Teaching

Topological States of Matter 

Place: 

1) Lectures online

2) Exercises  in-person  at the Jagiellonian University

USOS code name and link:

WFAIS.SDSP-025 

Topics:

1) Electronic band structure in solids, Bloch theorem 

2) Simplest models with non-trivial topology and with bulk-boundary correspondence

3) Crystalline and non-crystalline symmetries, tenfold classification of topological insulators and superconductors 

4) Different generations of topological invariants and the way if calculating them

5) Crystalline insulators and semimetals

6) Majorana fermions and related phenomena

7) Exotic statistics of Majorana fermions

Prerequisites:

Knowledge of English and of basics of linear algebra and mathematical analysis.  Basic knowledge of any program that allows for matrix calculations, e.g. Mathematica/MatLab/Python. Knowledge of basic quantum mechanics and solid state physics will be an asset.

References:

[1] D. J. Thouless, Topological quantum numbers in nonrelativistic physics, World Scientific, (1998).

[2] G. E. Volovik, The Universe in a Helium Droplet, Oxford University Press, (2003).

[3] M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010).

[4] X.-L. Qi and S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011).

[5] C.-K. Chiu, J. C. Teo, A. P. Schnyder, Rev. Mod. Phys. 88, 035005 (2016).

[6] A. Akhmerov, J. Sau, B. van Heck, S. Rubbert, R. Skolasiński, online course "Topology in Condensed Matter" at Delft University of Technology