The role of nonlinearities in topological protection: using magnetically coupled fidget spinners

TL;DR

This study explores how nonlinearities affect topologically protected interface modes in a magnetic spinner lattice, showing that increased amplitude can destroy topological protection and cause modes to merge with bulk bands.

Contribution

It provides experimental and analytical evidence that nonlinearities can eliminate topological protection in a mechanical lattice with magnetic coupling.

Findings

Topologically protected modes exist at small amplitudes.

Nonlinearities cause modes to shift outside bandgaps.

Edge-to-bulk transition leads to loss of protection.

Abstract

We investigate and experimentally observe the existence of topologically protected interface modes in a one-dimensional mechanical lattice, and we report on the effect of nonlinearities on topological protection. The lattice consists of a one-dimensional array of spinners with nearest neighbor coupling resulting from magnetic interactions. The distance between the spinners is spatially modulated to obtain a diatomic configuration, and to produce a non-trivial interface by breaking spatial inversion symmetry. For small amplitudes of motion, the interactions are approximately linear, and the system supports topologically protected interface modes at frequencies inside the bulk bandgaps of the lattice. Nonlinearities induced by increasing amplitude of motion cause the interface modes to shift outside the bandgaps and merge with the bulk bands. The resulting edge-to-bulk transition causes the extinction of the topologically protected interface mode and extends it to the entire length of the chain. Such transition is predicted by analytical calculations and verified by experimental observations. The paper thus investigates the existence of topologically protected interface modes obtained through broken spatial inversion symmetry, and documents their lack of robustness in the presence of nonlinearities.