Lucien Jezequel (KTH)

Salle 523, couloir 12-13, 5è étage

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

In quantum or classical wave systems, some properties of wave systems are known to be topologically protected. Due to their increased robustness, such properties have attracted much interest in the past decades.

The most studied case is the existence of unidirectional edge states in the quantum Hall effect and, more generally, the existence of protected states at the edges of topologically insulators. An important result is then the bulk-edge correspondence that links the existence of topological edge states to a topological index defined in the volume of the material.

This is not the only case studied in topological physics and different, yet similar, results have been obtained for topological semimetals, higher order insulators or continuous wave systems. In this talk I will explain how all these results can be understood in a unifying theory using the mode-shell correspondence formalism which relates the existence of isolated topological modes in phase space, to a topological invariant defined in the surface which encloses these modes in phase space. Invariant that reduces to Chern or winding numbers in the semiclassical limit.

Mode-shell correspondence, a unifying phase space theory in topological physics
[1] Part I: Chiral number of zero-modes https://www.scipost.org/10.21468/SciPostPhys.17.2.060
[2] Part II: Higher-dimensional spectral invariants https://arxiv.org/abs/2501.13550