Higher order topology

In a conventional topological insulator the bulk of the system is insulating and the current propagates only along the conducting edges. An insulating edge, however, is not necessarily trivial. This is the case for the recently predicted higher-order topological insulators, where the non-trivial topology manifests itself only at the boundaries of a boundary, e.g., at the zero-dimensional corners of a two-dimensional system.

Here, we provide the first experimental realization of such a system dubbed quadrupole-insulator. We do not synthesize a new material. Rather, we cleverly design a periodic geometric pattern in a 6 inch silicon wafer that reproduces the sought-after phenomenology. Our metamaterial is composed of 100 small plates with well isolated modes of vibration that are then coupled via weak links to realize a periodic arrangement of perturbatively coupled resonators.

When we excite the sample with ultrasound, only the plates at the corner vibrate while the others remain still, despite the links connecting them. Our mechanical metamaterial behaves exactly as predicted by the theory of higher-order topological insulator.

Our experiment proves that the previously overlooked higher-order insulators are not just a theoretical dream. Moreover, the fact that the first observation occurred in a mechanical metamaterial rather than in an electronic material or in a cold-atom setup establishes these platforms as an ideal tool to experimentally verify new theoretical ideas originating in topological band theory.

In a follow up work we implemented the same model in a LC network, where the local oscillators are not mechanical but electromagnetic. Using non-linear elements in the form of varactor diodes we can ramp through topological phase transitions, study the evolution of the corner modes and expoit non-linear physics.