Syllabus
In order to describe vibrations of atoms we introduce such basic concepts of solids as the Brillouine zone, Born-Karman boundary conditions or energy dispersion bands. Within the second quantisation we evaluate for instance the phonon specific heat, the neutron diffraction and the Mössbauer effect.
Within the approximation of free electrons we evaluate the electronic specific heat, spin and orbital magnetic susceptibilities, de Haas-van Alphen effect and cyclotron resonance.
For electrons in real crystals we derive electronic energy bands from the Bloch theorem. Using Kane and Kronig-Penney models we explain the origin and meaning of specific featuers of these bands. Within the second quantisation we introduce a filling of bands which is responsible for a distinction between metals and isolators. A competition of physical processes leading to these two types of crystals is demonstrated on the Peierls transition.
Effects of an electro-electron interaction we demonstrate on the superconductivity. After a phenomenological introduction involving the thermodynamic description, the two-fluid model, the London's theory and the Ginzbur-Landau theory, we derive some properties from the microscopic model of Bardeen, Cooper and Schrieffer.
A systematic theory of interacting electrons we introduce only for the zero temperature. We derive Feynman diagrams for the Coulomb interaction. We evaluate the polarization operator, from which we obtain the screening and the plasma oscillation.
Annotation
Atomic vibrations are expressed in terms of bosonic fields (phonons), while electrons form a Fermi liquid embedeed in the periodic potential of nuclei. From these fields we evaluate elementary properties of crystals.