* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code | 9360-0137/06 | |||||
---|---|---|---|---|---|---|

Number of ECTS Credits Allocated | 4 ECTS credits | |||||

Type of Course Unit * | Optional | |||||

Level of Course Unit * | Second Cycle | |||||

Year of Study * | ||||||

Semester when the Course Unit is delivered | Summer Semester | |||||

Mode of Delivery | Face-to-face | |||||

Language of Instruction | Czech, English | |||||

Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester | |||||

Name of Lecturer(s) | Personal ID | Name | ||||

LEG0015 | Ing. Dominik Legut, Ph.D. | |||||

Summary | ||||||

Student is introduced into the field of the state of the art first principles methods to calculate electronic structure of solids, employing number of approximations as well as the to learn about the limits of the methodology. Following theoretical treatment of many physical quantities based on simple models, the practic training to obtain the same quantities from first principles calculations will be utilized. | ||||||

Learning Outcomes of the Course Unit | ||||||

Student is introduced into the field of the state of the art first principles methods to calculate electronic structure of solids, employing number of approximations as well as the to learn about the limits of the methodology. Following theoretical treatment of many physical quantities based on simple models, the practic training to obtain the same quantities from first principles calculations will be utilized. | ||||||

Course Contents | ||||||

THEORY
1. Introduction to electronic structure of solids 2. Symmetry of crystals and its relation to he electronic struture 3. Density functional theory - foundation of first-principles (ab initio) calculations 4. State-of-the-art methodology, approximations and limits of ab initio 5. Exchange and correlations approximaions, localization and orbial polarizatin, Hubbard model 6. Phase stability, enthalphy of formation, determination of the elastic constants, pressure induced transformations, mechanical criteria of stability 7. Phonons (lattice vibrations). Dynamical critera of crystalline stability, thermal expansion, lattice specific heat, thermodynamical quantities 8. Magnetism and electronic structure, Stoner moel, rigid band model, Heiseneberg model for magnetism, exchange and Zeeman splitting 9. Spin-orbit interaction and its effect on electronic structure, magnetism (easy and hard axis), phase stabiliy, magneto-crystalline anisotropy 10. Optical properties of solids, selection rules in dipole approximation, dielectric tensor, Kubo formula, joint density of states and Kramers-Kronig relations, magneto-optical interactions PRACTICAL sessions 11. Determination mechanical properties of transitional cubic metals, limits of elastic shear and volue moduli, Young modulus, Poisson ratio and elastic anisotropy from single elastic constants 12. Lattice vibrations (phonons) calculations for Si, phonon density of stateas and dispersion relation, determination of thermodynamical properties like lattice specific heat, entropy etc. 13. Magnetic ordering, ferro, antiferro-, ferri, etc. Decomposition of total moment into spin and orbital contributions, determination of magneto-crystalline anisotropy (effect of spin-orbit interaction) 14. Calculations of optical and magneto-optical properties, determinatin of dielectric tensor elements based on Kubo formula, absorption and dispersion in UV-VIS an X-ray energy range for 3d metals, calculations of Kerr rotation and ellipticity | ||||||

Recommended or Required Reading | ||||||

Required Reading: | ||||||

Charles Kittels, Introduction to Solid State Physics, Wiley (1985).
N. Ashcroft, N. Mermin, Solid State Physics, Cengage Learning (1976). R. M. Martin, Electronic Structure – Basic Theory and Practical Methods, Cambridge University Press (2004). | ||||||

Úvod do fyziky pevných látek, Charles Kittel, Academia Praha (1985).
Solid State Physics, N. Ashcroft, N. Mermin, Cengage Learning (1976). Electronic Structure – Basic Theory and Practical Methods, R. M. Martin, Cambridge University Press (2004). | ||||||

Recommended Reading: | ||||||

P. M. Chaikin, T. C. Lubensky, Principles of Condensed Matter Physics, Cambridge Press (2000).
J. Singleton, Band Theory and Electronic Properties of Solids, Oxford Master Series in Physics (2001). S. Blundell, Magnetism in Condensed Matter, Oxford Master Series in Physics (2001). J. Stohr, H. C. Siegmann, Magnetism: from Fundamentals to Nanoscale Dynamics, Springer (2006). M. Fox, Quantum Optics, Oxford Master Series in Physics (2006). | ||||||

Principles of Condensed Matter Physics, P. M. Chaikin, T. C. Lubensky, Cambridge Press (2000).
Band Theory and Electronic Properties of Solids, J. Singleton, Oxford Master Series in Physics (2001). Magnetism in Condensed Matter, S. Blundell, Oxford Master Series in Physics (2001). Magnetism: from Fundamentals to Nanoscale Dynamics, J. Stohr, H. C. Siegmann, Springer (2006). Quantum Optics, M. Fox, Oxford Master Series in Physics (2006). | ||||||

Planned learning activities and teaching methods | ||||||

Lectures, Individual consultations, Tutorials, Project work | ||||||

Assesment methods and criteria | ||||||

Tasks are not Defined |