JCMS: The "Mode-Shell" correspondence, a unifying concept in topological physics

by Lucien Jezequel (ENS de Lyon)

Thursday 14 Dec 2023, 11:00 → 12:00 Europe/Stockholm

Albano 3: 6231 - Giga (8 seats) (Albano Building 3)

The bulk-edge correspondence is a concept that relates the existence of low-energy excitations localized at the edges of an insulator to topological properties defined in its bulk. Such theory was first developped to understand the quantum hall effect and has since become a cornerstone concept in topological physics. At the same time, many physical systems, like higher-order insulators or continuous systems, have been shown to exhibit topological properties that do not fit the bulk-edge paradigm.

In this talk, I will show how such results can be unified in a more general theory called "mode-shell correspondence" which provides a common understanding for them all. Such theory shows that, in general, the topological properties of zero modes can be re-expressed as topological invariants defined on the shell, which is the surface enclosing those zero modes in phase space. The theory is explicit and the expression of the invariants is prone to numerical evaluation as well as explicit computations in semi-classical regime. This will therefore allow me to provide explicit illustrations of the correspondence in different physical systems.