Tomoki Ozawa (Tohoku University) Universality of topological physics: from electrons and photons to geophysics and biological matter

In 1980, the quantum Hall effect was discovered in two-dimensional semiconductors under a strong magnetic field. The quantum Hall system is an example of a topological insulator, where the “shape” or “topology” of electrons has a peculiar structure, and the integer number that characterizes this “shape” appears in Hall conductivity, which is related to the current flowing around the sample in a chiral manner. After more than two decades, analogs of the quantum Hall effect and chiral edge states were found to exist also in purely classical setups of electromagnetic waves governed by Maxwell’s equations. Since then, topological insulator physics have been studied in various settings beyond electrons in semiconductors. In this presentation, I will discuss universality and versatility of the idea of topological insulators in various setups including, photonics, Newtonian mechanics, geophysical phenomena, biological matter, etc. One can even realize analogs of topological insulators in “synthetic dimensions” where non-spatial degrees of freedom are used as dimensions. The idea of topological insulators provides a novel perspective to understand various phenomena from a unified point of view.