Finite-Frequency Topological Maxwell Modes in Mechanical Self-Dual Kagome Lattices

In this Letter, an elastic twisted kagome lattice at a critical twist angle, called self-dual kagome lattice, is shown to exhibit peculiar finite-frequency topological modes which emerge when certain conditions are satisfied. These states are topologically reminiscent of the zero energy (floppy) modes of Maxwell lattices, but they occur at a finite frequency in the band gap of the self-dual kagome lattice. Thus, we present a completely new class of topological modes that share similarities with both the zero frequency floppy modes in Maxwell lattices and the finite energy in-gap modes in topological insulators. We envision the presented mathematical and numerical framework to be invaluable for many technological advances pertaining to wave phenomena, such as reconfigurable waveguide designs.