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 Angle-Resolved Photoemission Spectroscopy Sr2RuO4 Parallel multi-angle recording l Improved energy resolution l Improved momentum resolution l Improved data-acquisition efficiency DE (meV) Dq Momentum past 20-40 2° now 2-10 0.2° Binding Energy 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