Grand Séminaire d'Institut

Vendredi 19 Octobre 2018 à 11h00.

Topological Properties of Matter

''Topology is a branch of mathematics which focuses on properties of objects insensitive to smooth deformations. Its first occurrence in the description of matter happened in the 70s : while ordered phases are identified by their broken symmetries, topological numbers allow to classify stable defects of these ordered phases, such as vortices, dislocations or skyrmions. With the discovery of the Quantum Hall Effect in 1980, it was soon realized that a quantum electronic phase as a whole could be associated with a topological property. In this presentation, I will first describe these pioneering works which were awarded the 2016 Nobel prize. Then I will turn to the more recent evolution of this topological characterization of matter. This includes the discovery of insulators of a new kind, which are identified not by a standard broken symmetry but by a topological property of their ground state. Finally, I will describe some of the recently identified topological properties of waves beyond electronic states, such as lattices of optical wave-guides with robust edge properties, mechanical meta-materials with localized deformations, or quantum bits immune from perturbations by their environment.''