Course data
Course name: Topological Insulators
Neptun ID: BMETE11MF34
Responsible teacher: András Pályi
Department: Department of Physics
Programme: Courses for Physicist MSc students
Course data sheet: BMETE11MF34
Requirements, Informations

Topological Insulators

[Last update: 2021-09-14]


Course for physics MSc and PhD students at
Budapest University of Technology and Economics (BME), and
Eotvos Lorand University (ELTE)
2021 Fall Semester





Janos Asboth (BME)
Laszlo Oroszlany (ELTE)
Andras Palyi (BME)



  1. Sep 13. Introduction
  2. Sep 20. SSH model. Reading material: SSH-2021Fall.pdf. Summary slides and peer instruction questions: SummarySlides-SSH-2021.pdf
  3. Sep 27. Berry phase, Chern number. Reading material: Chapter 2 from the book (see arxiv link below).




Through simple one- and two-dimensional model Hamiltonians, participants will acquire a good physical understanding of the core concepts of topological insulators and semimetals. Among the questions covered: What is topological in a band insulator? What are edge states? How is their number given by the so-called bulk-boundary correspondence principle? How and against what are edge states protected?

Participants are required to have good knowledge of basic quantum mechanics and familiarity with basic concepts in condensed matter physics (Bloch theorem, energy bands, etc.). No prior knowledge of topology is assumed.


Location: ELTE TTK, South Building / Déli tömb, 1st floor, 1-105 Sárfalvi Béla room / terem.
Map of ELTE campus:
Time: Mondays 12-14
First lecture: Sep 13 Monday, 12:15
Title of Teams group: Topological Insulators 2021 Fall
Course language: English


Format: Peer Instruction. For each class, the corresponding chapter of the lecture notes should be read as a preparation, before the class. The first, shorter part of the class is a frontal presentation, where one of the lecturers summarizes the chapter the students have already read. The second, longer part of the class is used for solving a quiz about the chapter, in an interactive, collaborative fashion. Grades are based on an oral exam at the end of the semester.


The lecture will be broadcasted and recorded. Nevertheless, we strongly recommend that students located in Budapest join in person, to enable and enjoy the peer instruction experience.


For broadcasting, we’ll use ELTE’s Teams platform. If you’re not an ELTE person, but you’d like to watch the live broadcast or the recording, please contact Laci Oroszlany via oroszlanyl at gmail dot com. If you already have a non-ELTE Teams account, then please include that in your email to Laci.

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)


Earlier courses


Lectures in 2019

  1. Sep 10: Introduction
    slides: [pdf]
  2. Sep 17: SSH model
    reading material: Chapter1.pdf
    peer-instruction exercises: [svg]
  3. Sep 24: Berry phase, Chern number
    reading material: Chapter2.pdf
    peer-instruction exercises: [svg]
  4. Oct 1: Polarization and Berry phase / Adiabatic charge pumping, Rice-Mele model
    reading material: Chapters 3 and 4 from the Lecture notes (see below for link)
    summary and peer-instruction exercises: [pdf]
  5. Oct 8: Current operator and particle pumping
    reading material: Chapter 5
    summary and peer-instruction exercises: [pdf]
  6. Oct 15: Two-dimensional Chern insulators - the Qi-Wu-Zhang model
    reading material: Chapter 6
    summary and peer-instruction exercises: [pdf]
  7. Oct 22: Continuum models of localized states at a domain wall
    reading material: Chapter 7
    summary and peer-instruction exercises: [pdf]
  8. Oct 29: Time-reversal symmetric two-dimensional topological insulators
    reading material: Chapter 8
    summary and peer-instruction exercises: [pdf]
  9. Nov 5: The Z2 invariant
    reading material: Chapter 9
    suggested reading: Fukui-Hatsugai paper
  10. Nov 19 (Nov 12 is a break): Weyl semimetals
    reading material: weyl_semimetals.pdf
  11. Nov 26: Electrical conduction of edge states
    reading material: Chapter 10
    summary and peer-instruction exercises: [pdf]
  12. Dec 3: Topology and topological insulators
    reading material: lecture notes [pdf]
  13. Dec 10: Topological quantum computing, topological superconductivity
    slides: Andras' slides [pdf] on poor man's quantum gate
    Janos' slides [pdf] on topological superconductivity and the 2nd semester of the course

The course website from 2017 Fall is here.