Solid state theory

Enrollment into the program.

Positive result from a seminar is necessary to enter the oral exam.

Symmetries in crystals: Symmetry operations  in crystals. Point groups. Space groups. Representations. Electron states in crystals. Time-reversal symmetry,

Lattice vibrations: Electron-ion coupling, adiabatic approximation, vibronic coupling, Jahn-Teller effect. Matrix of lattice spring constants. Classical lattice vibrations, acoustic and optical branches. Theory of elasticity. Quantisation of lattice vibrations. 

Phonon processes: Dynamical structure factor. Elastic and inelastic scattering.

Electrons in Crystals: Single-particle effective theories. Density functional theory. Spin-orbit coupling. Topological insulators.

Transport: Electron motion in Wannier picture. Boltzmann equation, scattering time. Conductivity tensor, magnetoresistivity, Hall constant.

Fermi liquid theory: Adiabaticity, quasiparticle concept. Quasiparticle lifetime. Quasiparticle distribution. Residual interactions and Landau phenomenological parameters. Specific heat, compressibility, spin susceptibility, effective mass.

Matter-light interaction: Optical transitions. Excitons.

Dielectric constant: Lindhardt equation, derivation using linear response formalism. Static screening, screening length. Dynamic screening and plasma oscillations. Dielectric constant of semiconductor. Connection between dielectric constant and conductivity.

Strongly correlated electrons: Hubbard model, Mott insulator. Fermi and non-Fermi liquids, bad metals, strange metals.

Magnetic properties: Spin models, ground and excited states. Magnetic space groups. Magnetic oscillations (de Haas-van Alphen effect). Magnetic impurities. Spin liquids.

Superconductivity: Attractive interaction between electrons, Cooper pairs. Ground state of a superconductor – BCS theory. BCS wavefunction and ored parameter. Excited states of a superconductor. Andreev reflection, proximity effect. Topological superconductors.

- N.W. Ashcroft, N.D. Mermin: Solid State Physics, Holt-Saunders 1976.
- M.P. Marder: Condensed Matter Physics, J. Wiley, 2000.
- G. Burns: Solid State Physics, Academic Press, 1990.
- J.M. Ziman: Principles of the Theory of Solids, Cambridge University Press 1964,1972.
- C. Kittel: Quantum Theory of Solids, J. Wiley 1963.
- O. Madelung: Introduction to Solid-State Theory, Springer-Verlag 1978.
- W. Harrison: Solid State Theory, McGraw-Hill, 1970.

- S. M. Girvin, K. Yang: Modern Condensed Matter Physics, Cambridge University Press, 2019.

- M. Glazer, G. Burns: Space Groups for Solid State Scientists, Academic Press, 2016.

- T. Inui, Y. Tanabe, Y. Onodera: Group Theory and Its Applications in Physics, Springer, 1976.

- G. D. Mahan: Condensed Matter in a Nutshell, Princeton University Press, 2011.

- U. Roessler: Solid State Theory: An Introduction, Springer-Verlag, 2009.

- M. L. Cohen, S. G. Louie: Fundamentals of Condensed Matter Physics, Cambridge University Press, 2016.

- D. Arovas: Lecture Notes on Condensed Matter Physics, UCSD, 2023.

Advanced  understanding of crystal symmetries dielectric, magnetic,  mechanical properties of matter,  collective ordered states and phase transitions at low temperatures.

Knowledge and understanding:

Advanced understanding of crystal symmetries and their applications in solving problems in the field of lattice vibrations and electron states in condensed matter. Understanding electron correlations and their consequences on many body states in solid matter such as magnetism and superconductivity.

Application:

Achieved knowledge enables basic understanding of condensed matter properties. It represents the foundation for comprehensive study of materials and their applications in modern technology.

Reflection:

Application of group theory, quantum mechanics and statistical physics for understanding properties of real materials.

Transferable skills:

Transition from theoretical physical topics towards understanding of basic properties of condensed matter and its technological applications.

Lectures, exercises, seminars, homework, consultations

Seminar
Oral exam
5 - 10, a student passes the exam if he is graded from 6 to 10

Janez Bonča:

1. MIERZEJEWSKI, Marcin, PRELOVŠEK, Peter, BONČA, Janez. Einstein relation for a driven disordered quantum chain in the subdiffusive regime. Physical review letters. 2019, vol. 122, iss. 20, str. 206601-1-206601-7

2. VIDMAR, Lev, KRAJEWSKI, Bartosz, BONČA, Janez, MIERZEJEWSKI, Marcin. Phenomenology of spectral functions in disordered spin chains at infinite temperature. Physical review letters. 2021, vol. 127, iss. 23, str. 230603-1-230603-7

3. ŠUNTAJS, Jan, BONČA, Janez, PROSEN, Tomaž, VIDMAR, Lev. Quantum chaos challenges many-body localization. Physical review. E. 2020, vol. 102, iss. 6, str. 062144-1-062144-12

4. BONČA, Janez. Spectral function of an electron coupled to hard-core bosons. Physical review. B. 2020, vol. 102, iss. 3, str. 035135-1-035135-9

5. KRAJEWSKI, Bartosz, VIDMAR, Lev, BONČA, Janez, MIERZEJEWSKI, Marcin. Restoring ergodicity in a strongly disordered interacting chain. Physical review letters. 2022, vol. 129, iss. 26, str. 260601-1-260601-7

6. BONČA, Janez, TRUGMAN, Stuart A. Electron removal spectral function of a polaron coupled to dispersive optical phonons. Physical review. B. 2022, vol. 106, iss. 17, str. 174303-1-174303-9

Rok Žitko:

7. Universal Magnetic Oscillations of dc Conductivity in the Incoherent Regime of Correlated Systems
Jakša Vučičević, Rok Žitko
Phys. Rev. Lett 127, 196601 (2021)

8. Electrical conductivity in the Hubbard model: Orbital effects of magnetic field
Jakša Vučičević, Rok Žitko
Phys. Rev. B 104, 205101 (2021)

9. Iron phthalocyanine on Au(111) is a “non-Landau” Fermi liquid
R. Žitko, G. G. Blesio, L. O. Manuel, A. A. Aligia
Nat. Commun. 12, 6027 (2021)

10. Kondo screening in a charge-insulating spinon metal
M. Gomilšek, R. Žitko, M. Klanjšek, M. Pregelj, C. Baines, Y. Li, Q. M. Zhang, A. Zorko
Nat. Phys. 15, 754 (2019)

11. Conductivity in the Square Lattice Hubbard Model at High Temperatures: Importance of Vertex Corrections
J. Vučičević, J. Kokalj, R. Žitko, N. Wentzell, D. Tanasković, and J. Mravlje
Phys. Rev. Lett. 123, 036601 (2019)

12. Mottness collapse without metallisation in the domain walls of triangular-lattice Mott insulator 1T-TaS2
J. Skolimowski, Ya. Gerasimenko, R. Žitko
Phys. Rev. Lett. 122, 036802 (2019)