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A phononic quadrupole insulator
Wave guiding in metamaterials can be achieved using a variety of design principles. We propose and implement the idea of employing topological surface states as a means to create stable and backscattering-free channels for mechanical vibrations. I will review our efforts in this direction, with a focus on a recent idea that involves a "quadrupole topological insulator". The quadrupole insulators on one hand seems to be particularly well suited phase for metamaterials. On the other hand, it represents a new class of topological systems that has not been observed in any other platform, underlying the power of mechanical systems for the investigation of non-trivial band effects.