Topological phonon modes in filamentous structures

Abstract

Topological phonon modes are robust vibrations localized at the edges of special structures. Their existence is determined by the bulk properties of the structures and, as such, the topological phonon modes are stable to changes occurring at the edges. The first class of topological phonons was recently found in 2-dimensional structures similar to that of Microtubules. The present work introduces another class of topological phonons, this time occurring in quasi one-dimensional filamentous 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.

accepted for publication (Phys. Rev. E)

References in corpus (13)

• Topological Insulators
• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
• Analogs of quantum Hall effect edge states in photonic crystals
• The quantum spin Hall effect and topological insulators
• Topological phonon modes and their role in dynamic instability of microtubules
• Topological Nature of the Phonon Hall Effect
• The edge spectrum of Chern insulators with rough boundaries
• Mechanism of phonon localized edge modes
• An edge index for the Quantum Spin-Hall effect

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• Sonic Landau-level lasing and synthetic gauge fields in mechanical metamaterials
• Topological nodal states in circuit lattice
• Non-Abelian braiding of light
• Topological networks for quantum communication between distant qubits
• Dynamical Majorana Edge Modes in a Broad Class of Topological Mechanical Systems
• The phonon Hall effect: theory and application
• Thermal Hall effect of magnons in collinear antiferromagnetic insulators: signatures of magnetic and topological phase transitions
• Topological Edge Modes by Smart Patterning
• Excitation band topology and edge matter waves in Bose-Einstein condensates in optical lattices
• Directional mechanical response in the bulk of topological metamaterials
• Kink-antikink asymmetry and impurity interactions in topological mechanical chains
• Topologically protected interface phonons in two-dimensional nanomaterials: hexagonal boron nitride and silicon carbide
• Manifestly gauge independent formulations of the Z2 invariants
• Topological quantization of energy transport in micro- and nano-mechanical lattices
• Edge states of mechanical diamond and its topological origin
• Topological Phonon Modes in A Two-Dimensional Wigner Crystal
• Analytical solutions of topological surface states in a series of lattice models