Topological physics with microwaves

Fabrice Mortessagne
Université Côte d'Azur, INPHYNI, CNRS, Parc Valrose, Nice, France

Band theory has been one of the major achievements of condensed matter physics during the second half of the last century. Tight-binding model and Bloch theorem give a clear understanding of electronic dispersion relations in metals and semiconductors. The discovery of quantum Hall effect in the 80’s marks the emergence of topology in transport properties: The recognition that the Hall conductance at the plateaus can be understood in terms of topological invariants known as Chern numbers. Playing the role of an order parameter in a “topological phase transition“, Chern number and others topological invariants are nowadays intensively studied in the active field of topological insulators. These concepts extend far beyond the scope of solid-state physics, and several research groups proposed alternative experimental platforms using cold atoms, photons, polaritons, and other classical waves. The Waves in Complex Systems group in Nice has developed artificial condensed-matter systems by means of microwave resonator lattices. I will present a selection of results obtained the last 5 years.