Classical analogue to the Kitaev model and Majorana-like topological bound states

TL;DR

This paper demonstrates a classical mechanical analogue to the quantum Kitaev model, showing topologically non-trivial bound states similar to Majorana modes, and explores their potential for classical topological braiding.

Contribution

It introduces a classical mechanical system that mimics the Kitaev model's topological features and bound states, providing a new platform for studying topological phenomena.

Findings

Classical analogue exhibits Majorana-like bound states

Topological band structure confirms non-trivial topology

Potential for classical topological braiding

Abstract

This study explores the possibility and presents a methodology to synthesize a classical mechanical analogue to the quantum mechanical 1D Kitaev model. While being fundamentally different, we will identify significant conceptual similarities between the two models that culminate in the occurrence, in the classical analogue system, of topologically non-trivial bound states that are akin to Majorana zero modes. By reformulating the Hamiltonian of the classical system in a form reminiscent of second quantization, we show that a 1D staggered classical mechanical chain can exhibit dynamic characteristics analogous to the Kitaev's 1D superconducting model, as well as its characteristic bound states. The non-trivial topological nature of the bound states is further confirmed by the topological band structure analysis and by the topological invariant. While the non-Abelian nature of these states remains an open question, these results allow envisioning the possibility to achieve topological braiding in classical mechanical systems.