Topologically protected elastic waves in one-dimensional phononic crystals of continuous media

Abstract

We report the design of silica-based 1D phononic crystals (PnCs) with topologically distinct complete phononic bandgaps (PnBGs) and the observation of a topologically protected state of elastic waves at their interface. By choosing different structural parameters of unit cells, two PnCs can possess a common PnBG with different topological nature. At the interface between the two PnCs, a topological interface mode with a quality factor of ~5,650 is observed in the PnBG. Spatial confinement of the interface mode is also confirmed by using photoelastic imaging technique. Such topologically protected elastic states are potentially applicable for constructing novel phononic devices. 2 Topological phenomena in quantum Hall, quantum spin Hall systems and topological insulators have been extensively studied in condensed matter physics 1,2 . A hallmark of such phenomena is topologically protected edge states which are robust against defects and imperfection. The presence of the topological edge states is due to topological characters of bulk electronic bands, which is called the bulk-edge correspondence 3,4 . Recently, topological concepts have also been extended to bosonic systems including photonic and phononic structures which support the topologically protected states of light [5][6][7][8][9][10][11][12][13][14][15][16] , acoustic 17-24 and mechanical [25][26][27][28][29][30] waves for various applications. Most of experimental studies in mechanical systems have focused on discrete structures such as coupled pendula 27,28 or granular chains 30 .Although they are useful for describing topological concepts in mechanical systems, continuous solid structures supporting topological elastic waves are highly expected to realize practical high speed phononic applications. In contrast to the intensive theoretical studies of the topological elastic waves [31][32][33][34] , there is a lack of an experimental demonstration in the continuous structures. One of the main challenges is due to high modal densities of elastic waves in continuous-solid structures, preventing the formation of complete PnBGs with topologically distinct properties. Very recently, experimental demonstration of topological elastic waves using continuous structures has been reported 35,36 . However, the structures have only partial phononic bandgap (PnBG) which can cause loss of the topological elastic states by coupling with other propagation modes. Thus, it remains a challenge to realize topological elastic waves in continuous structures with complete PnBGs.To the best of our knowledge, experimental demonstration of topological elastic waves in continuous structures with complete PnBGs is very limited even in one-dimensional (1D) periodic system due to their high modal densities.In this report, we report the experimental realization of topological interface state in solidstructured quasi 1D phononic crystals (PnCs) 37 . In 1D periodic systems, topologically protected edge states are zero-dimensional (0D), localized at the interface between two PnCs...

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