Topological phonon modes in filamentary structures

This work describes a class of topological phonon modes, that is, mechanical vibrations localized at the edges of special structures that are robust against the deformations of the structures. A class of topological phonons was recently found in two-dimensional structures similar to that of microtubules. The present work introduces another class of topological phonons, this time occurring in quasi-one-dimensional filamentary structures with inversion symmetry. The phenomenon is exemplified using a structure inspired from that of actin microfilaments, present in most live cells. The system discussed here is probably the simplest structure that supports topological phonon modes, a fact that allows detailed analysis in both time and frequency domains. We advance the hypothesis that the topological phonon modes are ubiquitous in the biological world and that living organisms make use of them during various processes.