Předmět Elementary excitations in Solids (Elementární excitace v pevných látkách) (F7301)

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Materiál	Typ	Datum	Počet stažení

Cíl

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 groundstate. 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 tounderstand 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.

Osnova

1. Introduction.(a) Excited states in solids.(b) The concept of elementary excitations, quasiparticlesand collective excitations, examples.2. Quasiparticles in Fermi liquids - three aproaches.(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 methodsaccording to the choice of the effective potential andaccording 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 interactionon the dispersion relations.

Literatura

ANDERSON, P. W. Concepts in solids :lectures on the theory of solids. Singapore: World Scientific, 1997. xiii, 188. ISBN 981-02-3231-4. infoASHCROFT, Neil W. a N. David MERMIN. Solid state physics. South Melbourne: Brooks/Cole, 1976. xxi, 826 s. ISBN 0-03-083993-9. infoMATTUCK, 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. infoCELÝ, Jan. Kvazičástice v pevných látkách. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1977. 283 s. info

Garant

prof. RNDr. Josef Humlíček, CSc.

Vyučující

doc. Mgr. Dominik Munzar, Dr.doc. Mgr. Dominik Munzar, Dr.