Physics 250-06 “Advanced Electronic Structure” Lecture 1. Theoretical Background Contents: 1. Historical Overview. 2. Basic Equations for Interacting Electrons.

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Presentation transcript:

Physics “Advanced Electronic Structure” Lecture 1. Theoretical Background Contents: 1. Historical Overview. 2. Basic Equations for Interacting Electrons.

Overview. Electronic structure as a field of condensed matter physics: 1920es: Band Theory of Independent Electrons of Felix Bloch. Insulators, Semiconductors, Metals. Emergence of Quantitative Calculations. Works of Hartree (self- consistent electrostatic potentials) and Fock (antisymmetrized determinant) on atoms. 1930es: Method of Wigner and Seitz (1933) and electronic states of Na metal. Augmented plane waves of Slater (1937). Pseudopotentials by Fermi.

Overview. 1950es: First calculations of electronic states by Herman, Callaway, Slater for atoms and crystals. 1960es: Density Functional Theory by Hohenberg, Kohn, Sham 1970es: Linear Methods of Band Theory for solving Schroedinger’s equation by Ole Andersen.

Overview. 1980es: First self-consistent programs for electronic structure calculations developed. Energy bands and properties of many materials have been computed. 1990es: Discovery of High-Temperature Superconductivity: Phonons and electron phonon interactions, importance of correlations in electronic structure. Simulations of more complex materials, Car Parinello molecular dynamics

Overview. Current Research in Electronic Structure Quantitative theories for correlated materials. Quantitative theories for complex systems (nano, bio).

Overview. Fundamental variables to study ground state properties: Density Total Energy Volume Pressure Fundamental questions: Nature of bonding Equations of state Phase transitions under pressure Theory of Elasticity Theory of Magnetism, Ferroelectricity Phonons, Magnons Surfaces, Interfaces, Defects.

Overview. Fundamental variables to study excitations: One-Electron Energy Bands Wave Functions and transition matrix elements Fundamental questions: Angle Resolve Photoemission Optical Spectroscopy Excitons Core Level Spectroscopy Transport Properties Superconductivity

Basic Equations for Interacting Electrons Many Body Hamiltonian and Schroedinger’s equation Ground State and Excited States Hellmann-Feynman Theorem Coulomb Interactions: Hartree approximation and self-consistent theory Exchange and Hartree-Fock approximation. Koopmans’ theorem Beyond Hartree-Fock: correlation effects

Periodic Solids and Electron Bands Crystal structures, primitive translations and basis vectors. Brillouin zone, high symmetry directions Bloch theorem, band of eigenvalues Symmetry considerations, irreducible BZ. Integration over BZ: Special point method. Tetrahedron method.

Uniform Electron Gas and Simple Metals. Model of uniform electron gas, r s and density as two parameters Hartree-Fock approximation for eigenvalues. Dielectric screening, Friedel oscillations Hartree-Fock potential for uniform electron gas. Slater x-Alpha method as a prerequisite to DFT