Solid state theory

Objectives of the course

Students recognize the pretending chapters of solid state theory which can be used in analysis of synchrotronic measurements on crystal structures.

Prerequisites

Not required.

Assessment methods

Written exam.

Course contents

1. Quantum statistical mechanics
   • Thermodynamic guantities
   • Fermi-Dirac statistics
   • Bose-Einstein statistics
2. Free-electron gas
   • Fermi levels
   • Thermodynamic properties
3. Electron levels in a periodic potential: general properties
   • Bloch theorem
   • Brillouin zones
   • Free electron bands in 1, 2 and 3 dimension
   • Outline of group theory and symmetry of wave functions
   • Symmetry operations in crystals
   • Symmetry properties of energy bands
4. Energy bands in crystals
   • Weak binding approximation
   • Tight binding method
   • Wannier functions
   • Hartree and Hartree-Fock approximations
   • Fermi surface
   • Band structure of selected metals
5. Quantuum transport theory
   • Conduction
   • Cyclotron resonance
   • Hall effect and quantum Hall effect
   • Landau quantization and de Haas-van Alphen effect
6. Semiconductors
   • Dynamics of electrons and holes in semiconductors
   • Donor and acceptor levels in semiconductors
   • The p-n junction
   • Transistors
   • Heterojunctions and outline of solid state lasers
7. The binding of solids
   • Ionic crystals
   • Covalent crystals
   • metallic bond: the jellium model
   • Molecular crystals
   • Hydrogen-bonded solid
8. Quantum theory of lattice vibrations
   • Normal vibration modes and phonon bands
   • Phonon level density
   • Comparison of lattice and electronic specific heats in the infrared and in the ultraviolet
   • Neutron scattering by a crystal
   • Mössbauer effect
   • Debye-Waller factor
9. Magnetism
   • Hund rules
   • Diamagnetism and paramagnetism of the free atom
   • Heisenberg exchange Hamiltonian
   • Ferromagnetism, antiferromagnetism, ferrimagnetism
   • Magnetic domains
   • Ising model in 2 and 3 dimensions, order/disorder transitions
10. Superconductivity
    • Bardeen-Cooper-Schrieffer (BCS) theory
    • Ginzburg-landau theory
    • Flux quantization
    • Josephson effect

Recommended reading

• C. Kittel, ISSP, Wiley, New York 1987
• Aschroft & Mermin,SSP, W. Harrison Solid state theory