Observation of a phononic quadrupole topological insulator

A two-dimensional phononic quadrupole topological insulator is demonstrated experimentally using mechanical metamaterials, which has both the one-dimensional edge states and the zero-dimensional corner states predicted by theory. The properties of many materials with topological band structures can be understood in terms of a quantization of the electric polarization. By considering a quantization of higher-order polarizations, a new class of higher-order topological insulators has recently been predicted. Marc Serra-Garcia et al. use a mechanical metamaterial to demonstrate such a system experimentally: a two-dimensional phononic quadrupole topological insulator, which has both one-dimensional states at the edges as well as zero-dimensional states at the corners. As these topological corner states are two dimensions lower than the bulk, they could provide a route to engineering one-dimensional channels along the edges of three-dimensional systems. The modern theory of charge polarization in solids1,2 is based on a generalization of Berry’s phase3. The possibility of the quantization of this phase4,5 arising from parallel transport in momentum space is essential to our understanding of systems with topological band structures6,7,8,9,10. Although based on the concept of charge polarization, this same theory can also be used to characterize the Bloch bands of neutral bosonic systems such as photonic11 or phononic crystals12,13. The theory of this quantized polarization has recently been extended from the dipole moment to higher multipole moments14. In particular, a two-dimensional quantized quadrupole insulator is predicted to have gapped yet topological one-dimensional edge modes, which stabilize zero-dimensional in-gap corner states14. However, such a state of matter has not previously been observed experimentally. Here we report measurements of a phononic quadrupole topological insulator. We experimentally characterize the bulk, edge and corner physics of a mechanical metamaterial (a material with tailored mechanical properties) and find the predicted gapped edge and in-gap corner states. We corroborate our findings by comparing the mechanical properties of a topologically non-trivial system to samples in other phases that are predicted by the quadrupole theory. These topological corner states are an important stepping stone to the experimental realization of topologically protected wave guides12,15 in higher dimensions, and thereby open up a new path for the design of metamaterials16,17.