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PřF:F7301 Element. excitation in solids - Course Information

## F7301 Elementary excitation in solids

**Faculty of Science**

Autumn 2018

**Extent and Intensity**- 2/0/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
**Teacher(s)**- prof. Mgr. Dominik Munzar, Dr. (lecturer)

prof. Mgr. Dominik Munzar, Dr. (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 **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 the course is directly associated with****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 higly 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**- 1. Introduction. (a) Excited states in solids. (b) The concept of elementary excitations, quasiparticles and collective excitations, examples. 2. Quasiparticles in Fermi liquids - three approaches. (a) Hartree-Fock theory. (b) Landau's theory of Fermi liquids. (c) Method of Green's functions. 3. One-electron description of electronic states in crystalline solids. (a) Bloch theorem in a broader context, classification of electronic states based on group theory. (b) Band structure and density of states. (c) Examples of band structures. (d) Methods of measuring the band structure. 4. Methods for calculating the band structure. (a) A survey of the methods, classification of the methods according to the choice of the effective potential and according to the method of solving the Schroedinger equation. (b) Empirical tight-binding method, a unified approach to the electronic structure of atoms, molecules, and solids. (c) Augmented plane waves and pseudopotentials. 5. One-electron theory in the presence of perturbing fields. (a) Effective Hamiltonian and semiclassical approximation. (b) Impurity states in semiconductors. (c) Dynamics of electrons in an external electric field. (d) Dynamics of electrons in a magnetic field. (e) Methods of measuring the Fermi surface. 6. Theory of lattice vibrations. (a) Equations of motion for a lattice in the harmonic approximation. (b) Dispersion relation, density of states, polarization vectors. (c) Quantum properties, phonons. (d) Methods of measuring the phonon dispersion relation. (e) Methods for calculating the dispersion relation. 7. Electron-phonon interaction. (a) Interaction Hamiltonian. (b) Scattering of electrons by phonons. (c) Influence of the electron-phonon interaction on the dispersion relations.

**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. Solution of a certain amount of problems by a student.
**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**- English
**Further Comments**- The course can also be completed outside the examination period.

The course is taught annually.

The course is taught: every week.

- Enrolment Statistics (recent)

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