Self-Dual 2D Elastic Lattices with Finite Frequency Topological Maxwell Modes

This work presents our recent discovery of a new class of topological modes intrinsic to elastic self-dual lattices localized near pinned (i.e., restricted to move) lattice sites. This new topological phenomenon lies at the intersection of the two existing major topological classes: first, the finite frequency in-gap modes of topological insulators, and second, the zero-frequency dispersionless modes in Maxwell lattices. The new Maxwell-like topological modes in self-dual lattices appear at finite frequencies similar to the topological modes of topological insulators. In contrast, they follow the same topological structure as observed for the dispersionless zero-frequency flat bands in Maxwell lattices. Thus, the topological winding number defined for zero frequency modes of Maxwell lattices is utilized with a modified basis (displacement field) to explain the existence and topological origin of the finite frequency Maxwell-like topological modes in self-dual lattices. Unlike the existing topological phenomena, these modes are topologically protected against hybridization; thus, they offer avenues for seamless wave transport along the waveguides of pinned lattice sites. Further, the waveguides are reconfigurable by simply pinning and unpinning the lattice sites in a homogeneous lattice, unlike the fixed heterogeneous interfaces in topological insulators. Hence, we envision this new topological phenomenon to benefit many wave applications.