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Topological mechanics is a recently discovered field devoted to the study of topological insulator-like features in classical mechanical systems. In this talk, I will be discussing a theoretical discovery that quantum computing inspired Majorana fermions also appear in these simple mechanical models. I will demonstrate this by employing supersymmetry to connect a Majorana
fermion system with a mechanical (bosonic) counterpart. The latter is then endowed with the same topological features as their fermionic counterparts and can be engineered to investigate a variety of hitherto unexplored perspectives on topological mechanics. Exploiting this SUSY formulation, we construct mechanical avatars of Kitaev’s honeycomb model of a Z2 spin liquid and a second-order topological insulator with topologically protected corner modes. The resulting mechanical models then provide an easy experimental setup to demonstrate Majorana fermion physics. Furthermore, our SUSY formulation allows for defining topological invariants in terms of a modified Berry connection for bosonic eigenstates that characterize the topological floppy modes in the mechanical systems and might lead to a deeper understanding of the classification of bosonic insulators. |