Topological Insulators
[Last update: 20231008]
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

Sep 11. Introduction. Slides: 20230918BME_Topins_SSH.pdf

Sep 18. SSH model. Reading material: Chapter 1 from the book (see arxiv link below). Slides: 20230918BME_Topins_SSH.pdf

Sep 25. Berry phase, Chern number. Reading material: Chapter 2 from the book (see arxiv link below). Slides: 20230925BMETopins_BerryChern.pdf

Oct 2: Polarization and Pumping. Reading material: Chapters 3 and 4 from the book (see arxiv link below). Summary slides and exercises: 20231002BME_Topins_PolarizationAndPumping_Summary.pdf  20231002BME_Topins_PolarizationAndPumping_Exercises.pdf

Oct 9: Current operator and adiabatic pumping. Reading material: Chapter 5 from the book (see arxiv link below). Slides: 20231009BMETopins_CurrentOperator.pdf

Oct 16: QiWuZhang model. Reading: Chapter 6. Summary slides and exercises: 2023_7_qwz.pdf  2023_7_qwz_questions.pdf

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

Nov 13: BHZ model. Reading: Chapter 8. Summary slides and exercises: ...

Nov 20: Z2 invariant. Reading: Chapter 9 + Z2_Fukui_Hatsugai_jpsj.76.053702.pdf (see also Janos' email instructions)

Nov 27: Experiments. Reading: Chapter 10. Summary: 2023_10_experiments.pdf

Dec 4: Weyl semimetals. Reading: weyl_semimetals.pdf
Details
Through simple one and twodimensional 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 socalled bulkboundary 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 12:1513:45
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
A Short Course on Topological Insulators: Bandstructure topology and edge states in one and two dimensions
J. K. Asboth, L. Oroszlany, A. Palyi
Springer, Lecture Notes in Physics, 919 (2016)
Description of the 2023 edition of the course ends here.
  
Outdated  Earlier editions of the course
Lectures in 2019

Sep 10: Introduction
slides: [pdf]

Sep 17: SSH model
reading material: Chapter1.pdf
peerinstruction exercises: [svg]

Sep 24: Berry phase, Chern number
reading material: Chapter2.pdf
peerinstruction exercises: [svg]

Oct 1: Polarization and Berry phase / Adiabatic charge pumping, RiceMele model
reading material: Chapters 3 and 4 from the Lecture notes (see below for link)
summary and peerinstruction exercises: [pdf]

Oct 8: Current operator and particle pumping
reading material: Chapter 5
summary and peerinstruction exercises: [pdf]

Oct 15: Twodimensional Chern insulators  the QiWuZhang model
reading material: Chapter 6
summary and peerinstruction exercises: [pdf]

Oct 22: Continuum models of localized states at a domain wall
reading material: Chapter 7
summary and peerinstruction exercises: [pdf]

Oct 29: Timereversal symmetric twodimensional topological insulators
reading material: Chapter 8
summary and peerinstruction exercises: [pdf]

Nov 5: The Z2 invariant
reading material: Chapter 9
suggested reading: FukuiHatsugai paper

Nov 19 (Nov 12 is a break): Weyl semimetals
reading material: weyl_semimetals.pdf

Nov 26: Electrical conduction of edge states
reading material: Chapter 10
summary and peerinstruction exercises: [pdf]

Dec 3: Topology and topological insulators
reading material: lecture notes [pdf]

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.