Observation of phononic helical edge states in a mechanical topological insulator

Abstract

A topological insulator, as originally proposed for electrons governed by quantum mechanics, is characterized by a dichotomy between the interior and the edge of a finite system: The bulk has an energy gap, and the edges sustain excitations traversing this gap. However, it has remained an open question whether the same physics can be observed for systems obeying Newton's equations of motion. We conducted experiments to characterize the collective behavior of mechanical oscillators exhibiting the phenomenology of the quantum spin Hall effect. The phononic edge modes are shown to be helical, and we demonstrate their topological protection via the stability of the edge states against imperfections. Our results may enable the design of topological acoustic metamaterials that can capitalize on the stability of the surface phonons as reliable wave guides.

Conical wave propagation and diffraction in two-dimensional hexagonally packed granular lattices

“…Finally, this realization, in turn, would pave the way for additional intriguing features such as potential acoustic realizations [58] of topological edge states cf. [59][60][61][62], among others. These themes are currently under study and will be reported in future publications.…”

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

“…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 .…”

“…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.…”

Experimental verification of acoustic pseudospin multipoles in a symmetry-broken snowflakelike topological insulator

“…Topological states have also been extended to condensed-matter physics based on the quantum Hall effect (QHE) [1,2], the quantum spin Hall effect (QSHE) [3,4], and topological insulators (TIs) [5,6]. Over the past ten years, investigation into new topologically protected edge states has started to grow in other subfields of physics, such as photonics [7][8][9][10][11][12][13][14][15][16], phononics [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32], and mechanics [33][34][35][36]. The intrinsic difference between electrons and acoustic waves represents a great challenge in creating the spinlike degree of freedom for sound only possessing longitudinal polarization.…”