Topological Soft Matter: from Metamaterials to Polymers

Topological phenomena lie at the forefront of condensed matter physics. When a physical observable is linked to a topological index characterizing a system, it is unaffected by local changes and thus robust against a range of perturbations. This concept of topological protection, originally developed in electronic systems, has recently been applied to soft matter as well. In this talk, I'll show how a recent mapping between spring lattices and electronic topological insulators can be exploited to design topologically protected mechanical response in artificial repetitive structures (metamaterials). Theoretical results will be demonstrated in real-world prototypes of topological mechanical metamaterials, and point towards new ways of designing robust mechanical phenomena across different scales. I'll then describe an interacting system of polymers whose equilibrium behaviour realizes a soft analogue of the quantized adiabatic pump. The topological invariant manifests itself in a geometric feature of the polymer conformations, inspiring a new mechanism for robust polymer patterning.