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

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.