Topological Insulators

Course for MSc and PhD students at
Eotvos University Budapest (ELTE), and
Budapest University of Technology and Economics (BME)
2017 Fall semester

Course ad: pdf.

If you are interested in joining the course, please sign up in Neptun, and contact us at palyi at mail dot bme dot hu.


János Asbóth, Wigner Research Centre for Physics
László Oroszlány, Eötvös University
András Pályi, Budapest University of Technology and Economics


Location: ELTE Northern Block, Pazmany Peter setany 1/A, room 5.128
(Take the elevator on the Danube side of the building to the 5th floor. Stepping out from the elevator, this room is the nearest one on the left.)
Time: Friday, 10:15-11:45.
First lecture: September 15, 10:15
Course language: English
Course website:

Course materials

Slides of the first lecture: [pdf]

Summary slides for chapter 3, "Polarization and Berry phase": [pdf]

Summary slides for chapter 6, "Two-dimensional Chern insulators - the Qi-Wu-Zhang model": [pdf]

Summary slides for chapter 7, "Continuum model of localized states at a domain wall": [pdf]

Lecture notes on topological semimetals: [pdf]

Peer instruction exercises:

  • 1. Su-Schrieffer-Heeger model: [svg]
  • 2. Berry phase, Chern number: [svg]
  • 3. Polarization and Berry phase: [svg]
  • 4. Adiabatic pumping, Rice-Mele model: [svg]
  • 5. Current operator and particle pumping [pdf]
  • 6. Two-dimensional Chern insulators - the Qi-Wu-Zhang model [svg]
  • 7. Continuum model of localized states at a domain wall [pdf]
  • 10. Electrical conduction of edge states [svg]

iPython notebooks: There are ipython notebooks that accompany the class. We collect them here. We encourage you to experiment with the notebooks, using the interactive plots (sliders) as well as to modify them according to your needs. For this, you need to download the whole directory using the "Download ZIP" button to the right, unzip it on your computer. You can then upload the individual notebooks to Jupyter (using the Upload button in the upper right corner). Alternatively, you can run the notebooks on your own computer, if you have already installed Jupyter.

Lecture notes

A Short Course on Topological Insulators: Band-structure topology and edge states in one and two dimensions
J. K. Asboth, L. Oroszlany, A. Palyi
Springer, Lecture Notes in Physics, 919 (2016)
An updated version, with typos corrected: pdf