Syllabus
* 1. Elements of group theory
Definition of a group, cosets, classes, factor groups. Theory of representations, irreducible representations, orthogonality theorems. Decomposition of a representation in irreducible components.
* 2. Structure of crystalline solids
Types of chemical bonds. Geometrical description of three-and two-dimensional crystal lattices, translational and point lattice symmetries. International and Schoenflies notation, syngony, crystallographic classes, space groups. Example: space group Oh and its subgroups. Example: Space group Td, table of characters, basis functions. Reciprocal lattice, Brillouin zones. Reciprocal-space representation of periodic functions.
* 3. Structure of solid surfaces
Bravais lattices in 2D, simple and centered lattices. Reciprocal lattice in 2D, the 1st Brillouin zone. Surface relaxation and reconstruction, some examples (Si(111) 7x7, GaAs(001) 2x4). Surface steps, roughening transition. Surface energy, the Wolff construction.
* 4. Ideal electron gas
Classical model of electron gas, transport properties. Qunatum model of electron gas, Fermi-Dirac statistics. Fermi energy, chemical potential, density of electron states. Response of the electron gas to external electromagnetic field - plasmons.
* 5. Electron gas in a crystalline solid
Electron in a periodic crystal field, one-, two-, and three-dimensional electron gas. Bloch theorem, energy bands. The Fermi surface in reduced and periodic zone scheme. Transport properties of Bloch electrons, effective mass. Basics of the methods of band structure calculation.
* 6. Surface electron states
Jellium model at a solid surface, surface charge. Free electrons in an one-dimensional continuum. Solution of the Schroedinger equation for a semi-infinite chain of atoms, surface electron states. Generalization to 3D. Surface states and band structure, two-dimensional gas of free carriers. Surface plasmons, Schottky barrier, FET transistor. Basic of the quantum Hall effects.
* 7. Vibrations of crystal lattices
Normal oscillation modes of a lattice, phonons. Quantum phonon statistics, phonons as elementary excitations. Heat capacity of a lattice, density of phonon states. Response of an ionic crystal to external electromagnetic field - polaritons.
* 8. Surface phonon states
Eigenoscillations of a semi-infinite anisotropic elastic continuum - Raleigh waves. Oscillations of a semi-infinite atomic chain, surface phonon states. Surface phonons in 3D. Interaction of the surface of a ionic crystal with electromagnetic waves - surface polaritons.
Annotation
The lecture presents a basic piece of information on quantities, phenomena and basic theoretical models in solid-state physics; the extent of the lecture is sufficient for experimentalists. Together with seminar, the lecture brings a comprehensive picture of solid-state physics that is sufficient for an interpretation of experiments and experimental data.
In the lecture, the emphasis is laid to classical chapters of solid-state physics, such as structure of crystalline solids, basic electronic properties (ideal electron gas, electrons in a periodic crystal filed) and phonons in lattices. Basic information is given on crystallography of surfaces, surface electron and phonon states.
Group theory and its application in solid-state physics will be discussed as well.