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

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.

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Cited by in corpus (8)

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• Revealing the boundary Weyl physics of the four-dimensional Hall effect via phason engineering in metamaterials
• Anyonic Topological Order in Twisted Equivariant Differential (TED) K-Theory
• Differences between quantum and classical adiabatic evolution
• Topological split-ring resonator based metamaterials with $\mathcal{P}\mathcal{T}$ symmetry relying on gain and loss
• Topological Computation by non-Abelian Braiding in Classical Metamaterials
• Physical rendering of synthetic spaces for topological sound transport
• Embedding 1D BDI topological dynamics into continuous elastic plates