skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

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]
  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.
Wang, Pai, Lu, Ling, & Bertoldi, Katia. Topological Phononic Crystals with One-Way Elastic Edge Waves. United States. doi:https://doi.org/10.1103/physrevlett.115.104302
Wang, Pai, Lu, Ling, and Bertoldi, Katia. Fri . "Topological Phononic Crystals with One-Way Elastic Edge Waves". United States. doi:https://doi.org/10.1103/physrevlett.115.104302. https://www.osti.gov/servlets/purl/1505735.
@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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 104 works
Citation information provided by
Web of Science

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

Save / Share:

Works referenced in this record:

Wave beaming effects in two-dimensional cellular structures
journal, April 2003

  • Ruzzene, Massimo; Scarpa, Fabrizio; Soranna, Francesco
  • Smart Materials and Structures, Vol. 12, Issue 3
  • DOI: 10.1088/0964-1726/12/3/307

Topological insulators and superconductors
journal, October 2011


Waveguiding in two-dimensional piezoelectric phononic crystal plates
journal, June 2007

  • Vasseur, J. O.; Hladky-Hennion, A. -C.; Djafari-Rouhani, B.
  • Journal of Applied Physics, Vol. 101, Issue 11
  • DOI: 10.1063/1.2740352

Elastic analog of graphene: Dirac cones and edge states for flexural waves in thin plates
journal, March 2013


Dynamics of Phononic Materials and Structures: Historical Origins, Recent Progress, and Future Outlook
journal, May 2014

  • Hussein, Mahmoud I.; Leamy, Michael J.; Ruzzene, Massimo
  • Applied Mechanics Reviews, Vol. 66, Issue 4
  • DOI: 10.1115/1.4026911

On modifications of Newton's second law and linear continuum elastodynamics
journal, November 2006

  • Milton, Graeme W.; Willis, John R.
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 463, Issue 2079
  • DOI: 10.1098/rspa.2006.1795

Observation of phononic helical edge states in a mechanical topological insulator
journal, July 2015


Vortex-type elastic structured media and dynamic shielding
journal, May 2012

  • Brun, M.; Jones, I. S.; Movchan, A. B.
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 468, Issue 2146
  • DOI: 10.1098/rspa.2012.0165

Surface phonons, elastic response, and conformal invariance in twisted kagome lattices
journal, June 2012

  • Sun, K.; Souslov, A.; Mao, X.
  • Proceedings of the National Academy of Sciences, Vol. 109, Issue 31
  • DOI: 10.1073/pnas.1119941109

Dispersion properties of vortex-type monatomic lattices
journal, June 2014


Frequency Modulation in the Transmittivity of Wave Guides in Elastic-Wave Band-Gap Materials
journal, November 2000


Dirac cones at k→=0 in acoustic crystals and zero refractive index acoustic materials
journal, February 2012

  • Liu, Fengming; Huang, Xueqin; Chan, C. T.
  • Applied Physics Letters, Vol. 100, Issue 7
  • DOI: 10.1063/1.3686907

Acoustic band structure of periodic elastic composites
journal, September 1993


Sound Isolation and Giant Linear Nonreciprocity in a Compact Acoustic Circulator
journal, January 2014


Elastic metamaterials with inertial locally resonant structures: Application to lensing and localization
journal, May 2013


Effective theory of quadratic degeneracies
journal, June 2008


Topological photonics
journal, October 2014


Topological Acoustics
journal, March 2015


Narrow Low-Frequency Spectrum and Heat Management by Thermocrystals
journal, January 2013


Collimation of sound assisted by acoustic surface waves
journal, October 2007

  • Christensen, J.; Fernandez-Dominguez, A. I.; de Leon-Perez, F.
  • Nature Physics, Vol. 3, Issue 12
  • DOI: 10.1038/nphys774

Geometric phase and band inversion in periodic acoustic systems
journal, February 2015

  • Xiao, Meng; Ma, Guancong; Yang, Zhiyu
  • Nature Physics, Vol. 11, Issue 3
  • DOI: 10.1038/nphys3228

Topologically protected one-way edge mode in networks of acoustic resonators with circulating air flow
journal, May 2015


Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
journal, January 2008


Acoustic Analogue of Graphene: Observation of Dirac Cones in Acoustic Surface Waves
journal, April 2012


Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal
journal, January 2008


Experimental demonstration of an acoustic magnifying hyperlens
journal, October 2009

  • Li, Jensen; Fok, Lee; Yin, Xiaobo
  • Nature Materials, Vol. 8, Issue 12
  • DOI: 10.1038/nmat2561

Topological modes bound to dislocations in mechanical metamaterials
journal, January 2015

  • Paulose, Jayson; Chen, Bryan Gin-ge; Vitelli, Vincenzo
  • Nature Physics, Vol. 11, Issue 2
  • DOI: 10.1038/nphys3185

First-principles study of Dirac and Dirac-like cones in phononic and photonic crystals
journal, July 2012


Double Dirac cones in phononic crystals
journal, July 2014

  • Li, Yan; Wu, Ying; Mei, Jun
  • Applied Physics Letters, Vol. 105, Issue 1
  • DOI: 10.1063/1.4890304

Experiments on Seismic Metamaterials: Molding Surface Waves
journal, March 2014


The quantized Hall effect
journal, July 1986


Dark acoustic metamaterials as super absorbers for low-frequency sound
journal, January 2012

  • Mei, Jun; Ma, Guancong; Yang, Min
  • Nature Communications, Vol. 3, Issue 1
  • DOI: 10.1038/ncomms1758

Band structure of elastic waves in two dimensional systems
journal, April 1993


Colloquium: Topological insulators
journal, November 2010


Coriolis force induced topological order for classical mechanical vibrations
journal, July 2015


Topological Phonon Modes and Their Role in Dynamic Instability of Microtubules
journal, December 2009


Multimode One-Way Waveguides of Large Chern Numbers
journal, September 2014


Hybrid elastic solids
journal, June 2011

  • Lai, Yun; Wu, Ying; Sheng, Ping
  • Nature Materials, Vol. 10, Issue 8
  • DOI: 10.1038/nmat3043

Tunable filtering and demultiplexing in phononic crystals with hollow cylinders
journal, April 2004


Harnessing Buckling to Design Tunable Locally Resonant Acoustic Metamaterials
journal, July 2014


Sonic Band Gaps in Finite Elastic Media: Surface States and Localization Phenomena in Linear and Point Defects
journal, April 1999

  • Torres, M.; Montero de Espinosa, F. R.; García-Pablos, D.
  • Physical Review Letters, Vol. 82, Issue 15
  • DOI: 10.1103/PhysRevLett.82.3054

Locally Resonant Sonic Materials
journal, September 2000


Ultrasonic metamaterials with negative modulus
journal, April 2006

  • Fang, Nicholas; Xi, Dongjuan; Xu, Jianyi
  • Nature Materials, Vol. 5, Issue 6
  • DOI: 10.1038/nmat1644

Wave propagation in two-dimensional periodic lattices
journal, April 2006

  • Phani, A. Srikantha; Woodhouse, J.; Fleck, N. A.
  • The Journal of the Acoustical Society of America, Vol. 119, Issue 4
  • DOI: 10.1121/1.2179748

Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the "Parity Anomaly"
journal, October 1988


Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
journal, June 2005

  • Fukui, Takahiro; Hatsugai, Yasuhiro; Suzuki, Hiroshi
  • Journal of the Physical Society of Japan, Vol. 74, Issue 6
  • DOI: 10.1143/JPSJ.74.1674

Topological boundary modes in isostatic lattices
journal, December 2013

  • Kane, C. L.; Lubensky, T. C.
  • Nature Physics, Vol. 10, Issue 1
  • DOI: 10.1038/nphys2835

Topological Nature of the Phonon Hall Effect
journal, November 2010


Interaction of a Contact Resonance of Microspheres with Surface Acoustic Waves
journal, July 2013


Observation of unidirectional backscattering-immune topological electromagnetic states
journal, October 2009

  • Wang, Zheng; Chong, Yidong; Joannopoulos, J. D.
  • Nature, Vol. 461, Issue 7265
  • DOI: 10.1038/nature08293

Nonlinear conduction via solitons in a topological mechanical insulator
journal, August 2014

  • Chen, B. G. -g.; Upadhyaya, N.; Vitelli, V.
  • Proceedings of the National Academy of Sciences, Vol. 111, Issue 36
  • DOI: 10.1073/pnas.1405969111

Acoustic imaging and collimating by slabs of sonic crystalsmade from arrays of rigid cylinders in air
journal, August 2004

  • Chen, Liang-Shan; Kuo, Chao-Hsien; Ye, Zhen
  • Applied Physics Letters, Vol. 85, Issue 6
  • DOI: 10.1063/1.1781351

Metamaterial with Simultaneously Negative Bulk Modulus and Mass Density
journal, August 2007


Nanophononic Metamaterial: Thermal Conductivity Reduction by Local Resonance
journal, February 2014


Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials
journal, May 2011

  • Huang, Xueqin; Lai, Yun; Hang, Zhi Hong
  • Nature Materials, Vol. 10, Issue 8, p. 582-586
  • DOI: 10.1038/nmat3030

    Works referencing / citing this record:

    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

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


    Unusual one-way edge state in acoustic gyroscopic continuum
    journal, September 2018


    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

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


    Non-Abelian Braiding of Light
    journal, August 2016


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


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


    Applications of Topological Photonics in Integrated Photonic Devices
    journal, August 2017


    Topological Phononics: From Fundamental Models to Real Materials
    journal, August 2019

    • Liu, Yizhou; Chen, Xiaobin; Xu, Yong
    • Advanced Functional Materials, Vol. 30, Issue 8
    • DOI: 10.1002/adfm.201904784

    Flexible mechanical metamaterials
    journal, October 2017

    • Bertoldi, Katia; Vitelli, Vincenzo; Christensen, Johan
    • Nature Reviews Materials, Vol. 2, Issue 11
    • DOI: 10.1038/natrevmats.2017.66

    Topological magnetoplasmon
    journal, November 2016

    • Jin, Dafei; Lu, Ling; Wang, Zhong
    • Nature Communications, Vol. 7, Issue 1
    • DOI: 10.1038/ncomms13486

    Topologically protected elastic waves in phononic metamaterials
    journal, November 2015

    • Mousavi, S. Hossein; Khanikaev, Alexander B.; Wang, Zheng
    • Nature Communications, Vol. 6, Issue 1
    • DOI: 10.1038/ncomms9682

    Three-dimensional all-dielectric photonic topological insulator
    journal, December 2016


    Observation of elastic topological states in soft materials
    journal, April 2018


    Metamaterials with amplitude gaps for elastic solitons
    journal, August 2018


    Topological analog signal processing
    journal, May 2019


    Amorphous topological insulators constructed from random point sets
    journal, January 2018


    Simultaneous multi-band valley-protected topological edge states of shear vertical wave in two-dimensional phononic crystals with veins
    journal, September 2017


    Band transition and topological interface modes in 1D elastic phononic crystals
    journal, May 2018


    Experimental demonstration of coherent superpositions in an ultrasonic pseudospin
    journal, October 2019


    Manipulation of Dirac Cones in Mechanical Graphene
    journal, December 2015

    • Kariyado, Toshikaze; Hatsugai, Yasuhiro
    • Scientific Reports, Vol. 5, Issue 1
    • DOI: 10.1038/srep18107

    Pseudo-time-reversal symmetry and topological edge states in two-dimensional acoustic crystals
    journal, September 2016

    • Mei, Jun; Chen, Zeguo; Wu, Ying
    • Scientific Reports, Vol. 6, Issue 1
    • DOI: 10.1038/srep32752

    Topologically protected interface phonons in two-dimensional nanomaterials: hexagonal boron nitride and silicon carbide
    journal, January 2018

    • Jiang, Jin-Wu; Wang, Bing-Shen; Park, Harold S.
    • Nanoscale, Vol. 10, Issue 29
    • DOI: 10.1039/c8nr04314k

    Perspective: Acoustic metamaterials in transition
    journal, March 2018

    • Wu, Ying; Yang, Min; Sheng, Ping
    • Journal of Applied Physics, Vol. 123, Issue 9
    • DOI: 10.1063/1.5007682

    Valley-projected edge modes observed in underwater sonic crystals
    journal, January 2019

    • Shen, Yuanyuan; Qiu, Chunyin; Cai, Xiangxi
    • Applied Physics Letters, Vol. 114, Issue 2
    • DOI: 10.1063/1.5049856

    Su-Schrieffer-Heeger model inspired acoustic interface states and edge states
    journal, November 2018

    • Li, Xin; Meng, Yan; Wu, Xiaoxiao
    • Applied Physics Letters, Vol. 113, Issue 20
    • DOI: 10.1063/1.5051523

    Prestress tuning of negative refraction and wave channeling from flexural sources
    journal, January 2019

    • Bordiga, G.; Cabras, L.; Piccolroaz, A.
    • Applied Physics Letters, Vol. 114, Issue 4
    • DOI: 10.1063/1.5084258

    Broadband modulation of subwavelength topological interface states in a one-dimensional acoustic system
    journal, January 2020

    • Wang, Zhenyu; Zhao, Degang; Luo, Jinlong
    • Applied Physics Letters, Vol. 116, Issue 1
    • DOI: 10.1063/1.5135948

    Classification of topological phonons in linear mechanical metamaterials
    journal, August 2016

    • Süsstrunk, Roman; Huber, Sebastian D.
    • Proceedings of the National Academy of Sciences, Vol. 113, Issue 33
    • DOI: 10.1073/pnas.1605462113

    Pseudomagnetic fields for sound at the nanoscale
    journal, April 2017

    • Brendel, Christian; Peano, Vittorio; Painter, Oskar J.
    • Proceedings of the National Academy of Sciences, Vol. 114, Issue 17
    • DOI: 10.1073/pnas.1615503114

    Intrinsic spin of elastic waves
    journal, September 2018

    • Long, Yang; Ren, Jie; Chen, Hong
    • Proceedings of the National Academy of Sciences, Vol. 115, Issue 40
    • DOI: 10.1073/pnas.1808534115

    Elastic phononic plates with first-order and second-order topological phases
    journal, January 2020

    • Tong, Liang; Fan, Haiyan; Xia, Baizhan
    • Journal of Physics D: Applied Physics, Vol. 53, Issue 11
    • DOI: 10.1088/1361-6463/ab6055

    Topologically protected edge transport of sound in coupled cavities of a modified honeycomb lattice
    journal, July 2018

    • Geng, Zhi-Guo; Peng, Yu-Gui; Shen, Ya-Xi
    • Journal of Physics: Condensed Matter, Vol. 30, Issue 34
    • DOI: 10.1088/1361-648x/aad398

    Topological phase transition with p orbitals in the exciton-polariton honeycomb lattice
    journal, June 2019

    • Zhang, Chuanyi; Wang, Yuanxu; Zhang, Weifeng
    • Journal of Physics: Condensed Matter, Vol. 31, Issue 33
    • DOI: 10.1088/1361-648x/ab2289

    Two-dimensionally confined topological edge states in photonic crystals
    journal, November 2016


    Edge waves in plates with resonators: an elastic analogue of the quantum valley Hall effect
    journal, February 2017


    Edge states of mechanical diamond and its topological origin
    journal, March 2017

    • Takahashi, Yuta; Kariyado, Toshikaze; Hatsugai, Yasuhiro
    • New Journal of Physics, Vol. 19, Issue 3
    • DOI: 10.1088/1367-2630/aa5edb

    Topological acoustic polaritons: robust sound manipulation at the subwavelength scale
    journal, July 2017


    Nonreciprocal wave propagation and parametric amplification of bulk elastic waves in nonlinear anisotropic materials
    journal, February 2020

    • Zakeri, Mahsa; Keller, Scott M.; Wang, Yuanxun Ethan
    • New Journal of Physics, Vol. 22, Issue 2
    • DOI: 10.1088/1367-2630/ab61d9

    Acoustic topological devices based on emulating and multiplexing of pseudospin and valley indices
    journal, January 2020


    Topology of triple-point metals
    journal, July 2019


    Magnonic analogs of topological Dirac semimetals
    journal, September 2017


    Gyro-elastic beams for the vibration reduction of long flexural systems
    journal, July 2017

    • Carta, G.; Jones, I. S.; Movchan, N. V.
    • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 473, Issue 2203
    • DOI: 10.1098/rspa.2017.0136

    Wave polarization and dynamic degeneracy in a chiral elastic lattice
    journal, December 2019

    • Carta, G.; Jones, I. S.; Movchan, N. V.
    • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 475, Issue 2232
    • DOI: 10.1098/rspa.2019.0313

    One-way interfacial waves in a flexural plate with chiral double resonators
    journal, November 2019

    • Carta, G.; Colquitt, D. J.; Movchan, A. B.
    • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 378, Issue 2162
    • DOI: 10.1098/rsta.2019.0350

    Experimental Evidence of Robust Acoustic Valley Hall Edge States in a Nonresonant Topological Elastic Waveguide
    journal, January 2019


    Observation of Edge Waves in a Two-Dimensional Su-Schrieffer-Heeger Acoustic Network
    journal, September 2019


    Collective Resonances of a Chain of Coupled Phononic Microresonators
    journal, January 2020


    Tunable Topological Phononic Crystals
    journal, May 2016


    Sonic valley-Chern insulators
    journal, January 2020


    Phononic Weyl nodal straight lines in MgB 2
    journal, January 2020


    Unidirectional transport in electronic and photonic Weyl materials by Dirac mass engineering
    journal, December 2015


    Transport and localization in a topological phononic lattice with correlated disorder
    journal, October 2016


    Model for topological phononics and phonon diode
    journal, August 2017


    Line nodes, Dirac points, and Lifshitz transition in two-dimensional nonsymmorphic photonic crystals
    journal, August 2017


    Topological phononic insulator with robust pseudospin-dependent transport
    journal, September 2017


    Experimental verification of acoustic pseudospin multipoles in a symmetry-broken snowflakelike topological insulator
    journal, December 2017


    Coexistent three-component and two-component Weyl phonons in TiS, ZrSe, and HfTe
    journal, February 2018


    Subwavelength and directional control of flexural waves in zone-folding induced topological plates
    journal, February 2018


    Realization of a topological phase transition in a gyroscopic lattice
    journal, March 2018


    Weyl points of mechanical diamond
    journal, January 2019


    Disorder and Metal-Insulator Transitions in Weyl Semimetals
    journal, December 2015


    Experimental Observation of Large Chern Numbers in Photonic Crystals
    journal, December 2015


    Valley Vortex States in Sonic Crystals
    journal, February 2016


    Circular Phonon Dichroism in Weyl Semimetals
    journal, August 2017


    Sonic Landau Levels and Synthetic Gauge Fields in Mechanical Metamaterials
    journal, November 2017


    Pseudospins and Topological Effects of Phonons in a Kekulé Lattice
    journal, December 2017


    Edge Modes and Asymmetric Wave Transport in Topological Lattices: Experimental Characterization at Finite Frequencies
    journal, August 2018


    Experimental Demonstration of Acoustic Chern Insulators
    journal, January 2019


    Klein-Gordon Representation of Acoustic Waves and Topological Origin of Surface Acoustic Modes
    journal, August 2019


    Gradient-Index Granular Crystals: From Boomerang Motion to Asymmetric Transmission of Waves
    journal, November 2019


    Phononic Helical Nodal Lines with PT Protection in MoB 2
    journal, December 2019


    Inverse design of discrete mechanical metamaterials
    journal, September 2019


    Fragile topologically protected perfect reflection for acoustic waves
    journal, February 2020


    Experimental Observation of Topologically Protected Helical Edge Modes in Patterned Elastic Plates
    journal, September 2018


    Topological Boundary Floppy Modes in Quasicrystals
    journal, June 2019


    Modulating Band Gap Structure by Parametric Excitations
    journal, April 2018

    • Yang, Xiao-Dong; Cui, Qing-Dian; Qian, Ying-Jing
    • Journal of Applied Mechanics, Vol. 85, Issue 6
    • DOI: 10.1115/1.4039755

    Doppler-Based Acoustic Gyrator
    journal, July 2018

    • Zangeneh-Nejad, Farzad; Fleury, Romain
    • Applied Sciences, Vol. 8, Issue 7
    • DOI: 10.3390/app8071083

    Three-Dimensional Topological States of Phonons with Tunable Pseudospin Physics
    journal, July 2019


      Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.