The course aims at mastering the main concepts of the solid state theory such as properties of the phonon and electronic states, solid body interaction with the electromagnetic excitations and collective effects such as electron-phonon interaction and superconductivity.
1. Crystal lattice vibrations and phonon states.
- One-component chain quantization. Phonons.
- Two-component chain quantization. Аcoustic and optical phonons.
- Phonons in the three-dimensional crystal.
- Phonon-phonon interaction, anharmonic effects. Solid state heat capacity. Debye and Einstein approximations. Debye temperature.
2. Electronic states and electronic properties of the solid state.
- Electrons in periodic potentials. Bloch theorem. Main concepts of the electronic band structure. Metals, semiconductors and insulators.
- Nearly free electron model.
- Tight binding approximation.
- Electron effective mass. Inertial effective mass tensor.
- Density of states.
- Electron in a crystal under in the external magnetic field. Cyclotron mass.
- Electron statistics in solid state. Chemical potential for metals and semiconductors.
3. Electron-phonon interaction.
- Electron-phonon interaction for covalent crystals. Deformational potential method.
- Virtual phonon creation due to electron motion in the covalent crystal.
- Electron spectrum and effective mass renormalization in covalent crystals.
- Electron-phonon interaction in ionic crystals.
- Electron intraction with optical phonons. Pekar polaron.
4. Cooperative phenomena.
- Spin waves in ferromagnets. Magnons.
- Main properties of superconductors. Meissner effect.
- Bardeen-Cooper-Schrieffer theory (BCS).
- Superconducting ground state. Excited states of a superconductor. Experimental consqeuncies.
- Josephson effect.