Fragile topology

Topological insulators usually posses scatter-free gapless modes localized at their boundaries which cross the energetic bulk band gap. These modes cannot be gapped unless other topological degrees of freedom are added to the system. Their envisioned applications triggered a gargantuan effort to discover new topological materials.

Recently proposed fragile topological insulators, however, challenge this conventional notion of topological robustness. In fact, their edge modes can be gapped, or in other words, the topology can be trivialized by the addition of trivial degrees of freedom.

This new topology has been proposed as an explanation of certain phenomena observed in twisted bilayer graphene, but no clear experimental signature of fragile topology has yet been put forward.  In this work, we realize an acoustic metamaterial with fragile topology. By slowly cutting our sample in two disconnected halves, we observe the flow of one state crossing the bulk gap. This spectral flow is the robust signature of fragile topological insulators. With our findings, we establish for the first time a clear experimental signature of fragile topology. Moreover, the exquisite control of localized individual modes available in our sample increases the potential of topological mechanical metamterials in wave-control applications