Topological Mechanics from Supersymmetry

TL;DR

This paper introduces a systematic method to construct topological mechanical systems using supersymmetry, linking mechanical and electronic models, and defining new topological invariants for bosonic systems.

Contribution

It presents an exact supersymmetry framework to relate mechanical and electronic degrees of freedom, enabling the design of novel topological mechanical systems with unique invariants.

Findings

Constructed mechanical analogues of topological models like the Kitaev honeycomb.

Defined new topological invariants for bosonic systems using SUSY-related fermionic Berry curvature.

Demonstrated mechanical systems with floppy boundary and corner modes.

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.