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

TL;DR

This paper introduces a new class of finite-frequency topological modes in a self-dual kagome lattice, combining features of Maxwell floppy modes and topological insulator in-gap states, with potential for wave-based technologies.

Contribution

It demonstrates the existence of finite-frequency topological modes in a self-dual kagome lattice, a novel finding linking Maxwell lattice modes and topological insulator states.

Findings

Finite-frequency topological modes are observed at a critical twist angle.

These modes are topologically protected and occur within the band gap.

The framework has potential applications in reconfigurable waveguides.

Abstract

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 to the zero energy (floppy) modes of Maxwell lattices but they occur at a finite frequency in the band gap of self-dual kagome lattice. Thus, we present a completely new class of topological modes which 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 phenomenon such as reconfigurable waveguide designs.