Solid State Theory
0800-TECIS
1. Symmetry of crystals.
a. introduction to group theory
b. translation symmetry
c. point groups and rotation group
d. Bravais lattice, physical lattices
e. space groups
f. theory of representations
g. reciprocal lattice
h. wave vector group
2. Chemical bonds and relation to the lattice types
a. the ionic bond
b. the covalent bond
c. hybridization of atomic orbitals
d. the Van dr Waals bond
3. Adiabatic approximation
4. One-electron approximation
5. Hartree-Fock method
6. Bloch theorem
7. Periodic boundary conditions
8. Methods in the band theory
a. free electrons
b. nearly free electrons
- the appearance of the energy bands
- metals and semiconductors
- the concept of the effective mass
- the Fermi level
- the Fermi surface
c. tight-binding theory
- the appearance of bands
- 1D lattice
- 2D lattices (examples, graphene)
- 3D lattices
d. the kp method
e. effective mass tensor
f. pseudopotentials method
g. some other methods (cellular, OPW, APW)
9. The influence of the electric and magnetic fields
10 Lattice vibrations
a. Debye model
b. discrete model - optical and acoustic bands
c. normal modes, quantization and phonons
d. scattering processes
11. Basic introduction to superconductivity
Total student workload
- classes realized with professor/lecturer: 60 per week, i.e., 40 - lectures, 20 - exercises/practice;
- time needed to pass the exam: 40 h;
- time needed to be well prepared for evaluation: 25 h
Learning outcomes - knowledge
W1 - The graduate has basic knowledge of physics corresponding to the second cycle programme level as well as advanced knowledge of a selected area of physics, in particular: has knowledge about crystaline structure and symmetry of the solid state and their relation with physical properties of crystals. Has knowledge about trends and achievments in some areas of physics and its applications, in particular about graphene and superconductivity. (Physics K_W01);
W2 - The graduate has in-depth knowledge of physics within the selected specialisation. Has basic knowledge on quantum physics in application to the solid state. In particular, has knowledge about: (a) group theory in the solid state physics, (b) fundamental approximations of quantum physics used in the theory of solid state, (c) methods of description of the electronic structure of crystals, (d) methods of description of elstic waves and phonons in crystals. (Physics K_W05).
Learning outcomes - skills
K1 - The graduate is able to use fundamentl methods in problem-solving and conclusive reasoning. Is able to use fundamental mathematical formalism for the description of the properties of the electronic structure of the solid state (Physics K_U01, K_U03). In particular, the graduate is able to relate the Bloch theorem with the translational symmetry and the band electronic structure of crystals.
K2 - The graduate is able to find relevant information in specialist literature and is able to reconstruct the reasoning taking into account the assumptions and approximations made (Physics K_U04).
K3 - The graduate is able to use the language of mathematisc for the description of physical processes in the condensed matter. (Physics K_U03). In particular, she/he can define mathematical forms of basic operators in the theory of many-elecctron systems.
Learning outcomes - social competencies
K1 - The graduate knows the level of his or her knowledge, skills and limitations; is able to formulate questions adequately. The graduate understands the need for further education (Physics K_K01).
K2 - The graduate is aware of the social aspects and responsibility for practical applications of her/his knowledge (K_K02).
K3 - The graduate understands the need to spread and promote the knowledge of physics, including the latest scientific and technological developments (Physics K_K04).
Teaching methods
Lecture: multimedia presentation of the fundamentals of the theory of solid state.
Practice: exercises covering group theory, theory of representations,chemical bonds in crystals, band theory of crystals, elsatic waves and phonons in crystaline lattice.
Expository teaching methods
- informative (conventional) lecture
Exploratory teaching methods
- practical
- classic problem-solving
Type of course
compulsory course
Prerequisites
Elementary quantum mechanics and introduction to solid state physics
Course coordinators
Term 2023/24L: | Term 2025/26L: | Term 2022/23L: | Term 2024/25L: |
Assessment criteria
Practice: a couple of tests (exercises to solve);
Lecture: written exam, N=10-15 questions (problems) covering all the material. Answers to questions are evaluated in the scale 0-3 (or 0-1). To pass the exam one has obtain more than 50% of the total number of points.
The table of notes:
< 50% - 2,
(50-60%) - 3
(61-70%) - 3+
(71-80%) - 4
(81-90%) - 4+
(91-100%) - 5
Practical placement
Bibliography
1. G. Burns, Solid State Physics, Academic Press, London 1985
2. H.Ibach and H.Luth, Solid-State Physics, Springer
3. Any textbook about group theory in physics/chemistry, e.g., M.Dresselhaus, G.Dresselhaus, A.Jorio, Group Theory - Application to the Physics of Condensed Matter, Springer 2008
Additional information
Additional information (registration calendar, class conductors,
localization and schedules of classes), might be available in the USOSweb system: