Experimental observation of topological phase transitions in a one-dimensional elastic string model

Topological insulators are a type of material that allows the existence of unidirectional currents at the quantum scale. These currents, called edge states, are unaffected by material imperfections, which makes topological insulators an active research topic with potential applications in quantum computing. Protected edge states - analogous to the unidirectional current of electronic topological insulators - have recently been demonstrated not only with electrons, but also with photons, sound waves, and mechanical waves. Using a well-known model of topological insulators known as the Su-Schrieffer-Heeger (SSH) model, we constructed a one-dimensional mechanical model of topological insulators that propagates transverse waves in an elastic string. Our device demonstrated a phase transition between the insulator, conductor, and topological insulator phases of the SSH model, with clearly defined edge states in the topological insulator phases. Our findings are supported both by numerical simulations using the finite element method and a mathematical model that we derived from the mechanics of harmonic oscillators. The simplicity of our device facilitates its construction and observation, making it a valuable teaching tool to visually demonstrate topological phase transitions.