Topological Insulators

[Last update: 2023-10-08]

Course for physics MSc and PhD students at
Budapest University of Technology and Economics (BME), and
Eotvos Lorand University (ELTE)
2023 Fall Semester

Lecturers

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

Lectures

1. Sep 11. Introduction. Slides: 2023-09-18-BME_Topins_SSH.pdf
2. Sep 18. SSH model. Reading material: Chapter 1 from the book (see arxiv link below). Slides: 2023-09-18-BME_Topins_SSH.pdf
3. Sep 25. Berry phase, Chern number. Reading material: Chapter 2 from the book (see arxiv link below). Slides: 2023-09-25-BME-Topins_BerryChern.pdf
4. Oct 2: Polarization and Pumping. Reading material: Chapters 3 and 4 from the book (see arxiv link below). Summary slides and exercises:  2023-10-02-BME_Topins_PolarizationAndPumping_Summary.pdf -- 2023-10-02-BME_Topins_PolarizationAndPumping_Exercises.pdf
5. Oct 9: Current operator and adiabatic pumping. Reading material: Chapter 5 from the book (see arxiv link below). Slides: 2023-10-09-BME-Topins_CurrentOperator.pdf
6. Oct 16: Qi-Wu-Zhang model. Reading: Chapter 6. Summary slides and exercises: 2023_7_qwz.pdf -- 2023_7_qwz_questions.pdf
7. Nov 6: Continuum model of localized states at a domain wall. Reading: Chapter 7. Summary slides and exercises: 2023_8_continuumtheory.pdf -- 2023_8_continuumtheory_questions.pdf
8. Nov 13: BHZ model. Reading: Chapter 8. Summary slides and exercises: ...
9. Nov 20: Z2 invariant. Reading: Chapter 9 + Z2_Fukui_Hatsugai_jpsj.76.053702.pdf (see also Janos' email instructions)
10. Nov 27: Experiments. Reading: Chapter 10. Summary: 2023_10_experiments.pdf
11. Dec 4: Weyl semimetals. Reading: weyl_semimetals.pdf

Details

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: BME CH building, lecture room CH 302.
Time: Mondays 12:15-13:45
Title of Teams group: 2023 Fall - Topological Insulators
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.

Lecture notes

Description of the 2023 edition of the course ends here.

- - -

Outdated - Earlier editions of the course

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.