Topological mechanics from supersymmetry

In topological mechanics, the identification of a mechanical system's rigidity matrix with an electronic tight-binding model allows one 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 analogs of the Kitaev honeycomb model and of a second-order topological insulator with floppy corner modes. Our SUSY construction naturally defines a set of topological invariants for bosonic (mechanical) systems, such as bosonic Wilson loop operators that are formulated in terms of a SUSY-related fermionic Berry curvature.