Multiband topologically protected states realized by elastic honeycomb structures based on fundamental mechanical elements

Al Ba’ba’a, 2020, Elastically-supported lattices for tunable mechanical topological insulators, Extreme Mech. Lett., 38 Anigbogu, 2021, Layered metamaterial beam structures with local resonators for vibration attenuation: Model and experiment, Front. Mech. Eng., 7, 10.3389/fmech.2021.768508 Asorey, 2016, Space, matter and topology, Nat. Phys., 12, 616, 10.1038/nphys3800 Chaunsali, 2018, Experimental demonstration of topological waveguiding in elastic plates with local resonators, New J. Phys., 20, 10.1088/1367-2630/aaeb61 Chaunsali, 2018, Subwavelength and directional control of flexural waves in zone-folding induced topological plates, Phys. Rev. B, 97, 10.1103/PhysRevB.97.054307 Chaunsali, 2021, Stability of topological edge states under strong nonlinear effects, Phys. Rev. B, 103, 10.1103/PhysRevB.103.024106 Chen, 2019, Topological phase transition in mechanical honeycomb lattice, J. Mech. Phys. Solids, 122, 54, 10.1016/j.jmps.2018.08.021 Chen, 2021, Creating acoustic topological insulators through topology optimization, Mech. Syst. Signal Process., 146, 10.1016/j.ymssp.2020.107054 Chen, 2018, A study of topological effects in 1D and 2D mechanical lattices, J. Mech. Phys. Solids, 117, 22, 10.1016/j.jmps.2018.04.013 Chen, 2021, Elastic foundation induced wide bandgaps for actively-tuned topologically protected wave propagation in phononic crystal beams, Int. J. Mech. Sci., 194, 10.1016/j.ijmecsci.2020.106215 Chen, 2016, Tunable topological phononic crystals, Phys. Rev. A, 5 Chen, 2021, Low-frequency tunable topological interface states in soft phononic crystal cylinders, Int. J. Mech. Sci., 191, 10.1016/j.ijmecsci.2020.106098 Chen, 2019, Mechanical quantum Hall effect in time-modulated elastic materials, Phys. Rev. A, 11 Christiansen, 2019, Topological insulators by topology optimization, Phys. Rev. Lett., 122, 10.1103/PhysRevLett.122.234502 Darabi, 2019, Tunable nonlinear topological insulator for acoustic waves, Phys. Rev. A, 12 Deng, 2017, Observation of zone folding induced acoustic topological insulators and the role of spin-mixing defects, Phys. Rev. B, 96, 10.1103/PhysRevB.96.184305 2013, Acoustic metamaterials and phononic crystals, vol. 173 Fleury, 2016, Floquet topological insulators for sound, Nature Commun., 7, 11744, 10.1038/ncomms11744 Foehr, 2018, Spiral-based phononic plates: From wave beaming to topological insulators, Phys. Rev. Lett., 120, 10.1103/PhysRevLett.120.205501 Fruchart, 2013, An introduction to topological insulators, C. R. Phys., 14, 779, 10.1016/j.crhy.2013.09.013 Gao, 2020, Acoustic topological devices based on emulating and multiplexing of pseudospin and valley indices, New J. Phys., 22, 10.1088/1367-2630/ab6633 Garau, 2018, Interfacial waveforms in chiral lattices with gyroscopic spinners, Proc. R. Soc. A: Math., Phys. Eng. Sci., 474, 10.1098/rspa.2018.0132 Geradin, 2015 Haldane, 1988, Model for a quantum Hall effect without Landau levels: Condensed-matter realization of the “parity anomaly”, Phys. Rev. Lett., 61, 2015, 10.1103/PhysRevLett.61.2015 Haldane, 2008, Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry, Phys. Rev. Lett., 100, 10.1103/PhysRevLett.100.013904 Hasan, 2010, Colloquium : Topological insulators, Rev. Modern Phys., 82, 3045, 10.1103/RevModPhys.82.3045 He, 2016, Acoustic topological insulator and robust one-way sound transport, Nat. Phys., 12, 1124, 10.1038/nphys3867 Hong, 2020, Valley-dependent topologically protected elastic waves using continuous graphene membranes on patterned substrates, Nanoscale, 12, 8997, 10.1039/C9NR09809G Jin, 2018, Robustness of conventional and topologically protected edge states in phononic crystal plates, Phys. Rev. B, 98, 10.1103/PhysRevB.98.054307 Kane, 2005, Quantum spin hall effect in graphene, Phys. Rev. Lett., 95, 10.1103/PhysRevLett.95.226801 Khanikaev, 2015, Topologically robust sound propagation in an angular-momentum-biased graphene-like resonator lattice, Nature Commun., 6, 8260, 10.1038/ncomms9260 Kittel, 2005 Lera, 2018, Topological mechanical metamaterial with nonrectilinear constraints, Phys. Rev. B, 98, 10.1103/PhysRevB.98.014101 Li, 2014, Double Dirac cones in phononic crystals, Appl. Phys. Lett., 105, 10.1063/1.4890304 Li, 2018, Observation of elastic topological states in soft materials, Nature Commun., 9, 1370, 10.1038/s41467-018-03830-8 Liu, 2021, Reconfigurable topologically protected wave propagation in metastable structure, J. Sound Vib., 492, 10.1016/j.jsv.2020.115819 Liu, 2018, Tunable acoustic Valley–Hall edge states in reconfigurable phononic elastic waveguides, Phys. Rev. A, 9 Lu, 2016, Valley vortex states in sonic crystals, Phys. Rev. Lett., 116, 10.1103/PhysRevLett.116.093901 Lu, 2014, Dirac cones in two-dimensional artificial crystals for classical waves, Phys. Rev. B, 89, 10.1103/PhysRevB.89.134302 Lu, 2017, Observation of topological valley transport of sound in sonic crystals, Nat. Phys., 13, 369, 10.1038/nphys3999 Ma, 2019, Topological phases in acoustic and mechanical systems, Nat. Rev. Phys., 1, 281, 10.1038/s42254-019-0030-x Makwana, 2018, Geometrically navigating topological plate modes around gentle and sharp bends, Phys. Rev. B, 98, 10.1103/PhysRevB.98.184105 Mao, 2018, Maxwell lattices and topological mechanics, Annu. Rev. Condens. Matter Phys., 9, 413, 10.1146/annurev-conmatphys-033117-054235 Miniaci, 2018, Experimental observation of topologically protected helical edge modes in patterned elastic plates, Phys. Rev. X, 8 Mitchell, 2018, Amorphous topological insulators constructed from random point sets, Nat. Phys., 14, 380, 10.1038/s41567-017-0024-5 Mousavi, 2015, Topologically protected elastic waves in phononic metamaterials, Nature Commun., 6, 8682, 10.1038/ncomms9682 Muhammad, 2021, From photonic crystals to seismic metamaterials: A review via phononic crystals and acoustic metamaterials, Arch. Comput. Methods Eng. Nanthakumar, 2019, Inverse design of quantum Spin Hall-based phononic topological insulators, J. Mech. Phys. Solids, 125, 550, 10.1016/j.jmps.2019.01.009 Nash, 2015, Topological mechanics of gyroscopic metamaterials, Proc. Natl. Acad. Sci., 112, 14495, 10.1073/pnas.1507413112 Nguyen, 2019, Tunable topological bandgaps and frequencies in a pre-stressed soft phononic crystal, J. Appl. Phys., 125, 10.1063/1.5066088 Nieves, 2018, Vibrations and elastic waves in chiral multi-structures, J. Mech. Phys. Solids, 121, 387, 10.1016/j.jmps.2018.07.020 Pal, 2017, Edge waves in plates with resonators: An elastic analogue of the Quantum Valley Hall effect, New J. Phys., 19, 10.1088/1367-2630/aa56a2 Pal, 2016, Helical edge states and topological phase transitions in phononic systems using Bi-layered lattices, J. Appl. Phys., 119, 10.1063/1.4942357 Pratapa, 2018, Bloch wave framework for structures with nonlocal interactions: Application to the design of origami acoustic metamaterials, J. Mech. Phys. Solids, 118, 115, 10.1016/j.jmps.2018.05.012 Qian, 2018, Topology of the Valley-Chern effect, Phys. Rev. B, 98, 10.1103/PhysRevB.98.155138 Rao, 2019 Rosa, 2020, Dynamics and topology of non-Hermitian elastic lattices with non-local feedback control interactions, New J. Phys., 22, 10.1088/1367-2630/ab81b6 Rycerz, 2007, Valley filter and valley valve in graphene, Nat. Phys., 3, 172, 10.1038/nphys547 Sigalas, 1992, Elastic and acoustic wave band structure, J. Sound Vib., 158, 377, 10.1016/0022-460X(92)90059-7 Sirota, 2020, Non-Newtonian topological mechanical metamaterials using feedback control, Phys. Rev. Lett., 125, 10.1103/PhysRevLett.125.256802 Song, 2021, Frequency band-selected one-way topological edge mode via acoustic metamaterials and metasurface, J. Appl. Phys., 130, 10.1063/5.0058546 Souslov, 2017, Topological sound in active-liquid metamaterials, Nat. Phys., 13, 1091, 10.1038/nphys4193 Süsstrunk, 2015, Observation of phononic helical edge states in a mechanical topological insulator, Science, 349, 47, 10.1126/science.aab0239 Swinteck, 2015, Bulk elastic waves with unidirectional backscattering-immune topological states in a time-dependent superlattice, J. Appl. Phys., 118, 10.1063/1.4928619 Takahashi, 2017, Edge states of mechanical diamond and its topological origin, New J. Phys., 19, 10.1088/1367-2630/aa5edb Tang, 2020, Observations of symmetry-induced topological mode steering in a reconfigurable elastic plate, Phys. Rev. B, 102, 10.1103/PhysRevB.102.214103 Tian, 2020, Dispersion tuning and route reconfiguration of acoustic waves in valley topological phononic crystals, Nature Commun., 11, 762, 10.1038/s41467-020-14553-0 Torrent, 2013, Elastic analog of graphene: Dirac cones and edge states for flexural waves in thin plates, Phys. Rev. B, 87, 10.1103/PhysRevB.87.115143 Vila, 2017, Observation of topological valley modes in an elastic hexagonal lattice, Phys. Rev. B, 96, 10.1103/PhysRevB.96.134307 Wang, 2015, Topological phononic crystals with one-way elastic edge waves, Phys. Rev. Lett., 115, 10.1103/PhysRevLett.115.104302 Wang, 2015, Coriolis force induced topological order for classical mechanical vibrations, New J. Phys., 17, 10.1088/1367-2630/17/7/073031 Xia, 2021, Experimental observation of temporal pumping in electromechanical waveguides, Phys. Rev. Lett., 126, 10.1103/PhysRevLett.126.095501 Xiao, 2015, Geometric phase and band inversion in periodic acoustic systems, Nat. Phys., 11, 240, 10.1038/nphys3228 Xiao, 2007, Valley-contrasting physics in graphene: Magnetic moment and topological transport, Phys. Rev. Lett., 99, 10.1103/PhysRevLett.99.236809 Xin, 2020, Topological mechanical metamaterials: A brief review, Curr. Opin. Solid State Mater. Sci., 24, 10.1016/j.cossms.2020.100853 Yan, 2018, On-chip valley topological materials for elastic wave manipulation, Nature Mater., 17, 993, 10.1038/s41563-018-0191-5 Yang, 2015, Topological acoustics, Phys. Rev. Lett., 114, 10.1103/PhysRevLett.114.114301 Zhang, 2020, Dirac degeneracy and elastic topological valley modes induced by local resonant states, Phys. Rev. B, 101, 10.1103/PhysRevB.101.014101 Zhang, 2018, Topological acoustic delay line, Phys. Rev. A, 9 Zhang, 2018, Topological sound, Commun. Phys., 1, 1, 10.1016/j.phycom.2017.12.015 Zheng, 2022, Progress in topological mechanics, Appl. Sci. (Switzerland), 12 Zhou, 2018, Quantum-spin-Hall topological insulator in a spring-mass system, New J. Phys., 20, 10.1088/1367-2630/aaf341 Zhou, 2020, Voltage-controlled quantum valley Hall effect in dielectric membrane-type acoustic metamaterials, Int. J. Mech. Sci., 172, 10.1016/j.ijmecsci.2019.105368 Zhou, 2020, Actively controllable topological phase transition in homogeneous piezoelectric rod system, J. Mech. Phys. Solids, 137, 10.1016/j.jmps.2019.103824 Zhu, 2018, Design and experimental observation of Valley-Hall edge states in diatomic-graphene-like elastic waveguides, Phys. Rev. B, 97, 10.1103/PhysRevB.97.174301