April 21 (Thu) at 15:00 - 17:00, 2022 (JST)
  • Tomoki Ozawa (Associate Professor, Advanced Institute for Materials Research (AIMR), Tohoku University)
  • via Zoom
Yalong Cao

In this set of lectures, I give an introduction to topological insulators. A goal is to provide an overall understanding of basic concepts of the physics of topological insulators to mathematicians and physicists with no prior knowledge on the subject. Very roughly speaking, topological insulators are materials whose wavefunctions show nontrivial topological structure in momentum space. Materials with topologically nontrivial wavefunction in momentum space have been found to host modes which are localized at the surface (edge) of the material: a property known as the bulk-edge correspondence. The bulk-edge correspondence results in experimentally observable signature of somewhat abstract notion of topology of the wavefunction in momentum space. Originally, topological insulators were found and studied for electrons in solid-state materials, which are quantum mechanical. However, certain properties of topological insulators, including the bulk-edge correspondence, have been found to hold also for purely classical materials, such as electromagnetic waves obeying Maxwell’s equations, or waves described by Newtonian mechanics. I will try to introduce topological insulators in a way general enough to be applied to quantum as well as classical materials. In the final part of the lectures, I take this opportunity to discuss some of my own works, where I studied some relations between the two-dimensional topological insulators and Kähler geometry.

Plan of four lectures:

  1. Su-Schrieffer-Heeger model and the introduction to bulk-edge correspondence
  2. Two and higher dimensional topological insulators and their basic phenomenology
  3. Various realizations of topological insulator physics, including photonics and other classical waves
  4. Two dimensional Chern insulators, from the perspective of quantum metric and Kähler geometry

Date and time:

  1. 15:00-17:00 JPT on April 7 (Thursday)
  2. 15:00-17:00 JPT on April 14 (Thursday)
  3. 15:00-17:00 JPT on April 21 (Thursday) 
  4. 15:00-17:00 JPT on April 27 (Wednesday)

This is a closed event for scientists. Non-scientists are not allowed to attend. If you are not a member or related person and would like to attend, please contact us using the inquiry form. Please note that the event organizer or speaker must authorize your request to attend.

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