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
Lecturers
Janos Asboth (BME)
Laszlo Oroszlany (ELTE)
Andras Palyi (BME)
Lectures
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Sep 13. Introduction
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Sep 20. SSH model. Reading material: SSH-2021Fall.pdf. Summary slides and peer instruction questions: SummarySlides-SSH-2021.pdf
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Sep 27. Berry phase, Chern number. Reading material: Chapter 2 from the book (see arxiv link below).
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: ELTE TTK, South Building / Déli tömb, 1st floor, 1-105 Sárfalvi Béla room / terem.
Map of ELTE campus: https://ttk.elte.hu/content/terkep.t.1014?m=32
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
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Sep 10: Introduction
slides: [pdf]
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Sep 17: SSH model
reading material: Chapter1.pdf
peer-instruction exercises: [svg]
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Sep 24: Berry phase, Chern number
reading material: Chapter2.pdf
peer-instruction exercises: [svg]
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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]
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Oct 8: Current operator and particle pumping
reading material: Chapter 5
summary and peer-instruction exercises: [pdf]
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Oct 15: Two-dimensional Chern insulators - the Qi-Wu-Zhang model
reading material: Chapter 6
summary and peer-instruction exercises: [pdf]
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Oct 22: Continuum models of localized states at a domain wall
reading material: Chapter 7
summary and peer-instruction exercises: [pdf]
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Oct 29: Time-reversal symmetric two-dimensional topological insulators
reading material: Chapter 8
summary and peer-instruction exercises: [pdf]
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Nov 5: The Z2 invariant
reading material: Chapter 9
suggested reading: Fukui-Hatsugai paper
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Nov 19 (Nov 12 is a break): Weyl semimetals
reading material: weyl_semimetals.pdf
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Nov 26: Electrical conduction of edge states
reading material: Chapter 10
summary and peer-instruction exercises: [pdf]
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Dec 3: Topology and topological insulators
reading material: lecture notes [pdf]
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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.
