# Topological braiding of non-Abelian mid-gap defects in classical meta-materials

## TL;DR

This paper demonstrates how classical meta-materials can emulate non-Abelian braiding of mid-gap defects, revealing potential for topological quantum-like behaviors in classical systems through domain-wall modes.

## Contribution

It introduces a classical analogue of the Kitaev chain with topologically protected domain-wall modes exhibiting non-Abelian braiding properties, previously thought exclusive to quantum systems.

## Key findings

- Mid-gap modes show distinct fusion channels.
- Explicit braiding matrices are calculated.
- Classical systems can mimic quantum topological phenomena.

## Abstract

Non-trivial braid-group representations appear as non-Abelian quantum statistics of emergent Majorana zero modes in one and two-dimensional topological superconductors. Here, we generate such representations with topologically protected domain-wall modes in a classical analogue of the Kitaev superconducting chain, with a particle-hole like symmetry and a Z2 topological invariant. The mid-gap modes are found to exhibit distinct fusion channels and rich non-Abelian braiding properties, which are investigated using a T-junction setup. We employ the adiabatic theorem to explicitly calculate the braiding matrices for one and two pairs of these mid-gap topological defects.