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PřF:F8800 Condensed matter physics I - Course Information

## F8800 Condensed matter physics I

**Faculty of Science**

Autumn 2014

**Extent and Intensity**- 3/1. 4 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
**Teacher(s)**- prof. Mgr. Dominik Munzar, Dr. (lecturer)

Mgr. Břetislav Šopík, Ph.D. (seminar tutor) **Guaranteed by**- prof. RNDr. Josef Humlíček, CSc.

Department of Condensed Matter Physics - Physics Section - Faculty of Science

Contact Person: prof. Mgr. Dominik Munzar, Dr.

Supplier department: Department of Condensed Matter Physics - Physics Section - Faculty of Science **Timetable**- Tue 15:00–17:50 Kontaktujte učitele
- Timetable of Seminar Groups:

**Course Enrolment Limitations**- The course is also offered to the students of the fields other than those the course is directly associated with.
**fields of study / plans the course is directly associated with**- Condensed Matter Physics (programme PřF, N-FY)

**Course objectives**- Description of excited states of solids could be expected to be more complicated than that of the ground state. This is certainly true for highly excited states, that are very different from the ground state. Most of the relevant properties of solids (e.g., thermal, electrical, optical properties), however, can be understood in terms of low energy excited states that are close to the ground state. Surprisingly, these states have a fairly simple structure: they can be viewed as consisting of a few building blocks that are called elementary excitations. The concept of elementary excitations will be introduced and the most important examples (quasielectrons, quasiholes, phonons, plasmons etc.) presented. At the end of the course students should be able to understand the concepts of elementary excitations, collective excitations etc., to apply these concepts when discussing results of simple models and/or experimental data, to solve simple related problems, e.g., to compute the electronic band structures of semiconductors and simple transition metals using the semiempirical tight-binding method or to compute the phonon dispersion relations using common semiempirical models.
**Syllabus**- I. Introduction. 1. Excited states and elementary excitations of simple models (Sommerfeld model, the common simple model of a semiconductor, ``chain'' of equal masses connected by strings). 2. Low-energy excited states of solids, relations between the ``real world" and the models. 3. The concept of elementary excitations, quasiparticles and collective excitations. 4. Solid state hamiltonian and the adiabatic approximation. 5. ``Second quantization''. II. Electronic subsystem. 1. The statement of the problem, the concept of one-particle approximation, description of the ground state and of elementary excitations at the Hartree-Fock level and at the DFT level. 2. Relation between the symmetry of a hamiltonian and the properties of its eigenfunctions, the Bloch theorem as a special case, the concepts of band structure and density of states. 3. Examples of band structures (simple metals, transition metals, semiconductors, oxide materials). 4. Methods of measuring the band structure and methods for calculating the band structure. 5. Dynamics of electrons in external fields: effective hamiltonian in the k-representation and in the R-representation, semiclassical approximation, examples (homogeneous electric field, impurity states in semiconductors, nanostructures, homogeneous magnetic field). III. Lattice subsystem. 1. Hamiltonian of the lattice and the harmonic approximation. 2. Classical approach: equations of motion, the ``Bloch theorem'' for the lattice states, dispersion relations, polarization vectors, examples. 3. Quantum effects. 4. Methods of measuring the phonon dispersion relation and methods for calculating the dispersion relation. IV. Electron-phonon interaction. 1. Interaction part of the hamiltonian. 2. Influence of the electron-phonon interaction on the dispersion relations and lifetimes of the quasiparticles. 3. Lattice contribution to the resistivity of metals. 4. Effective attractive interaction between quasielectrons resulting from the electron-phonon coupling. V. Introduction to superconductivity.

**Literature**- ANDERSON, P. W.
*Concepts in solids : lectures on the theory of solids*. Singapore: World Scientific, 1997. xiii, 188. ISBN 9810232314. info - ASHCROFT, Neil W. and N. David MERMIN.
*Solid state physics*. South Melbourne: Brooks/Cole, 1976. xxi, 826 s. ISBN 0-03-083993-9. info - MATTUCK, Richard D.
*A guide to Feynman diagrams in the many-body problem*. 2nd ed. New York: Dover Publications, 1992. xv, 429 s. ISBN 0-486-67047-3. info - CELÝ, Jan.
*Kvazičástice v pevných látkách*. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1977. 283 s. info

- ANDERSON, P. W.
**Teaching methods**- Lectures and class exercises.
**Assessment methods**- Oral examination. Solution of a certain amount of problems by a student, before the examination, is required. During the examination, students are requested to answer 3-5 questions concerning the topic of the course. The final evaluation reflects the degree of understanding the concepts and applications thereof.
**Language of instruction**- Czech
**Further Comments**- Study Materials

The course is taught annually.

- Enrolment Statistics (Autumn 2014, recent)
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