BMETE11MF34

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

 

Course for MSc and PhD students at
Budapest University of Technology and Economics (BME), and
Eotvos Lorand University (ELTE)
2019 Fall Semester

 

Lectures

 

  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
  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
  12. Dec 3:
  13. Dec 10:

 

Lecturers

 

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

 

Details

 

Through simple one- and two-dimensional model Hamiltonians, participants will acquire a good physical understanding of the core concepts of topological insulators. 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 Building K, KF85 (ground floor, Southern corridor)
Time: Tuesdays, 12:15-13:45
First lecture: Sep 10, Tuesday, 12:15-13:45.
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: 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

 

The course website from 2017 Fall is here.