Self-induced topological transition in phononic crystals by nonlinearity management

Abstract

A new design paradigm of topology has recently emerged to manipulate the flow of phonons. At its heart lies a topological transition to a nontrivial state with exotic properties. This framework has been limited to linear lattice dynamics so far. Here we show a topological transition in a nonlinear regime and its implication in emerging nonlinear solutions. We employ nonlinearity management such that the system consists of masses connected with two types of nonlinear springs, "stiffening" and "softening" types, alternating along the length. We show, analytically and numerically, that the lattice makes a topological transition simply by changing the excitation amplitude and invoking nonlinear dynamics. Consequently, we witness the emergence of a new family of finite-frequency edge modes, not observed in linear phononic systems. We also report the existence of kink solitons at the topological transition point. These correspond to heteroclinic orbits that form a closed curve in the phase portrait separating the two topologically-distinct regimes. These findings suggest that nonlinearity can be used as a strategic tuning knob to alter topological characteristics of phononic crystals. These also provide fresh perspectives towards understanding a new family of nonlinear solutions in light of topology.

arXiv comment14 pages, 8 figures

References in corpus (16)

• Topological Insulators
• Topological Photonics
• Topological Boundary Modes in Isostatic Lattices
• The Zak phase and the existence of edge states in graphene
• Edge Solitons in Nonlinear Photonic Topological Insulators
• Classification of topological phonons in linear mechanical metamaterials
• Nonlinear conduction via solitons in a topological mechanical insulator
• Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics
• Self-induced topological transitions and edge states supported by nonlinear staggered potentials
• Observation and control of nonlinear electromagnetic topological edge states
• On the mechanical modeling of the extreme softening/stiffening response of axially loaded tensegrity prisms
• Demonstrating an in-situ topological band transition in cylindrical granular chains
• Amplitude-dependent topological edge states in nonlinear phononic lattices
• Chirality of topological gap solitons in bosonic dimer chains
• Ring Dirac Solitons in Nonlinear Topological Lattices
• Topological interface states mediated by spontaneous symmetry breaking

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