# 32nd Primakoff Lecture: "Metamaterials and Topological Mechanics"

Metamaterials are materials engineered to have a property or properties not found in nature, such as a negative optical index of refraction, one-way light or vibration waves, or exotic elastic behavior. Advances in materials processing, like 3D printing and laser cutting, over the last 10 to 15 years have made it possible to fabricate metamaterials with made-to-order structure at length scales as short as a micron. Topology is a unifying mathematical concept used in many fields of physics. After the discovery of topological insulators, the term *topological material *generally refers to materials whose bulk excitation spectrum is characterized by topological invariants, associated with the opening of bandgaps, that in turn determine physical properties like the Hall conductivity or the nature of edge excitations. After a brief pictorial introduction to metamaterials and a review of topological edge modes in the simplest one-dimensional context, this talk will discuss mechanical metamaterials with topologically protected edge state with a focus on a particular version, inspired by the work of J.C. Maxwell, of these materials in which the edge modes have zero energy in an idealized limit to be discussed. These modes exist at every wavenumber on the surface so that any shape distortion of the surface costs no energy. Changing the topological class of the material causes one or more zero modes to move from one side of a sample to the opposite creating a rigid and a supersoft edge.