**Lectures & Exersises:** Winter term 2021

**Timetable:** UFV/VTFTL/20, lectures + exercises, Monday 12:35, room: KNKTFA, due COVID resctriction the lecture goes online.

**Outline:**

- Tight-binding method, tridiagonal matrices, Lanczos and renormalization method.
- Dirac electrons in 1D, Su-Schrieffer-Heeger model.
- Electrons in magnetic field, Peierls substitution, Hofstadter‘s butterfly.
- Physics of graphene and Laundau levels.
- Topological aspects of band structure of insulators.
- Time-reversal symmetry, Kramer‘s theorem, topological and Chern insulator.
- Classification of topological phases.
- Berry‘s connectivity and phase, Aharonov-Bohm effect.
- Modern theory of crystalline polarization.
- Thouless-Kohmoto-Nightingale-den Nijs formula for Hall conductivity. Topological invariants.
- General two and four band Hamiltonians.
- Topological superconductors, Kitaev chain, Majorana fermions.

**Literature**

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

J. Sólyom, Fundamentals of the Physics of Solids, Volume II, Springer-Verlag, 2009

E. Kaxiras, Atomic and Electronic Structure of Solids, Cambridge University Press, 2003

E. Kaxiras, J. D. Joannopoulos, Quantum Theory of Materials, Cambridge University Press, 2019

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

P. Phillips, Advanced Solid State Physics. Cambridge University Press, 2012

M. El-Batanouny, Advanced Quantum Condensed Matter Physics. Cambridge University Press, 2020

**Homeworks & Supporting materials:** check webdisk