# Chiral topological phases in designed mechanical networks

## TL;DR

This paper demonstrates that designed mass-spring networks, influenced by Coriolis forces, can host topologically protected chiral edge modes, enabling robust unidirectional mechanical wave transmission, and are classified by a Chern invariant.

## Contribution

It introduces a method to realize topological phases in mechanical networks through design and Coriolis forces, expanding the scope of topological metamaterials.

## Key findings

- MSNs can host topologically protected chiral edge modes.
- Coriolis forces induce topological phases in MSNs.
- Edge modes enable robust unidirectional wave transmission.

## Abstract

Mass-spring networks (MSNs) have long been used as approximate descriptions of many biological and engineered systems, from actomyosin networks to mechanical trusses. In the last decade, MSNs have re-attracted theoretical interest as models for phononic metamaterials with exotic properties such as negative Poisson's ratio, negative effective mass, or gapped vibrational spectra. A practical advantage of MSNs is their tuneability, which allows the inverse design of materials with pre-specified bandgaps. Building on this fact, we demonstrate here that designed MSNs, when subjected to Coriolis forces, can host topologically protected chiral edge modes at predetermined frequencies, thus enabling robust unidirectional transmission of mechanical waves. Similar to other recently discovered topological materials, the topological phases of MSNs can be classified by a Chern invariant related to time-reversal symmetry breaking.