Theoretical Solid-State Physics Course, University of Basel, Fall Semester 2012
Lecturer: Dr. Vladimir M. Stojanović
Course Description
This course covers basic many-body theory of condensed-matter systems. It is intended for master students and
requires knowledge of quantum mechanics at an advanced undergraduate level, as well as familiarity with basic concepts of solid-state physics.
Approximately half ot the lecture material is based on the book "Many-body quantum theory in condensed matter physics"
by H. Bruus and K. Flensberg, while the rest is contained in the notes prepared by the lecturer.
Problem Sessions
Teaching Assistants: Patrick Hofer, Samuel Aldana, Dr. Gerson Ferreira, Dr. Rakesh Tiwari
Problem Sheets (in PDF format)
Problem Sheet 0 ( Hellman-Feynman theorem and its application to Bloch electrons ) |
Problem Sheet 1 ( Useful operator identities; Fermionic Bogoliubov transformation ) |
Problem Sheet 2 ( Tight-binding electrons on a checkerboard lattice; Critical points in the density-of-states ) |
Problem Sheet 3 ( Spin-polarized electron gas; Second-order perturbation theory for the electron gas ) |
Problem Sheet 4 ( Spin-orbit interaction in the 2DEG; Tight-binding model with Rashba spin-orbit coupling ) |
Problem Sheet 5 ( Spectral function for bosons; Single level coupled to the continuum ) |
Problem Sheet 6 ( Green's function for topological insulators; Momentum dependence of electron-phonon coupling ) |
Problem Sheet 7 ( Properties of thermal two-time correlation functions; Quantum diffusion formalism and optical conductivity ) |
Problem Sheet 8 ( Zero-sound collective mode in charge-neutral Fermi gases; Plasmon dispersion in an interacting electron gas ) |
Problem Sheet 9 ( Excitations in a two-dimensional electron gas ) |
Problem Sheet 10 ( Hubbard sectors; From the t-J model to the Heisenberg model; Holstein-Primakoff transformation ) |
Lecture Notes
Tentative Course Outline
I. Introduction- Second quantization
- Electrons in periodic potentials
- Lattice models
- Jellium approximation; non-interacting electrons in the jellium model
- Electron-electron interactions in Rayleigh-Schroedinger perturbation theory
- Spin-polarized electron gas and its region of stability
- Failure of second-order perturbation theory
- Physical origins of the spin-orbit interaction; implications for the bulk band structure of semiconductors within the framework of the method
- Two-dimensional electron gas (2DEG)
- Rashba and Dresselhaus-type spin-orbit interactions
- Green's function for the one-particle Schroedinger equation
- Single-particle Green's functions for many-body system
- Equation-of-motion theory for Green's functions
- Born-Oppenheimer approximation; the self-consistent electron-nuclear problem
- Lattice dynamics in the discrete (atomistic) model; quantization into phonons; acoustic and optical phonon modes
- Non-adiabatic corrections: electron-phonon coupling; inelastic scattering rates
- Polaron: the concept and generic features
- The general Kubo linear-response formalism; Kubo formula for the dielectric function
- Lindhard's polarization function for a non-interacting electron gas
- The random phase approximation (RPA): example of the polarization function of an interacting Fermi gas
- Zero-sound collective mode
- Plasmon mode in Fermi systems with Coulomb interaction
- Static screening in an interacting electron gas; Friedel oscillations
- Notion of the continuum and fields
- Long-wavelength modes: example of lattice dynamics in the continuum approach
- Broken continuous symmetry and Goldstone modes
- Three dimensions: Fermi liquid theory
- Microscopic basis of Fermi liquid theory
- Interacting electrons in one dimension
- The spinless Luttinger-Tomonaga model
- Examples of strongly-correlated electron systems; the Hubbard model
- The Hubbard model at half-filling and the Mott-Hubbard insulators
- Ferromagnetic and antiferromagnetic orders: similarities and differences, low-energy excitations
- Quantization of spin waves: the Holstein-Primakoff transformation; quantum fluctuations in the Neel state
- Spin ordering at weak coupling: spin density waves