Laboratoire de Physique Théorique

de la Matière Condensée

Marcelo Guzman (ENS Lyon)

Geometry and Topology Tango in Chiral Matter

 

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Building on direct analogies with electronic matter, the concept of topological state has been successfully applied to a host of different physical systems as diverse as photonics metamaterials, geophysical fluids and mechanical structures. In this talk we focus on a special class of systems enjoying a sublattice or chiral symmetry such as bead-and-spring networks and the SSH model describing polyacetylene.

 
Using mechanical systems as a guiding line, we first show that the topology of waves in chiral materials is naturally encoded in their chiral polarization. This new observable stems from both the topology of the hamiltonian and the geometry of the lattice. We then show how this chiral polarization allows detecting localized modes of zero energy both in crystals and heterogeneous materials. We conclude by showing how to experimentally determine the topological nature of a chiral phase through a direct probe of its chiral polarization.