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Topological Mechanics from Supersymmetry
In topological mechanics, the identification of a mechanical system's
rigidity matrix with an electronic tight-binding model allows to infer
topological properties of the mechanical system, such as the occurrence of
`floppy' boundary modes, from the associated electronic band structure. Here we
introduce an approach to systematically construct topological mechanical
systems by an exact supersymmetry (SUSY) that relates the bosonic (mechanical)
and fermionic (e.g. electronic) degrees of freedom. As examples we discuss
mechanical analogues of the Kitaev honeycomb model and of a second-order
topological insulator with floppy corner modes. Our SUSY construction naturally
defines hitherto unexplored topological invariants for bosonic (mechanical)
systems, such as bosonic Wilson loop operators that are formulated in terms of
a SUSY-related fermionic Berry curvature.Comment: 8 pages, 6 figure
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