The Fundamentals of the Theory of the Electronic Structure of Crystals 1200-1STKRW7

1. The origin of the electronic energy bands in periodic systems.
2. Systems periodic in one and two dimensions. The analysis of the band structures of selected polymers (pi-electron polymers), carbon nanotubes, and the graphite plane (graphene) - within the framework of the Hückel model.
3. Systems periodic in three dimensions - crystals. The description of the three-dimensional crystal lattice: lattice primitive vectors and the Bravais lattice, elementary cell, structural motive. The point symmetry of crystal lattice and the types of the Bravais lattices. Reciprocal lattice and the propagation of waves in the crystal (the diffraction laws). Translation symmetry. Irreducible representations of the crystal translation group, the first Brillouin zone. The Bloch theorem. Space groups. The composite symmetry elements: screw axes and glide planes. The space group as the full symmetry group of a crystal. Symorphic and nonsymorphic space groups. Irreducible representations of the space group.
4. The theory of crystal orbitals and the band structure of a crystal. Building the Bloch orbitals from the atomic orbitals, the factorization of the matrix eigenvalue equations. The graphical representation of the band structure. The physical meaning of band energies, connection to experiment.

Type of course

elective monographs

Mode

Classroom

Prerequisites (description)

Needed competence: - using linear algebra (vectors, matrices) and differential and integrl calculus. Needed the knowledge of basic: - crystallography, - quantum chemistry (molecular orbital theory).

Learning outcomes

1. The acquitance with the description of systems periodic in one, two, and three dimensions.
2. The knowledge of the theory of symmetry of such systems.
3. Learning of what is the band structure of periodic systems.
4. Learning how to determine the band structures of simple polymers.
5. Uderstanding of the basic terms associated with the electronic structure of polymers and crystals, which are found in theoretical and experimental works.

Assessment criteria

1. The initial condition: the presence on the majority of lectures.
2. The basic condition: solving (by oneself) two problems on the band theory of polymers.
3. The auxiliary condition: a qualifying talk after solving the problems.

Bibliography

1.J. M. Ziman, "Principles of the Theory of Solids", Cambridge University Press, Cambridge, 1972.
2.C. Kittel, "Introduction to Solid State Physics", Wiley, New York, 1966.

Additional information

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Description of 1200-1STKRW7 in USOSweb