Topological waves in non-reciprocal scattering networks | Prof. Romain Fleury

Prof. Romain Fleury
EPFL

Abstract: We study the topological properties of waves propagating in non-reciprocal scattering networks. Such networks, made of multiport non-reciprocal components connected by reciprocal transmission lines, can support three distinct topological phases: a trivial insulating phase, a Chern topological phase, and an extra anomalous topological phase. We will discuss, using simple graph theory arguments, the origin of the anomalous phase, and highlights its fundamental differences with the Chern phase. Using numerical studies and microwave experiments, we will demonstrate the superior robustness of anomalous edge transport over Chern edge transport, for various types of disorder, from random phase delays, to scattering and amorphous disorder. We will conclude on the potential applications of such networks in microwaves.

Main paper/arXiv, related to the seminar, and other references:
Zhang, Z., Delplace, P. & Fleury, R. Superior robustness of anomalous non-reciprocal topological edge states. Nature 598, 293–297 (2021). https://doi.org/10.1038/s41586-021-03...

https://www.epfl.ch/labs/lwe/


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00:00:00 Intro
00:01:20 What is topology?
00:02:56 Topological invariants
00:04:06 Topology in physics
00:05:39 Topology of Bloch band structures
00:09:23 A simple example: non-reciprocal scattering networks with no reflection
00:11:08 Chern numbers
00:14:29 An example of two different circulators with reflection
00:16:33 Two definition of topology (Hermitian and Floquet)
00:17:50 Topological Floquet states
00:20:08 Anomalous edge states
00:22:13 Two possible implementation of anomalous phase
00:25:42 Graph theory consideration of unitary scattering networks
00:28:44 Eulerian graphs
00:31:44 Canonical example: the honeycomb network
00:38:52 Topological phase diagram of the honeycomb network
00:40:23 Practical Implementation
00:44:14 Random phase disorder
00:48:27 Experiments: 5 different disorder realizations
00:49:07 Scattering disorder
00:51:04 Last source of disorder - amorphism
00:54:52 Perspective and applications
00:55:46 Questions and discussion
01:06:30 End