# Dynamical Majorana Edge Modes in a Broad Class of Topological Mechanical Systems

## TL;DR

This paper demonstrates that a broad class of topological mechanical systems, related to the BDI symmetry class, can host dynamical Majorana edge modes that absorb and store mechanical energy, with potential applications.

## Contribution

It introduces a class of self-assembled chains of rigid bodies with topological properties, enabling the realization of dynamical Majorana edge modes in mechanical systems.

## Key findings

- Existence of topological mechanical systems with BDI symmetry class.
- Ability to open a phonon gap and generate topological invariants by adjusting gyration radius.
- Observation of dynamical Majorana edge modes at finite frequency.

## Abstract

Mechanical systems can display topological characteristics similar to that of topological insulators. Here we report a large class of topological mechanical systems related to the BDI symmetry class. These are self-assembled chains of rigid bodies with an inversion center and no reflection planes. The particle-hole symmetry characteristic to the BDI symmetry class stems from the distinct behavior of the translational and rotational degrees of freedom under inversion. This and other generic properties led us to the remarkable conclusion that, by adjusting the gyration radius of the bodies, one can always simultaneously open a gap in the phonon spectrum, lock-in all the characteristic symmetries and generate a non-trivial topological invariant. The particle-hole symmetry occurs around a finite frequency, hence we can witness a dynamical topological Majorana edge mode. Contrasting a floppy mode occurring at zero frequency, a dynamical edge mode can absorb and store mechanical energy, potentially opening new applications of topological mechanics.