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arXiv · 2203.10311

Duality of Topological Edge States in a Mechanical Kitaev Chain

Florian Allein·Rajesh Chaunsali·Adamantios Anastasiadis·Ian Frankel·Nicholas Boechler·Fotios K. Diakonos·Georgios Theocharis
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Abstract

We theoretically investigate and experimentally demonstrate the existence of topological edge states in a mechanical analog of the Kitaev chain with a non-zero chemical potential. Our system is a one-dimensional monomer system involving two coupled degrees of freedom, i.e., transverse displacement and rotation of elastic elements. Due to the particle-hole symmetry, a topologically nontrivial bulk leads to the emergence of edge states in a finite chain with fixed boundaries. In contrast, a topologically trivial bulk also leads to the emergence of edge states in a finite chain, but with free boundaries. We unravel a duality in our system that predicts the existence of the latter edge states. This duality involves the iso-spectrality of a subspace for finite chains, and as a consequence, a free chain with topologically trivial bulk maps to a fixed chain with a nontrivial bulk. Lastly, we provide the conditions under which the system can exhibit perfectly degenerate in-gap modes, akin to Majorana zero modes. These findings suggest that mechanical systems with fine-tuned degrees of freedom can be fertile testbeds for exploring the intricacies of Majorana physics.

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Florian Allein, Rajesh Chaunsali, Adamantios Anastasiadis, Ian Frankel, Nicholas Boechler, Fotios K. Diakonos, Georgios Theocharis. 2022-03-19. Duality of Topological Edge States in a Mechanical Kitaev Chain. https://doi.org/10.1038/s41467-023-42321-3

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