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Title: Topological Phononic Crystals with One-Way Elastic Edge Waves

Abstract

We report here a new type of phononic crystals with topologically nontrivial band gaps for both longitudinal and transverse polarizations, resulting in protected one-way elastic edge waves. In our design, gyroscopic inertial effects are used to break the time-reversal symmetry and realize the phononic analogue of the electronic quantum (anomalous) Hall effect. We investigate the response of both hexagonal and square gyroscopic lattices and observe bulk Chern numbers of 1 and 2, indicating that these structures support single and multimode edge elastic waves immune to backscattering. These robust one-way phononic waveguides could potentially lead to the design of a novel class of surface wave devices that are widely used in electronics, telecommunication, and acoustic imaging.

Authors:
 [1];  [2];  [3]
+ Show Author Affiliations
  1. Harvard Univ., Cambridge, MA (United States). Harvard John A. Paulson School of Engineering and Applied Sciences
  2. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Dept. of Physics
  3. Harvard Univ., Cambridge, MA (United States). Harvard John A. Paulson School of Engineering and Applied Sciences. Kavli Inst.
Publication Date:
Research Org.:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Harvard Univ., Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF); US Army Research Office (ARO)
OSTI Identifier:
1505735
Alternate Identifier(s):
OSTI ID: 1213965
Grant/Contract Number:  
SC0001299; CMMI-1120724; CMMI-1149456; DMR-1420570; DMR-1419807; W911NF-13-D-0001
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 115; Journal Issue: 10; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 36 MATERIALS SCIENCE

Citation Formats

Wang, Pai, Lu, Ling, and Bertoldi, Katia. Topological Phononic Crystals with One-Way Elastic Edge Waves. United States: N. p., 2015. Web. doi:10.1103/physrevlett.115.104302.
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Wang, Pai, Lu, Ling, & Bertoldi, Katia. Topological Phononic Crystals with One-Way Elastic Edge Waves. United States. https://doi.org/10.1103/physrevlett.115.104302
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Wang, Pai, Lu, Ling, and Bertoldi, Katia. Fri . "Topological Phononic Crystals with One-Way Elastic Edge Waves". United States. https://doi.org/10.1103/physrevlett.115.104302. https://www.osti.gov/servlets/purl/1505735.
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@article{osti_1505735,
title = {Topological Phononic Crystals with One-Way Elastic Edge Waves},
author = {Wang, Pai and Lu, Ling and Bertoldi, Katia},
abstractNote = {We report here a new type of phononic crystals with topologically nontrivial band gaps for both longitudinal and transverse polarizations, resulting in protected one-way elastic edge waves. In our design, gyroscopic inertial effects are used to break the time-reversal symmetry and realize the phononic analogue of the electronic quantum (anomalous) Hall effect. We investigate the response of both hexagonal and square gyroscopic lattices and observe bulk Chern numbers of 1 and 2, indicating that these structures support single and multimode edge elastic waves immune to backscattering. These robust one-way phononic waveguides could potentially lead to the design of a novel class of surface wave devices that are widely used in electronics, telecommunication, and acoustic imaging.},
doi = {10.1103/physrevlett.115.104302},
journal = {Physical Review Letters},
number = 10,
volume = 115,
place = {United States},
year = {2015},
month = {9}
}
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Journal Article:
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https://doi.org/10.1103/physrevlett.115.104302
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Figures / Tables:

FIG. 1 FIG. 1: Ordinary and gyroscopic phononic crystals: (a) Schematic of the hexagonal lattice. The blue and grey spheres represent concentrated masses m1 and m2 = m1, respectively. The red and black straight rods represent massless linear springs with stiffness k1 and k2 = k1/20, respectively. The dashed cell is themore » primitive cell of the lattice. (b) Unit cell for the ordinary (nongyroscopic) phononic crystal. (c) Band structure of the ordinary (nongyroscopic) phononic crystal. The inset is the Brillouin zone. (d) Schematic of a gyroscope with the top tip pinned to a mass in the lattice. (e) Unit cell for the gyroscopic phononic crystal. (f) Band structure of the gyroscopic phononic crystal (α1 = α2 = 0.3m1) with the Chern numbers labeled on the bulk bands. The frequencies are normalized by ω0 = $\sqrt{k_{1}/m_{1}}$« less
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    Observation of topological edge states of acoustic metamaterials at subwavelength scale
    journal, April 2018

    • Dai, Hongqing; Jiao, Junrui; Xia, Baizhan
    • Journal of Physics D: Applied Physics, Vol. 51, Issue 17
    • DOI: 10.1088/1361-6463/aab504

    Topologically protected edge states for out-of-plane and in-plane bulk elastic waves
    journal, March 2018

    • Huo, Shao-Yong; Chen, Jiu-Jiu; Huang, Hong-Bo
    • Journal of Physics: Condensed Matter, Vol. 30, Issue 14
    • DOI: 10.1088/1361-648x/aab22a

    Directional mechanical response in the bulk of topological metamaterials
    journal, June 2017

    Acoustic topological insulator by honeycomb sonic crystals with direct and indirect band gaps
    journal, September 2018

    Flexural vibration systems with gyroscopic spinners
    journal, September 2019

    • Carta, G.; Nieves, M. J.; Jones, I. S.
    • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 377, Issue 2156
    • DOI: 10.1098/rsta.2019.0154

    Topological two-body bound states in the interacting Haldane model
    journal, January 2018

    Mechanical Quantum Hall Effect in Time-Modulated Elastic Materials
    journal, April 2019

    Tunable Nonlinear Topological Insulator for Acoustic Waves
    journal, October 2019

    Quasilossless acoustic transmission in an arbitrary pathway of a network
    journal, February 2017

    Observation of acoustic valley vortex states and valley-chirality locked beam splitting
    journal, May 2017

    Tailoring phonon band structures with broken symmetry by shaping spatiotemporal modulations of stiffness in a one-dimensional elastic waveguide
    journal, August 2017

    Robust edge states in amorphous gyromagnetic photonic lattices
    journal, September 2017

    Snowflake phononic topological insulator at the nanoscale
    journal, January 2018

    Simulating quantum spin Hall effect in the topological Lieb lattice of a linear circuit network
    journal, February 2018

    Observation of valleylike edge states of sound at a momentum away from the high-symmetry points
    journal, April 2018

    Tunable band topology in gyroscopic lattices
    journal, November 2018

    Double-Weyl Phonons in Transition-Metal Monosilicides
    journal, January 2018

    Topological Insulators by Topology Optimization
    journal, June 2019

    Chiral Voltage Propagation and Calibration in a Topolectrical Chern Circuit
    journal, June 2019

    Acoustic metamaterials: From local resonances to broad horizons
    journal, February 2016

    Topological insulator laser: Theory
    journal, February 2018

    Topological guiding of elastic waves in phononic metamaterials based on 2D pentamode structures
    journal, December 2017

    Soft self-assembly of Weyl materials for light and sound
    journal, April 2018

    • Fruchart, Michel; Jeon, Seung-Yeol; Hur, Kahyun
    • Proceedings of the National Academy of Sciences, Vol. 115, Issue 16
    • DOI: 10.1073/pnas.1720828115

    Guided transition waves in multistable mechanical metamaterials
    journal, January 2020

    • Jin, Lishuai; Khajehtourian, Romik; Mueller, Jochen
    • Proceedings of the National Academy of Sciences, Vol. 117, Issue 5
    • DOI: 10.1073/pnas.1913228117

    Topological chiral phonons in center-stacked bilayer triangle lattices
    journal, May 2018

    • Xu, Xifang; Zhang, Wei; Wang, Jiaojiao
    • Journal of Physics: Condensed Matter, Vol. 30, Issue 22
    • DOI: 10.1088/1361-648x/aabf5e

    Evidence for hidden order in a nonlinear model elastic system
    journal, January 2019

    Topological edge states in acoustic Kagome lattices
    journal, May 2017

    Fracturing of topological Maxwell lattices
    journal, June 2018

    Interfacial waveforms in chiral lattices with gyroscopic spinners
    journal, July 2018

    • Garau, M.; Carta, G.; Nieves, M. J.
    • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 474, Issue 2215
    • DOI: 10.1098/rspa.2018.0132

    Dispersion and topological characteristics of permutative polyatomic phononic crystals
    journal, June 2019

    • Al Ba'ba'a, H.; Nouh, M.; Singh, T.
    • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 475, Issue 2226
    • DOI: 10.1098/rspa.2019.0022

    Tunable Acoustic Valley–Hall Edge States in Reconfigurable Phononic Elastic Waveguides
    journal, January 2018

    Quasitopological rotational waves in mechanical granular graphene
    journal, February 2018

    Topological interface modes in local resonant acoustic systems
    journal, July 2018

    Kink-antikink asymmetry and impurity interactions in topological mechanical chains
    journal, February 2017

    Mechanical Weyl Modes in Topological Maxwell Lattices
    journal, April 2016

    Chiral Edge Mode in the Coupled Dynamics of Magnetic Solitons in a Honeycomb Lattice
    journal, August 2017

    Topological Edge Floppy Modes in Disordered Fiber Networks
    journal, February 2018

    Valley Topological Phases in Bilayer Sonic Crystals
    journal, March 2018

    Valley Physics in Non-Hermitian Artificial Acoustic Boron Nitride
    journal, June 2018

    Observation of Double Weyl Phonons in Parity-Breaking FeSi
    journal, July 2018

    Observation of Nonreciprocal Wave Propagation in a Dynamic Phononic Lattice
    journal, November 2018

    Topological Fano Resonances
    journal, January 2019

    Topological Waves in Fluids with Odd Viscosity
    journal, March 2019

    Edge States and Topological Pumping in Spatially Modulated Elastic Lattices
    journal, July 2019

    First-principle calculation of Chern number in gyrotropic photonic crystals
    journal, January 2020

    • Zhao, Ran; Xie, Guo-Da; Chen, Menglin L. N.
    • Optics Express, Vol. 28, Issue 4
    • DOI: 10.1364/oe.380077

    Recent Advances in Non-Traditional Elastic Wave Manipulation by Macroscopic Artificial Structures
    journal, January 2020

    • Park, Jeonghoon; Lee, Dongwoo; Rho, Junsuk
    • Applied Sciences, Vol. 10, Issue 2
    • DOI: 10.3390/app10020547

    Experimental demonstration of anomalous Floquet topological insulator for sound
    journal, November 2016

    • Peng, Yu-Gui; Qin, Cheng-Zhi; Zhao, De-Gang
    • Nature Communications, Vol. 7, Issue 1
    • DOI: 10.1038/ncomms13368

    Acoustic topological insulator and robust one-way sound transport
    journal, August 2016

    • He, Cheng; Ni, Xu; Ge, Hao
    • Nature Physics, Vol. 12, Issue 12
    • DOI: 10.1038/nphys3867

    Photoinduced Topological Phase Transitions in Topological Magnon Insulators
    journal, March 2018

    Brillouin optomechanics in nanophotonic structures
    journal, July 2019

    • Wiederhecker, Gustavo S.; Dainese, Paulo; Mayer Alegre, Thiago P.
    • APL Photonics, Vol. 4, Issue 7
    • DOI: 10.1063/1.5088169

    Dark state, zero-index and topology in phononic metamaterials with negative mass and negative coupling
    journal, September 2019

    Floquet topological system based on frequency-modulated classical coupled harmonic oscillators
    journal, February 2016

    Topological Mechanics of Origami and Kirigami
    journal, March 2016

    Infrared Topological Plasmons in Graphene
    journal, June 2017

    Geared Topological Metamaterials with Tunable Mechanical Stability
    journal, November 2016

    Robust Edge States in Amorphous Gyromagnetic Photonic Lattices
    conference, January 2017

    Topological sound in active-liquid metamaterials
    journal, July 2017

    • Souslov, Anton; van Zuiden, Benjamin C.; Bartolo, Denis
    • Nature Physics, Vol. 13, Issue 11
    • DOI: 10.1038/nphys4193

    Dial-in Topological Metamaterials Based on Bistable Stewart Platform
    journal, January 2018

    Topological boundary modes in jammed matter
    journal, January 2016

    • Sussman, Daniel M.; Stenull, Olaf; Lubensky, T. C.
    • Soft Matter, Vol. 12, Issue 28
    • DOI: 10.1039/c6sm00875e

    Polarization-dependent and valley-protected Lamb waves in asymmetric pillared phononic crystals
    journal, September 2019

    • Wang, Wei; Bonello, Bernard; Djafari-Rouhani, Bahram
    • Journal of Physics D: Applied Physics, Vol. 52, Issue 50
    • DOI: 10.1088/1361-6463/ab43f9

    L lines, C points and Chern numbers: understanding band structure topology using polarization fields
    journal, November 2017

    • Fösel, Thomas; Peano, Vittorio; Marquardt, Florian
    • New Journal of Physics, Vol. 19, Issue 11
    • DOI: 10.1088/1367-2630/aa8a9f

    Topological helical edge states in water waves over a topographical bottom
    journal, February 2018

    Acoustic graphene network loaded with Helmholtz resonators: a first-principle modeling, Dirac cones, edge and interface waves
    journal, January 2020

    • Zheng, Li-Yang; Achilleos, Vassos; Chen, Ze-Guo
    • New Journal of Physics, Vol. 22, Issue 1
    • DOI: 10.1088/1367-2630/ab60f1

    Dynamically generated synthetic electric fields for photons
    journal, August 2019

    Simulation of topological phases with color center arrays in phononic crystals
    journal, February 2020

    Mirror-symmetry induced topological valley transport along programmable boundaries in a hexagonal sonic crystal
    journal, April 2019

    • Geng, Zhi-Guo; Peng, Yu-Gui; Li, Peng-Qi
    • Journal of Physics: Condensed Matter, Vol. 31, Issue 24
    • DOI: 10.1088/1361-648x/ab0fcc

    Phononic topological states in 1D quasicrystals
    journal, September 2019

    • Silva, J. R. M.; Vasconcelos, M. S.; Anselmo, D. H. A. L.
    • Journal of Physics: Condensed Matter, Vol. 31, Issue 50
    • DOI: 10.1088/1361-648x/ab312a

    Nonreciprocal Wave Propagation in a Continuum-Based Metamaterial with Space-Time Modulated Resonators
    journal, June 2019

    Su-Schrieffer-Heeger Model Inspired Acoustic Interface States and Edge States
    text, January 2018

    Tunable topological bandgaps and frequencies in a pre-stressed soft phononic crystal
    text, January 2018

    Topological mechanics of gyroscopic metamaterials
    text, January 2015

    Experimental Observation of Large Chern numbers in Photonic Crystals
    text, January 2015

    Floquet Topological Insulators for Sound
    text, January 2015

    Topological boundary modes in jammed matter
    text, January 2015

    Model for Topological Phononics and Phonon Diode
    text, January 2016

    Sonic Landau-level lasing and synthetic gauge fields in mechanical metamaterials
    text, January 2016

    Edge states of mechanical diamond and its topological origin
    text, January 2016

    Topological edge floppy modes in disordered fiber networks
    text, January 2017

    Subwavelength and directional control of flexural waves in zone-folding induced topological plates
    text, January 2017

    Soft self-assembly of Weyl materials for light and sound
    text, January 2017

    Topological nodal states in circuit lattice
    text, January 2018

    Observation of nonreciprocal wave propagation in a dynamic phononic lattice
    text, January 2018

    Valley-projected edge modes observed in underwater sonic crystals
    text, January 2018

    Prethermalization and nonreciprocal phonon transport in a levitated optomechanical array
    text, January 2018

    Mechanical analogue of a Majorana bound state
    text, January 2019

    Simulation of topological phases with color center arrays in phononic crystals
    text, January 2020

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