Fractional solitons in non-Euclidian elastic plates

TL;DR

This paper demonstrates that non-Euclidean elastic plates can host fractional charge-1/2 solitons, exhibiting properties akin to quantum fractional states, with potential applications in mechanical metamaterials.

Contribution

It establishes a novel analogy between minimal-surface elastic plates and quantum spin chains, revealing fractional excitations and unique nonlinear behaviors in classical elastic systems.

Findings

Elastic plates support fractional charge-1/2 solitons.

Solitons exhibit deconfinement and braiding properties.

Potential for advanced mechanical metamaterials applications.

Abstract

We show that minimal-surface non-Euclidean elastic plates share the same low-energy effective theory as Haldane's dimerized quantum spin chain. As a result, such elastic plates support fractional excitations, which take the form of charge-$1/2$ solitons between degenerate states of the plates, in strong analogy to their quantum counterpart. These fractional solitons exhibit properties similar to fractional excitations in quantum fractional topological states, including deconfinement and braiding, as well as unique new features such as holographic properties and diode-like nonlinear response, demonstrating great potentials for applications as mechanical metamaterials.