Topological Mechanics from Supersymmetry

Abstract

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.

arXiv comment8 pages, 6 figures

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Cited by in corpus (10)

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• Square-root topological phase with time-reversal and particle-hole symmetry
• Circuit realization of tilted Dirac cone: A platform for fabrication of curved spacetime geometry on a chip
• Higher-Order Topological Insulator on a Martini Lattice and Its Square Root Descendant
• Entanglement dualities in supersymmetry
• Supersymmetry on the lattice: Geometry, Topology, and Flat Bands
• Supersymmetry dictated topology in periodic gauge fields and realization in strained and twisted 2D materials
• Supersymmetric Free Fermions and Bosons: Locality, Symmetry and Topology
• Mirror-symmetry protected higher-order topological zero-frequency boundary and corner modes in Maxwell lattices