First experimental evidence for the quantization of light UBC – 2005

Andrea Damascelli The Photoelectric Effect: History

1887 Hertz finds Maxwell’s waves; and something else

Receiver

Screen

Transmitter

The small RECEIVER SPARK was more UBC – 2005 vigorous when the receiver was exposed to the Andrea ultraviolet light form the TRANSMITTER SPARK Damascelli The Photoelectric Effect: History

1902 von Lenard varies the intensity and color of the light

Material Dependence

The NUMBER of electrons is proportional to the INTENSITY

UBC – 2005 2 The maximum Ekin=½ mv is proportional to the FREQUENCY Andrea Damascelli The Photoelectric Effect: History

1905 Einstein’ hypothesis: light quanta with E = hn = hc / l

E = hn h = 6.63x10-34 Jsec = 3.89x10-15 eVsec V Ekin = hn - W

W

Solid Vacuum

2 The maximum Ekin=½ mv is proportional to the FREQUENCY but depends also on the material work function W UBC – 2005

Andrea The NUMBER of electrons is proportional only to the INTENSITY Damascelli The Photoelectric Effect: History

1887 Heinrich Hertz

1897 Joseph Thomson: “for the theoretical and experimental 1906 investigations on the conduction of electricity by gases”

1888 Wilhelm Hallwachs

1902 Philipp von Lenard: 1905 “for his work on cathode rays”

1905 Albert Einstein: “for his services to Theoretical Physics, 1921 and …. for his discovery of the law of the photoelectric effect”

UBC – 2005 1916 Robert Millikan: “for his work on the elementary 1923 charge of electricity and on the photoelectric effect” Andrea Damascelli Einstein’s hypothesis is too revolutionary

In 1913 Einstein was elected to the Prussian Academy of Sciences and appointed to a research position in Berlin. In his nomination speech to the Prussian Academy, Planck says:

"Summing up, we may say that there is hardly one among the great problems in which modern physics is so rich, to which Einstein has not made an important contribution.”

“That he may sometimes have missed the target in his speculations, as for example, in his hypothesis of light quanta, cannot really be held too much against him, for it is not possible to introduce fundamentally new ideas, even in the most exact UBC – 2005 sciences, without occasionally taking a risk". Andrea Damascelli Scientific application: Spectroscopy

Electron Spectroscopy for Chemical Analysis (ESCA)

Kai Siegbahn: 1981

“for his contribution to the development

UBC – 2005 of high-resolution electron spectroscopy”

Andrea Ekin EB Damascelli Understanding the Solid State: Electrons in Reciprocal Space

Wave functions Allowed electronic states in a 1D lattice Repeated-zone scheme

EF

1D chain of atoms Second First Second Brillouin Brillouin Brillouin zone zone zone Understanding the Solid State: Electrons in Reciprocal Space

Many properties of a solids are

determined by electrons near EF (conductivity, magnetoresistance, Allowed electronic states superconductivity, magnetism) Repeated-zone scheme (E ,k)

EF

Only a narrow energy slice around Second First Second EF is relevant for these properties (kT=25 meV at room temperature) Brillouin Brillouin Brillouin zone zone zone Electronic Properties of Complex Systems

Angle Resolved PhotoElectron Spectroscopy FIRST EVIDENCE FOR THE QUANTIZATION OF LIGHT!

Velocity and direction of the electrons in the solid

Low-energy Electronic Structure Macroscopic Physical Properties Superconductivity, Magnetism, Density Waves, ....

X-ray diffraction Photoemission Interaction Effects between Electrons : “Many-body Physics”

Many-body effects are due to the interactions between the electrons and each other, or with other excitations inside the crystal :

1) A “many-body” problem : intrinsically hard to calculate and understand 2) Responsible for many surprising phenomena : Superconductivity, Magnetism, Density Waves, ....

Non-Interacting Interacting

Courtesy of Kyle Shen AngleA “Simple”-Resolved Example : MetalPhotoemission Surfaces (Cu and Ag) Spectroscopy

K = p = Ekin

Ekin, J, j

Vacuum Conservation laws Solid

Ekin EB K k AARPES: “Simple” Example One : -MetalStep Surfaces vs Three (Cu and- StepAg) Model

Photoemission Intensity I(k,w)

One-step model AARPES: “Simple” Example One : -MetalStep Surfaces vs Three (Cu and- StepAg) Model

Photoemission Intensity I(k,w)

One-step model Three-step model A “Simple”ARPES: Example The : Metal Sudden Surfaces (CuApproximation and Ag)

Photoemission Intensity I(k,w)

: Sudden approximation

: One Slater determinant

Excitation in the solid Vacuum Spectrum A “Simple”ARPES: Example Role : Metal of Surfaces the Cr (Cuystal and Ag) Potential

Photoemission Intensity I(k,w)

: Sudden approximation

: One Slater determinant

Excitation in the solid Vacuum Spectrum A “Simple”ARPES: Example Role : Metal of Surfaces the Cr (Cuystal and Ag) Potential

G. D. Mahan, Phys. Rev. B 2, 4334 (1970). ‘‘In a nearly-free electron gas, optical absorption may be viewed as a two-step process. The absorption of the photon provides the electron with the additional energy it needs to get to the excited state. The crystal potential imparts to the electron the additional momentum it needs to reach the excited state. This momentum comes in multiples of the reciprocal-lattice vectors G: So in a reduced zone picture, the transitions are vertical in wave-vector space. But in photoemission, it is more useful to think in an extended-zone scheme”.

Excitation in the solid Vacuum Spectrum ARPES:A “Simple” Three Example-step : Metal Model Surfaces & Sudden (Cu and Ag) Approximation

Photoemission Intensity I(k,w)

: Sudden approximation

: One Slater determinant

Excitation in the solid Vacuum Spectrum ARPES: Energetics and Kinematics

Ekin, J, j

Energy Conservation

Ekin EB Momentum Conservation

k|| K|| Ekin J ARPES: Energetics and Kinematics

Electrons in Reciprocal Space

k Ekin, J, j ||

kF

EF EB

Energy Conservation

Ekin EB

Momentum Conservation K||

k|| K|| Ekin J

EF Ekin ARPES: Interacting Systems

A. Damascelli, Z. Hussain, Z.-X Shen, Rev. Mod. Phys. 75, 473 (2003)

Photoemission intensity:

In general NOT orthogonal

ARPES: The One-Particle Spectral Function

A. Damascelli, Z. Hussain, Z.-X Shen, Rev. Mod. Phys. 75, 473 (2003)

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

Single-particle spectral function

S(k,w) : the “self-energy” captures the effects of interactions Many-Cody Correlation Effects in Sr2RuO4

Single-particle spectral function

EF Energy

Momentum

N.J.C. Ingle, K.M. Shen, A. Damascelli et al., PRB 72, 205114 (2005) Quantum Materials Spectroscopy Center at CLS Parallel multi l l l Angle Improved Improved Improved now past - data momentum resolution energy resolution Resolved PhotoemissionSpectroscopy D E (meV) - 20 acquisition efficiency - 2 angle recording - - 10 40 0.2° Dq 2°

Momentum Binding Energy Sr 2 RuO 4 SSRL Beamline 5-4 : NIM / Scienta System

DE (meV) Dq 2-10 0.2°

NIM/SCIENTA System Au sample hn=22.7 eV T=10 K

Total Resolutionresolution

Intensity (a.u.) 5.05.0 meVmeV

20 10 0 -10 Binding Energy (meV) • High energy resolution DE<1meV • High angular precision ± 0.05º • Low base temperature ~ 2 K • Photon energies

H2, He, Ne • Polarization control linear

• Ultra-high vacuum ~ 10-11 torr

• Surface / Thin films

• Low Energy Electron Diffr. AdvantagesARPES: and AdvantagesLimitations of ARPES and Limitations

Advantages Limitations

• Direct information about the electronic states!

• Straightforward comparison with theory - little or no modeling.

• High-resolution information about BOTH energy and momentum • Not bulk sensitive • Surface-sensitive probe • Requires clean, atomically flat • Sensitive to “many-body” effects surfaces in ultra-high vacuum

• Can be applied to small samples • Cannot be studied as a function of (100 mm x 100 mm x 10 nm) pressure or magnetic field

Courtesy of Kyle Shen AdvantagesARPES: and LimitationsSurface of ARPESvs Bulk Sensitivity

Mean-free path for CeRu Si excited electrons 2 2 TK=1000K

HeIa 21.2 eV

o 10 A CeRu2 TK=22K

Seah, Dench et al., SIA 1, 2 (1979) Sekiyama et al., Nature 403, 396 (2000) Direct Band Structure Visualization

Courtesy of Eli Rotenberg Advanced Light Source - Berkeley Electron-phonon and Electron-magnon coupling? OPTICS Ionic charge of 4??

FeSi

NO! the large effective charge is due to electron-phonon coupling

Damascelli et al., PRB 55, R4863 (1997) Electron-phonon and Resonance Bonding 1/2 Electron-magnon coupling? Y=[FII + FII]/(1+a)

FI

FII

Lattice vibrations lead to charge redistribution NO! the large effective charge is due to electron-phonon coupling

Damascelli et al., PRB 55, R4863 (1997) Electron-phonon and Resonance Bonding 1/2 Electron-magnon coupling? Y=[FII + FII]/(1+a)

FI

FII

Lattice vibrations lead to charge redistribution NO! the large effective charge is due to electron-phonon coupling

Damascelli et al., PRB 55, R4863 (1997) Electron-phonon and Electron-magnon coupling?

Phonon + 2 magnons! Electric dipole + DS=0

Gruninger et al., Phys. Rev. B 62, 12422 (2000) Lorenzana, Sawatzky, PRL 74, 1867 (1995) Electron-phonon and Mona Berciu Electron-magnon coupling? ARPES

Re (Self Energy) Im (Self Energy) Many-Cody Correlation Effects in Sr2RuO4

Single-particle spectral function

EF Energy

Momentum

N.J.C. Ingle, K.M. Shen, A. Damascelli et al., PRB 72, 205114 (2005) Tom Devereaux Electron-phonon and Z.X. Shen Electron-magnon coupling? ARPES Dressing of quasiparticles in high-Tc superconductors Sudden approximation

The N-1 system But the projection of final eigenstates don’t change on initial states does!

Adiabatic Sudden Koralek et al.,PRL 96, 017005 (2006)

The intensity changes but not the pole structure!