Topological Phase Transition in Mechanical Honeycomb Lattice

Abstract

Topological materials provide a new tool to direct wave energy with unprecedented precision and robustness. Three elastic topological phases, the valley Hall, Chern and spin Hall insulators, are currently studied, and they are achieved separately in rather distinct configurations. Here, we explore analytically various topological phase transitions for in-plane elastic wave in a unified mass-spring honeycomb lattice. It is demonstrated that the three elastic topological phases can be realized in this single lattice by designing mass, stiffness or introducing Coriolis' effect. In particular, the interface between valley Hall and Chern insulators is found to support topological interface mode for the first time. Perturbation method is used to derive the analytic effective continuum model in the neighbor of band degeneracy, and the physics in topological phase transitions are revealed through evaluation of topological invariants. The topologically protected interface states, their decaying profile as well as the pseudo-spin-indicating polarization specific for elastic wave are systematically analyzed, and these results are further confirmed numerically by Bloch wave analysis of domain wall strip and transient simulation of finite sized sample. This study offers a concise and unified analytical model to explore topology nature of elastic wave, and can provide intuitive guidance to design of continuum mechanical topological materials.

28 pages, 12 figures

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Cited by in corpus (18)

• Flat bands in magic-angle vibrating plates
• Valley and pseudospin-valley topologically protected edge states in symmetric pillared phononic crystals
• Elastic Valley Spin Controlled Chiral Coupling in Topological Valley Phononic Crystals
• Topological waves guided by a glide-reflection symmetric crystal interface
• Existence of Corner Modes in Elastic Twisted Kagome Lattices
• Multidimensional sound propagation in 3D high-order topological sonic insulator
• Polarization-dependent and Valley-protected Lamb Waves in Asymmetric Pillared Phononic Crystals
• Chiral Triclinic Metamaterial Crystals Supporting Isotropic Acoustical Activity and Isotropic Chiral Phonons
• Efficient Design of Helical Higher-Order Topological Insulators in 3D Elastic Medium
• A General Method to Design Acoustic Higher-Order Topological Insulators
• Rayleigh surface waves of extremal elastic materials
• Topological phase transition in disordered elastic quantum spin Hall system
• Characterization of elastic topological states using dynamic mode decomposition
• The topological dynamics of continuum lattice grid structures
• Omnidirectional domain wall modes protected by fragile topological states
• Zero-frequency corner modes in mechanical graphene
• Topological defect states in elastic phononic plates
• Classification of rotational zero modes in 2D micropolar solids