Helical edge states and topological phase transitions in phononic systems using bi-layered lattices

Abstract

We propose a framework to realize helical edge states in phononic systems using two identical lattices with interlayer couplings between them. A methodology is presented to systematically transform a quantum mechanical lattice which exhibits edge states to a phononic lattice, thereby developing a family of lattices with edge states. Parameter spaces with topological phase boundaries in the vicinity of the transformed system are illustrated to demonstrate the robustness to mechanical imperfections. A potential realization in terms of fundamental mechanical building blocks is presented for the hexagonal and Lieb lattices. The lattices are composed of passive components and the building blocks are a set of disks and linear springs. Furthermore, by varying the spring stiffness, topological phase transitions are observed, illustrating the potential for tunability of our lattices.

10 pages, 10 figures

References in corpus (12)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Topological Photonics
• Topological Acoustics
• Observation of phononic helical edge states in a mechanical 'topological insulator'
• Topological Phononic Crystals with One-Way Elastic Edge Waves
• Topologically protected elastic waves in phononic metamaterials
• Floquet Topological Insulators for Sound
• Synthetic gauge fields and Weyl point in Time-Reversal Invariant Acoustic Systems
• Topological Nature of the Phonon Hall Effect
• Manipulation of Dirac Cones in Mechanical Graphene
• Topological phases in a two-dimensional lattice: Magnetic field versus spin-orbit coupling
• Floquet topological system based on frequency-modulated classical coupled harmonic oscillators

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