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 photon in photon out electric dipole transition particle-hole excitations collective modes (phonons, magnons, plasmons) number of particles is conserved Photoemission photon in electron out electric dipole transition electron removal excitations collective modes? only as dressing of quasiparticles number of particles not conserved Electron transition Electron removal Particle-hole excitations of the N-particle system Single-particle excitations of the (N-1)-particle system
Optics Gruninger (1999)
Absorption coefficient in a semiconductor
Courtesy of
NiO is a charge transfer insulator
Courtesy of
NiO is a charge transfer insulator O 2p Jan Kunes Ni 3d(e g )
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. The photoelectric effect "On a heuristic viewpoint concerning the production and transformation of light" Annalen der Physik, 17 (1905), pp. 132-148. 1921 The special theory of relativity "On the electrodynamics of moving bodies Annalen der Physik, 17 (1905), pp. 891-921 UBC 2005 Mass-energy Equivalency E=mc 2 "Does the inertia of a body depend on its energy? Annalen der Physik, 18 (1905), pp. 639-41. 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 UBC 2005 First experimental evidence for the quantization of light Andrea Damascelli
The Photoelectric Effect: History 1887 Hertz finds Maxwell s waves; and something else Receiver Screen Transmitter UBC 2005 Andrea Damascelli The small RECEIVER SPARK was more vigorous when the receiver was exposed to the ultraviolet light form the TRANSMITTER SPARK
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 Andrea Damascelli The maximum E kin =½ mv 2 is proportional to the FREQUENCY
The Photoelectric Effect: History 1905 Einstein hypothesis: light quanta with E = hn = hc / l E = hn V h = 6.63x10-34 Jsec = 3.89x10-15 evsec E kin = hn - W W Solid Vacuum UBC 2005 Andrea Damascelli The maximum E kin =½ mv 2 is proportional to the FREQUENCY but depends also on the material work function W The NUMBER of electrons is proportional only to the INTENSITY
The Photoelectric Effect: History 1887 Heinrich Hertz 1897 Joseph Thomson: for the theoretical and experimental investigations on the conduction of electricity by gases 1906 1888 Wilhelm Hallwachs 1902 Philipp von Lenard: for his work on cathode rays 1905 1905 Albert Einstein: for his services to Theoretical Physics, and. for his discovery of the law of the photoelectric effect 1921 UBC 2005 Andrea Damascelli 1916 Robert Millikan: for his work on the elementary charge of electricity and on the photoelectric effect 1923
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 UBC 2005 Andrea Damascelli to introduce fundamentally new ideas, even in the most exact sciences, without occasionally taking a risk".
Scientific application: Spectroscopy Electron Spectroscopy for Chemical Analysis (ESCA) Kai Siegbahn: 1981 UBC 2005 Andrea Damascelli for his contribution to the development of high-resolution electron spectroscopy E kin E B
Understanding the Solid State: Electrons in Reciprocal Space Wave functions in a 1D lattice Allowed electronic states Repeated-zone scheme E F 1D chain of atoms Second Brillouin zone First Brillouin zone Second Brillouin zone
Understanding the Solid State: Electrons in Reciprocal Space Many properties of a solids are determined by electrons near E F (conductivity, magnetoresistance, superconductivity, magnetism) Allowed electronic states Repeated-zone scheme (E,k) E F Only a narrow energy slice around E F is relevant for these properties (kt=25 mev at room temperature) Second Brillouin zone First Brillouin zone Second Brillouin 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
Angle-Resolved A Simple Example : Metal Photoemission Surfaces (Cu and Ag) Spectroscopy K = p = E kin E kin, J, j Vacuum E kin K Conservation laws Solid E B k
A ARPES: Simple Example One-Step : Metal Surfaces vs Three-Step (Cu and Ag) Model Photoemission Intensity I(k,w) One-step model
A ARPES: Simple Example One-Step : Metal Surfaces vs Three-Step (Cu and Ag) Model Photoemission Intensity I(k,w) One-step model Three-step model
A Simple ARPES: Example The : Metal Sudden Surfaces (Cu Approximation 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 Crystal (Cu 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 Crystal (Cu 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-step Example : 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 E kin, J, j Energy Conservation E B E kin Momentum Conservation k K E kin J
ARPES: Energetics and Kinematics Electrons in Reciprocal Space E kin, J, j k k F E F E B Energy Conservation E B E kin Momentum Conservation k K E kin J K E F E kin
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) Photoemission intensity: I(k,w)=I 0 M(k,w) 2 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 Sr 2 RuO 4 Single-particle spectral function E F Energy Momentum N.J.C. Ingle, K.M. Shen, A. Damascelli et al., PRB 72, 205114 (2005)
Quantum Materials Spectroscopy Center at CLS
Angle-Resolved Photoemission Spectroscopy Parallel multi-angle recording Improved energy resolution Improved momentum resolution Improved data-acquisition efficiency DE (mev) Dq past 20-40 2 now 2-10 0.2 Momentum Sr 2 RuO 4 Binding Energy
SSRL Beamline 5-4 : NIM / Scienta System DE (mev) Dq 2-10 0.2 Intensity (a.u.) NIM/SCIENTA System Total Resolution resolution 5.0 mev Au sample hν=22.7 ev T=10 K 20 10 0-10 Binding Energy (mev)
High energy resolution DE<1meV High angular precision 0.05º Low base temperature ~ 2 K Photon energies H 2, He, Ne Polarization control linear Ultra-high vacuum ~ 10-11 torr Surface / Thin films Low Energy Electron Diffr.
ARPES: Advantages and Limitations Advantages and Limitations of ARPES Advantages Limitations Direct information about the electronic states! Straightforward comparison with theory - little or no modeling. High-resolution information about BOTH energy and momentum Surface-sensitive probe Sensitive to many-body effects Can be applied to small samples (100 µm x 100 µm 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 Courtesy of Kyle Shen
Advantages ARPES: and Limitations Surface of ARPES vs Bulk Sensitivity Mean-free path for excited electrons CeRu 2 Si 2 T K =1000K HeIa 21.2 ev 10 A o CeRu 2 T K =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 Electron-magnon coupling? Resonance Bonding Ψ=[Φ ΙΙ + Φ ΙΙ ]/(1+α) 1/2 Φ Ι Φ ΙΙ 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? Resonance Bonding Ψ=[Φ ΙΙ + Φ ΙΙ ]/(1+α) 1/2 Φ Ι Φ ΙΙ 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 Electron-magnon coupling? ARPES Mona Berciu Re (Self Energy) Im (Self Energy)
Many-Cody Correlation Effects in Sr 2 RuO 4 Single-particle spectral function E F Energy Momentum N.J.C. Ingle, K.M. Shen, A. Damascelli et al., PRB 72, 205114 (2005)
Electron-phonon and Electron-magnon coupling? ARPES Tom Devereaux Z.X. Shen Dressing of quasiparticles in high-tc superconductors
Sudden approximation The intensity changes but not the pole structure! The N-1 system eigenstates don t change But the projection of final on initial states does! Adiabatic Sudden Koralek et al.,prl 96, 017005 (2006)