Experimental Observation of Topologically Protected Helical Edge Modes in Patterned Elastic Plates

The investigation of topologically protected waves in classical media has opened unique opportunities to achieve exotic properties like one-way phonon transport, protection from backscattering and immunity to imperfections. Contrary to acoustic and electromagnetic domains, their observation in elastic solids has so far been elusive due to the presence of both shear and longitudinal modes and their modal conversion at interfaces and free surfaces. Here we report the experimental observation of topologically protected helical edge waves in elastic media. The considered structure consists of an elastic plate patterned according to a Kagome architecture with an accidental degeneracy of two Dirac cones induced by drilling through holes. The careful breaking of symmetries couples the corresponding elastic modes which effectively emulates spin orbital coupling in the quantum spin Hall effect. The results shed light on the topological properties of the proposed plate waveguide and opens avenues for the practical realization of compact, passive and cost-effective elastic topological waveguides.

[1]  K. Bertoldi,et al.  Topological Phononic Crystals with One-Way Elastic Edge Waves. , 2015, Physical review letters.

[2]  P. Sheng,et al.  Acoustic metamaterials: From local resonances to broad horizons , 2016, Science Advances.

[3]  Andrea Alù,et al.  Floquet topological insulators for sound , 2015, Nature Communications.

[4]  Gennady Shvets,et al.  Photonic topological insulators. , 2012, Nature materials.

[5]  Fei Gao,et al.  Topological acoustics. , 2014, Physical review letters.

[6]  Z. Wang,et al.  Topologically protected elastic waves in phononic metamaterials , 2015, Nature Communications.

[7]  F. Marquardt,et al.  Topological Phases of Sound and Light , 2014, 1409.5375.

[8]  Topological Photonics , 2014, 1408.6730.

[9]  T. Ozawa,et al.  Floquet topological system based on frequency-modulated classical coupled harmonic oscillators , 2015, 1510.04697.

[10]  A S Gliozzi,et al.  Proof of Concept for an Ultrasensitive Technique to Detect and Localize Sources of Elastic Nonlinearity Using Phononic Crystals. , 2017, Physical review letters.

[11]  Wang Yao,et al.  Valley-contrasting physics in graphene: magnetic moment and topological transport. , 2007, Physical review letters.

[12]  Emil Prodan,et al.  Topological phonon modes and their role in dynamic instability of microtubules. , 2009, Physical review letters.

[13]  E. J. Mele,et al.  Quantum spin Hall effect in graphene. , 2004, Physical review letters.

[14]  S. Huber,et al.  Classification of topological phonons in linear mechanical metamaterials , 2016, Proceedings of the National Academy of Sciences.

[15]  F. Semperlotti,et al.  Design and experimental observation of valley-Hall edge states in diatomic-graphene-like elastic waveguides , 2017, 1712.10271.

[16]  Camille Jouvaud,et al.  Robust reconfigurable electromagnetic pathways within a photonic topological insulator. , 2016, Nature materials.

[17]  Accidental degeneracy of double Dirac cones in a phononic crystal , 2014, Scientific reports.

[18]  Jiuyang Lu,et al.  Observation of topological valley transport of sound in sonic crystals , 2016, Nature Physics.

[19]  C. Kane,et al.  Phonons and elasticity in critically coordinated lattices , 2015, Reports on progress in physics. Physical Society.

[20]  M. Ruzzene,et al.  Edge waves in plates with resonators: an elastic analogue of the quantum valley Hall effect , 2016, 1611.08919.

[21]  D. Kleckner,et al.  Topological mechanics of gyroscopic metamaterials , 2015, Proceedings of the National Academy of Sciences.

[22]  Miss A.O. Penney (b) , 1974, The New Yale Book of Quotations.

[23]  Denis Bartolo,et al.  Topological sound in active-liquid metamaterials , 2016, Nature Physics.

[24]  Xueqin Huang,et al.  Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials. , 2011, Nature materials.

[25]  M. Soljačić,et al.  Topological photonics , 2014, Nature Photonics.

[26]  Gennady Shvets,et al.  Photonic topological insulators. , 2013, Nature materials.

[27]  J. Vasseur,et al.  Bulk elastic waves with unidirectional backscattering-immune topological states in a time-dependent superlattice , 2015 .

[28]  Manzhu Ke,et al.  Dirac cones in two-dimensional artificial crystals for classical waves , 2014 .

[29]  Massimo Ruzzene,et al.  Helical edge states and topological phase transitions in phononic systems using bi-layered lattices , 2015, 1511.07507.

[30]  Haldane,et al.  Model for a quantum Hall effect without Landau levels: Condensed-matter realization of the "parity anomaly" , 1988, Physical review letters.

[31]  David Schuster,et al.  Time- and Site-Resolved Dynamics in a Topological Circuit , 2015 .

[32]  R. Fleury,et al.  Sound Isolation and Giant Linear Nonreciprocity in a Compact Acoustic Circulator , 2014, Science.

[33]  R. Fleury,et al.  Topologically robust sound propagation in an angular-momentum-biased graphene-like resonator lattice , 2015, Nature Communications.

[34]  C. Kane,et al.  Topological Insulators , 2019, Electromagnetic Anisotropy and Bianisotropy.

[35]  Massimo Ruzzene,et al.  Observation of topological valley modes in an elastic hexagonal lattice , 2017, 1705.08247.

[36]  Volker Heine,et al.  Group Theory: Application to the Physics of Condensed Matter , 2008 .

[37]  K. Sakoda Double Dirac cones in triangular-lattice metamaterials. , 2012, Optics express.

[38]  Xu Ni,et al.  Acoustic topological insulator and robust one-way sound transport , 2015, Nature Physics.

[39]  S. Huber,et al.  Observation of phononic helical edge states in a mechanical topological insulator , 2015, Science.

[40]  O. Painter,et al.  Pseudomagnetic fields for sound at the nanoscale , 2016, Proceedings of the National Academy of Sciences.

[41]  Alessandro Marzani,et al.  Complete band gaps in a polyvinyl chloride (PVC) phononic plate with cross-like holes: numerical design and experimental verification. , 2015, Ultrasonics.