Topological Phononic Crystals with One-Way Elastic Edge Waves

Wang, Pai; Lu, Ling; Bertoldi, Katia

doi:10.1103/physrevlett.115.104302

Topological Phononic Crystals with One-Way Elastic Edge Waves

Journal Article · Fri Sep 04 00:00:00 EDT 2015 · Physical Review Letters

DOI:https://doi.org/10.1103/physrevlett.115.104302· OSTI ID:1505735

Wang, Pai ^[1]; Lu, Ling ^[2]; Bertoldi, Katia ^[3]

Harvard Univ., Cambridge, MA (United States). Harvard John A. Paulson School of Engineering and Applied Sciences; Harvard
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Dept. of Physics
Harvard Univ., Cambridge, MA (United States). Harvard John A. Paulson School of Engineering and Applied Sciences. Kavli Inst.

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.

View Accepted Manuscript (DOE)

Research Organization:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Harvard Univ., Cambridge, MA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); National Science Foundation (NSF) (United States); Army Research Office (ARO) (United States)

Grant/Contract Number:: SC0001299

OSTI ID:: 1505735

Alternate ID(s):: OSTI ID: 1213965

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 10 Vol. 115; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (61)

Band structure of elastic waves in two dimensional systems Sigalas, M.; Economou, E. N. Solid State Communications, Vol. 86, Issue 3 https://doi.org/10.1016/0038-1098(93)90888-T	journal	April 1993
The quantized hall effect Klitzing, Klaus v. Physica B+C, Vol. 126, Issue 1-3 https://doi.org/10.1016/0378-4363(84)90170-0	journal	November 1984
Dispersion properties of vortex-type monatomic lattices Carta, G.; Brun, M.; Movchan, A. B. International Journal of Solids and Structures, Vol. 51, Issue 11-12 https://doi.org/10.1016/j.ijsolstr.2014.02.026	journal	June 2014
Observation of unidirectional backscattering-immune topological electromagnetic states Wang, Zheng; Chong, Yidong; Joannopoulos, J. D. Nature, Vol. 461, Issue 7265 https://doi.org/10.1038/nature08293	journal	October 2009
Dark acoustic metamaterials as super absorbers for low-frequency sound Mei, Jun; Ma, Guancong; Yang, Min Nature Communications, Vol. 3, Issue 1 https://doi.org/10.1038/ncomms1758	journal	January 2012
Ultrasonic metamaterials with negative modulus Fang, Nicholas; Xi, Dongjuan; Xu, Jianyi Nature Materials, Vol. 5, Issue 6 https://doi.org/10.1038/nmat1644	journal	April 2006
Experimental demonstration of an acoustic magnifying hyperlens Li, Jensen; Fok, Lee; Yin, Xiaobo Nature Materials, Vol. 8, Issue 12 https://doi.org/10.1038/nmat2561	journal	October 2009
Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials Huang, Xueqin; Lai, Yun; Hang, Zhi Hong Nature Materials, Vol. 10, Issue 8, p. 582-586 https://doi.org/10.1038/nmat3030	journal	May 2011
Hybrid elastic solids Lai, Yun; Wu, Ying; Sheng, Ping Nature Materials, Vol. 10, Issue 8 https://doi.org/10.1038/nmat3043	journal	June 2011
Topological photonics Lu, Ling; Joannopoulos, John D.; Soljačić, Marin Nature Photonics, Vol. 8, Issue 11 https://doi.org/10.1038/nphoton.2014.248	journal	October 2014
Topological boundary modes in isostatic lattices Kane, C. L.; Lubensky, T. C. Nature Physics, Vol. 10, Issue 1 https://doi.org/10.1038/nphys2835	journal	December 2013
Topological modes bound to dislocations in mechanical metamaterials Paulose, Jayson; Chen, Bryan Gin-ge; Vitelli, Vincenzo Nature Physics, Vol. 11, Issue 2 https://doi.org/10.1038/nphys3185	journal	January 2015
Geometric phase and band inversion in periodic acoustic systems Xiao, Meng; Ma, Guancong; Yang, Zhiyu Nature Physics, Vol. 11, Issue 3 https://doi.org/10.1038/nphys3228	journal	February 2015
Collimation of sound assisted by acoustic surface waves Christensen, J.; Fernandez-Dominguez, A. I.; de Leon-Perez, F. Nature Physics, Vol. 3, Issue 12 https://doi.org/10.1038/nphys774	journal	October 2007
Acoustic imaging and collimating by slabs of sonic crystalsmade from arrays of rigid cylinders in air Chen, Liang-Shan; Kuo, Chao-Hsien; Ye, Zhen Applied Physics Letters, Vol. 85, Issue 6 https://doi.org/10.1063/1.1781351	journal	August 2004
Waveguiding in two-dimensional piezoelectric phononic crystal plates Vasseur, J. O.; Hladky-Hennion, A. -C.; Djafari-Rouhani, B. Journal of Applied Physics, Vol. 101, Issue 11 https://doi.org/10.1063/1.2740352	journal	June 2007
Dirac cones at k→=0 in acoustic crystals and zero refractive index acoustic materials Liu, Fengming; Huang, Xueqin; Chan, C. T. Applied Physics Letters, Vol. 100, Issue 7 https://doi.org/10.1063/1.3686907	journal	February 2012
Double Dirac cones in phononic crystals Li, Yan; Wu, Ying; Mei, Jun Applied Physics Letters, Vol. 105, Issue 1 https://doi.org/10.1063/1.4890304	journal	July 2014
Surface phonons, elastic response, and conformal invariance in twisted kagome lattices Sun, K.; Souslov, A.; Mao, X. Proceedings of the National Academy of Sciences, Vol. 109, Issue 31 https://doi.org/10.1073/pnas.1119941109	journal	June 2012
Nonlinear conduction via solitons in a topological mechanical insulator Chen, B. G. -g.; Upadhyaya, N.; Vitelli, V. Proceedings of the National Academy of Sciences, Vol. 111, Issue 36 https://doi.org/10.1073/pnas.1405969111	journal	August 2014
Wave beaming effects in two-dimensional cellular structures Ruzzene, Massimo; Scarpa, Fabrizio; Soranna, Francesco Smart Materials and Structures, Vol. 12, Issue 3 https://doi.org/10.1088/0964-1726/12/3/307	journal	April 2003
Topologically protected one-way edge mode in networks of acoustic resonators with circulating air flow Ni, Xu; He, Cheng; Sun, Xiao-Chen New Journal of Physics, Vol. 17, Issue 5 https://doi.org/10.1088/1367-2630/17/5/053016	journal	May 2015
Coriolis force induced topological order for classical mechanical vibrations Wang, Yao-Ting; Luan, Pi-Gang; Zhang, Shuang New Journal of Physics, Vol. 17, Issue 7 https://doi.org/10.1088/1367-2630/17/7/073031	journal	July 2015
On modifications of Newton's second law and linear continuum elastodynamics Milton, Graeme W.; Willis, John R. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 463, Issue 2079 https://doi.org/10.1098/rspa.2006.1795	journal	November 2006
Vortex-type elastic structured media and dynamic shielding Brun, M.; Jones, I. S.; Movchan, A. B. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 468, Issue 2146 https://doi.org/10.1098/rspa.2012.0165	journal	May 2012
Effective theory of quadratic degeneracies Chong, Y. D.; Wen, Xiao-Gang; Soljačić, Marin Physical Review B, Vol. 77, Issue 23 https://doi.org/10.1103/PhysRevB.77.235125	journal	June 2008
First-principles study of Dirac and Dirac-like cones in phononic and photonic crystals Mei, Jun; Wu, Ying; Chan, C. T. Physical Review B, Vol. 86, Issue 3 https://doi.org/10.1103/PhysRevB.86.035141	journal	July 2012
Elastic analog of graphene: Dirac cones and edge states for flexural waves in thin plates Torrent, Daniel; Mayou, Didier; Sánchez-Dehesa, José Physical Review B, Vol. 87, Issue 11 https://doi.org/10.1103/PhysRevB.87.115143	journal	March 2013
Elastic metamaterials with inertial locally resonant structures: Application to lensing and localization Bigoni, D.; Guenneau, S.; Movchan, A. B. Physical Review B, Vol. 87, Issue 17 https://doi.org/10.1103/PhysRevB.87.174303	journal	May 2013
Tunable filtering and demultiplexing in phononic crystals with hollow cylinders Pennec, Y.; Djafari-Rouhani, B.; Vasseur, J. O. Physical Review E, Vol. 69, Issue 4 https://doi.org/10.1103/PhysRevE.69.046608	journal	April 2004
Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry Haldane, F. D. M.; Raghu, S. Physical Review Letters, Vol. 100, Issue 1 https://doi.org/10.1103/PhysRevLett.100.013904	journal	January 2008
Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal Wang, Zheng; Chong, Y. D.; Joannopoulos, John D. Physical Review Letters, Vol. 100, Issue 1 https://doi.org/10.1103/PhysRevLett.100.013905	journal	January 2008
Topological Phonon Modes and Their Role in Dynamic Instability of Microtubules Prodan, Emil; Prodan, Camelia Physical Review Letters, Vol. 103, Issue 24 https://doi.org/10.1103/PhysRevLett.103.248101	journal	December 2009
Topological Nature of the Phonon Hall Effect Zhang, Lifa; Ren, Jie; Wang, Jian-Sheng Physical Review Letters, Vol. 105, Issue 22 https://doi.org/10.1103/PhysRevLett.105.225901	journal	November 2010
Acoustic Analogue of Graphene: Observation of Dirac Cones in Acoustic Surface Waves Torrent, Daniel; Sánchez-Dehesa, José Physical Review Letters, Vol. 108, Issue 17 https://doi.org/10.1103/PhysRevLett.108.174301	journal	April 2012
Narrow Low-Frequency Spectrum and Heat Management by Thermocrystals Maldovan, Martin Physical Review Letters, Vol. 110, Issue 2 https://doi.org/10.1103/PhysRevLett.110.025902	journal	January 2013
Interaction of a Contact Resonance of Microspheres with Surface Acoustic Waves Boechler, N.; Eliason, J. K.; Kumar, A. Physical Review Letters, Vol. 111, Issue 3 https://doi.org/10.1103/PhysRevLett.111.036103	journal	July 2013
Nanophononic Metamaterial: Thermal Conductivity Reduction by Local Resonance Davis, Bruce L.; Hussein, Mahmoud I. Physical Review Letters, Vol. 112, Issue 5 https://doi.org/10.1103/PhysRevLett.112.055505	journal	February 2014
Experiments on Seismic Metamaterials: Molding Surface Waves Brûlé, S.; Javelaud, E. H.; Enoch, S. Physical Review Letters, Vol. 112, Issue 13 https://doi.org/10.1103/PhysRevLett.112.133901	journal	March 2014
Harnessing Buckling to Design Tunable Locally Resonant Acoustic Metamaterials Wang, Pai; Casadei, Filippo; Shan, Sicong Physical Review Letters, Vol. 113, Issue 1 https://doi.org/10.1103/PhysRevLett.113.014301	journal	July 2014
Multimode One-Way Waveguides of Large Chern Numbers Skirlo, Scott A.; Lu, Ling; Soljačić, Marin Physical Review Letters, Vol. 113, Issue 11 https://doi.org/10.1103/PhysRevLett.113.113904	journal	September 2014
Topological Acoustics Yang, Zhaoju; Gao, Fei; Shi, Xihang Physical Review Letters, Vol. 114, Issue 11 https://doi.org/10.1103/PhysRevLett.114.114301	journal	March 2015
Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the "Parity Anomaly" Haldane, F. D. M. Physical Review Letters, Vol. 61, Issue 18 https://doi.org/10.1103/PhysRevLett.61.2015	journal	October 1988
Acoustic band structure of periodic elastic composites Kushwaha, M. S.; Halevi, P.; Dobrzynski, L. Physical Review Letters, Vol. 71, Issue 13 https://doi.org/10.1103/PhysRevLett.71.2022	journal	September 1993
Sonic Band Gaps in Finite Elastic Media: Surface States and Localization Phenomena in Linear and Point Defects Torres, M.; Montero de Espinosa, F. R.; García-Pablos, D. Physical Review Letters, Vol. 82, Issue 15 https://doi.org/10.1103/PhysRevLett.82.3054	journal	April 1999
Frequency Modulation in the Transmittivity of Wave Guides in Elastic-Wave Band-Gap Materials Kafesaki, M.; Sigalas, M. M.; García, N. Physical Review Letters, Vol. 85, Issue 19 https://doi.org/10.1103/PhysRevLett.85.4044	journal	November 2000
Metamaterial with Simultaneously Negative Bulk Modulus and Mass Density Ding, Yiqun; Liu, Zhengyou; Qiu, Chunyin Physical Review Letters, Vol. 99, Issue 9 https://doi.org/10.1103/PhysRevLett.99.093904	journal	August 2007
The quantized Hall effect von Klitzing, Klaus Reviews of Modern Physics, Vol. 58, Issue 3 https://doi.org/10.1103/RevModPhys.58.519	journal	July 1986
Colloquium: Topological insulators Hasan, M. Z.; Kane, C. L. Reviews of Modern Physics, Vol. 82, Issue 4, p. 3045-3067 https://doi.org/10.1103/RevModPhys.82.3045	journal	November 2010
Topological insulators and superconductors Qi, Xiao-Liang; Zhang, Shou-Cheng Reviews of Modern Physics, Vol. 83, Issue 4 https://doi.org/10.1103/RevModPhys.83.1057	journal	October 2011
Dynamics of Phononic Materials and Structures: Historical Origins, Recent Progress, and Future Outlook Hussein, Mahmoud I.; Leamy, Michael J.; Ruzzene, Massimo Applied Mechanics Reviews, Vol. 66, Issue 4 https://doi.org/10.1115/1.4026911	journal	May 2014
Wave propagation in two-dimensional periodic lattices Phani, A. Srikantha; Woodhouse, J.; Fleck, N. A. The Journal of the Acoustical Society of America, Vol. 119, Issue 4 https://doi.org/10.1121/1.2179748	journal	April 2006
Sound Isolation and Giant Linear Nonreciprocity in a Compact Acoustic Circulator Fleury, R.; Sounas, D. L.; Sieck, C. F. Science, Vol. 343, Issue 6170 https://doi.org/10.1126/science.1246957	journal	January 2014
Locally Resonant Sonic Materials Liu, Z. Science, Vol. 289, Issue 5485 https://doi.org/10.1126/science.289.5485.1734	journal	September 2000
Observation of phononic helical edge states in a mechanical topological insulator Süsstrunk, Roman; Huber, Sebastian D. Science, Vol. 349, Issue 6243 https://doi.org/10.1126/science.aab0239	journal	July 2015
Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances Fukui, Takahiro; Hatsugai, Yasuhiro; Suzuki, Hiroshi Journal of the Physical Society of Japan, Vol. 74, Issue 6 https://doi.org/10.1143/JPSJ.74.1674	journal	June 2005
Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal Wang, Zheng; Chong, Y. D.; Joannopoulos, John D. arXiv https://doi.org/10.48550/arxiv.0712.1776	text	January 2007
Vortex-type elastic structured media and dynamic shielding Brun, Michele; Jones, Ian S.; Movchan, Alexander B. arXiv https://doi.org/10.48550/arxiv.1201.5855	text	January 2012
Interaction of a Contact Resonance of Microspheres with Surface Acoustic Waves Boechler, N.; Eliason, J. K.; Kumar, A. arXiv https://doi.org/10.48550/arxiv.1302.4698	text	January 2013
Topological Boundary Modes in Isostatic Lattices Kane, C. L.; Lubensky, T. C. arXiv https://doi.org/10.48550/arxiv.1308.0554	text	January 2013
Acoustic imaging and collimating by slabs of sonic crystals made from arrays of rigid cylinders in air Chen, Liang-Shan; Kuo, Chao-Hsien; Ye, Zhen arXiv https://doi.org/10.48550/arxiv.cond-mat/0403749	text	January 2004

Cited By (191)

Experimental demonstration of anomalous Floquet topological insulator for sound Peng, Yu-Gui; Qin, Cheng-Zhi; Zhao, De-Gang Nature Communications, Vol. 7, Issue 1 https://doi.org/10.1038/ncomms13368	journal	November 2016
Transformable topological mechanical metamaterials Rocklin, D. Zeb; Zhou, Shangnan; Sun, Kai Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/ncomms14201	journal	January 2017
Observation of elastic topological states in soft materials Li, Shuaifeng; Zhao, Degang; Niu, Hao Nature Communications, Vol. 9, Issue 1 https://doi.org/10.1038/s41467-018-03830-8	journal	April 2018
Metamaterials with amplitude gaps for elastic solitons Deng, Bolei; Wang, Pai; He, Qi Nature Communications, Vol. 9, Issue 1 https://doi.org/10.1038/s41467-018-05908-9	journal	August 2018
Author Correction: Elastic pseudospin transport for integratable topological phononic circuits Yu, Si-Yuan; He, Cheng; Wang, Zhen Nature Communications, Vol. 10, Issue 1 https://doi.org/10.1038/s41467-019-08589-0	journal	January 2019
Topological analog signal processing Zangeneh-Nejad, Farzad; Fleury, Romain Nature Communications, Vol. 10, Issue 1 https://doi.org/10.1038/s41467-019-10086-3	journal	May 2019
“Deflecting elastic prism” and unidirectional localisation for waves in chiral elastic systems Carta, G.; Jones, I. S.; Movchan, N. V. Scientific Reports, Vol. 7, Issue 1 https://doi.org/10.1038/s41598-017-00054-6	journal	January 2017
Simultaneous multi-band valley-protected topological edge states of shear vertical wave in two-dimensional phononic crystals with veins Huo, Shao-yong; Chen, Jiu-jiu; Huang, Hong-bo Scientific Reports, Vol. 7, Issue 1 https://doi.org/10.1038/s41598-017-10857-2	journal	September 2017
Acoustic frequency filter based on anisotropic topological phononic crystals Chen, Ze-Guo; Zhao, Jiajun; Mei, Jun Scientific Reports, Vol. 7, Issue 1 https://doi.org/10.1038/s41598-017-15409-2	journal	November 2017
Dial-in Topological Metamaterials Based on Bistable Stewart Platform Wu, Ying; Chaunsali, Rajesh; Yasuda, Hiromi Scientific Reports, Vol. 8, Issue 1 https://doi.org/10.1038/s41598-017-18410-x	journal	January 2018
Photoinduced Topological Phase Transitions in Topological Magnon Insulators Owerre, S. A. Scientific Reports, Vol. 8, Issue 1 https://doi.org/10.1038/s41598-018-22779-8	journal	March 2018
Band transition and topological interface modes in 1D elastic phononic crystals Yin, Jianfei; Ruzzene, Massimo; Wen, Jihong Scientific Reports, Vol. 8, Issue 1 https://doi.org/10.1038/s41598-018-24952-5	journal	May 2018
Phononic topological insulators based on six-petal holey silicon structures Yu, Ziqi; Ren, Zongqing; Lee, Jaeho Scientific Reports, Vol. 9, Issue 1 https://doi.org/10.1038/s41598-018-38387-5	journal	February 2019
Experimental demonstration of coherent superpositions in an ultrasonic pseudospin Calderin, Lazaro; Hasan, M. Arif; Jenkins, Neil G. Scientific Reports, Vol. 9, Issue 1 https://doi.org/10.1038/s41598-019-50366-y	journal	October 2019
Contact Nonlinear Acoustic Diode Huang, Yao; Wang, Xiaoyu; Gong, Xun Scientific Reports, Vol. 10, Issue 1 https://doi.org/10.1038/s41598-020-59270-2	journal	February 2020
Stress Wave Isolation by Purely Mechanical Topological Phononic Crystals Chaunsali, Rajesh; Li, Feng; Yang, Jinkyu Scientific Reports, Vol. 6, Issue 1 https://doi.org/10.1038/srep30662	journal	August 2016
The effects of dissipation on topological mechanical systems Xiong, Ye; Wang, Tianxiang; Tong, Peiqing Scientific Reports, Vol. 6, Issue 1 https://doi.org/10.1038/srep32572	journal	September 2016
Pseudo-time-reversal symmetry and topological edge states in two-dimensional acoustic crystals Mei, Jun; Chen, Zeguo; Wu, Ying Scientific Reports, Vol. 6, Issue 1 https://doi.org/10.1038/srep32752	journal	September 2016
Interfacial waveforms in chiral lattices with gyroscopic spinners Garau, M.; Carta, G.; Nieves, M. J. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 474, Issue 2215 https://doi.org/10.1098/rspa.2018.0132	journal	July 2018
Wave polarization and dynamic degeneracy in a chiral elastic lattice Carta, G.; Jones, I. S.; Movchan, N. V. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 475, Issue 2232 https://doi.org/10.1098/rspa.2019.0313	journal	December 2019
Flexural vibration systems with gyroscopic spinners Carta, G.; Nieves, M. J.; Jones, I. S. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 377, Issue 2156 https://doi.org/10.1098/rsta.2019.0154	journal	September 2019
Edge Waves and Localization in Lattices Containing Tilted Resonators Tallarico, Domenico; Trevisan, Alessio; Movchan, Natalia V. Frontiers in Materials, Vol. 4 https://doi.org/10.3389/fmats.2017.00016	journal	June 2017
Manipulation of Dirac Cones in Mechanical Graphene Kariyado, Toshikaze; Hatsugai, Yasuhiro arXiv https://doi.org/10.48550/arxiv.1505.06679	text	January 2015
Floquet Topological Insulators for Sound Fleury, Romain; Khanikaev, Alex; Alu, Andrea arXiv https://doi.org/10.48550/arxiv.1511.08427	text	January 2015
Topological magnetoplasmon Jin, Dafei; Lu, Ling; Wang, Zhong arXiv https://doi.org/10.48550/arxiv.1602.00553	text	January 2016
Topological Phononics: From Fundamental Models to Real Materials Liu, Yizhou; Chen, Xiaobin; Xu, Yong Advanced Functional Materials, Vol. 30, Issue 8 https://doi.org/10.1002/adfm.201904784	journal	August 2019
Thermal Conductivity Reduction in a Nanophononic Metamaterial versus a Nanophononic Crystal: A Review and Comparative Analysis Hussein, Mahmoud I.; Tsai, Chia‐Nien; Honarvar, Hossein Advanced Functional Materials, Vol. 30, Issue 8 https://doi.org/10.1002/adfm.201906718	journal	November 2019
Programmable Coding Acoustic Topological Insulator Xia, Jian-Ping; Jia, Ding; Sun, Hong-Xiang Advanced Materials, Vol. 30, Issue 46 https://doi.org/10.1002/adma.201805002	journal	October 2018
Mechanical Analogue of a Majorana Bound State Chen, Chun‐Wei; Lera, Natalia; Chaunsali, Rajesh Advanced Materials, Vol. 31, Issue 51 https://doi.org/10.1002/adma.201904386	journal	November 2019
Applications of Topological Photonics in Integrated Photonic Devices Wu, You; Li, Chong; Hu, Xiaoyong Advanced Optical Materials, Vol. 5, Issue 18 https://doi.org/10.1002/adom.201700357	journal	August 2017
Unusual one-way edge state in acoustic gyroscopic continuum Zhou, XiaoMing; Zhao, YuChen Science China Physics, Mechanics & Astronomy, Vol. 62, Issue 1 https://doi.org/10.1007/s11433-018-9268-9	journal	September 2018
Flexible mechanical metamaterials Bertoldi, Katia; Vitelli, Vincenzo; Christensen, Johan Nature Reviews Materials, Vol. 2, Issue 11 https://doi.org/10.1038/natrevmats.2017.66	journal	October 2017
Photonic crystals possessing multiple Weyl points and the experimental observation of robust surface states Chen, Wen-Jie; Xiao, Meng; Chan, C. T. Nature Communications, Vol. 7, Issue 1 https://doi.org/10.1038/ncomms13038	journal	October 2016
Topological magnetoplasmon Jin, Dafei; Lu, Ling; Wang, Zhong Nature Communications, Vol. 7, Issue 1 https://doi.org/10.1038/ncomms13486	journal	November 2016
Topologically protected elastic waves in phononic metamaterials Mousavi, S. Hossein; Khanikaev, Alexander B.; Wang, Zheng Nature Communications, Vol. 6, Issue 1 https://doi.org/10.1038/ncomms9682	journal	November 2015
Three-dimensional all-dielectric photonic topological insulator Slobozhanyuk, Alexey; Mousavi, S. Hossein; Ni, Xiang Nature Photonics, Vol. 11, Issue 2 https://doi.org/10.1038/nphoton.2016.253	journal	December 2016
Symmetry-protected topological photonic crystal in three dimensions Lu, Ling; Fang, Chen; Fu, Liang Nature Physics, Vol. 12, Issue 4 https://doi.org/10.1038/nphys3611	journal	January 2016
Topological mechanics Huber, Sebastian D. Nature Physics, Vol. 12, Issue 7 https://doi.org/10.1038/nphys3801	journal	June 2016
Acoustic topological insulator and robust one-way sound transport He, Cheng; Ni, Xu; Ge, Hao Nature Physics, Vol. 12, Issue 12 https://doi.org/10.1038/nphys3867	journal	August 2016
Topological sound in active-liquid metamaterials Souslov, Anton; van Zuiden, Benjamin C.; Bartolo, Denis Nature Physics, Vol. 13, Issue 11 https://doi.org/10.1038/nphys4193	journal	July 2017
Elastic pseudospin transport for integratable topological phononic circuits Yu, Si-Yuan; He, Cheng; Wang, Zhen Nature Communications, Vol. 9, Issue 1 https://doi.org/10.1038/s41467-018-05461-5	journal	August 2018
Amorphous topological insulators constructed from random point sets Mitchell, Noah P.; Nash, Lisa M.; Hexner, Daniel Nature Physics, Vol. 14, Issue 4 https://doi.org/10.1038/s41567-017-0024-5	journal	January 2018
Topological guiding of elastic waves in phononic metamaterials based on 2D pentamode structures Guo, Yuning; Dekorsy, Thomas; Hettich, Mike Scientific Reports, Vol. 7, Issue 1 https://doi.org/10.1038/s41598-017-18394-8	journal	December 2017
Topological sound Zhang, Xiujuan; Xiao, Meng; Cheng, Ying Communications Physics, Vol. 1, Issue 1 https://doi.org/10.1038/s42005-018-0094-4	journal	December 2018
Topological phases in acoustic and mechanical systems Ma, Guancong; Xiao, Meng; Chan, C. T. Nature Reviews Physics, Vol. 1, Issue 4 https://doi.org/10.1038/s42254-019-0030-x	journal	March 2019
Manipulation of Dirac Cones in Mechanical Graphene Kariyado, Toshikaze; Hatsugai, Yasuhiro Scientific Reports, Vol. 5, Issue 1 https://doi.org/10.1038/srep18107	journal	December 2015
Topological boundary modes in jammed matter Sussman, Daniel M.; Stenull, Olaf; Lubensky, T. C. Soft Matter, Vol. 12, Issue 28 https://doi.org/10.1039/c6sm00875e	journal	January 2016
Topologically protected interface phonons in two-dimensional nanomaterials: hexagonal boron nitride and silicon carbide Jiang, Jin-Wu; Wang, Bing-Shen; Park, Harold S. Nanoscale, Vol. 10, Issue 29 https://doi.org/10.1039/c8nr04314k	journal	January 2018
Preparation and sound absorption properties of barium titanate/nitrile butadiene rubber-polyurethane foam composites with stratified structure Jiang, Xueliang; Wang, Zhijie; Yang, Zhen RSC Advances, Vol. 8, Issue 37 https://doi.org/10.1039/c8ra03330g	journal	January 2018
Helical edge states and topological phase transitions in phononic systems using bi-layered lattices Pal, Raj Kumar; Schaeffer, Marshall; Ruzzene, Massimo Journal of Applied Physics, Vol. 119, Issue 8 https://doi.org/10.1063/1.4942357	journal	February 2016
Perspective: Acoustic metamaterials in transition Wu, Ying; Yang, Min; Sheng, Ping Journal of Applied Physics, Vol. 123, Issue 9 https://doi.org/10.1063/1.5007682	journal	March 2018
Valley-projected edge modes observed in underwater sonic crystals Shen, Yuanyuan; Qiu, Chunyin; Cai, Xiangxi Applied Physics Letters, Vol. 114, Issue 2 https://doi.org/10.1063/1.5049856	journal	January 2019
Su-Schrieffer-Heeger model inspired acoustic interface states and edge states Li, Xin; Meng, Yan; Wu, Xiaoxiao Applied Physics Letters, Vol. 113, Issue 20 https://doi.org/10.1063/1.5051523	journal	November 2018
Prestress tuning of negative refraction and wave channeling from flexural sources Bordiga, G.; Cabras, L.; Piccolroaz, A. Applied Physics Letters, Vol. 114, Issue 4 https://doi.org/10.1063/1.5084258	journal	January 2019
Brillouin optomechanics in nanophotonic structures Wiederhecker, Gustavo S.; Dainese, Paulo; Mayer Alegre, Thiago P. APL Photonics, Vol. 4, Issue 7 https://doi.org/10.1063/1.5088169	journal	July 2019
Magnetically tunable topological interface states for Lamb waves in one-dimensional magnetoelastic phononic crystal slabs Feng, Luyang; Huang, Kan; Chen, Jiujiu AIP Advances, Vol. 9, Issue 11 https://doi.org/10.1063/1.5120054	journal	November 2019
Thermally controlled topological states for elastic waves Tang, Haocheng; Li, Honglang; Xie, Xiang Applied Physics Letters, Vol. 115, Issue 25 https://doi.org/10.1063/1.5123178	journal	December 2019
Broadband modulation of subwavelength topological interface states in a one-dimensional acoustic system Wang, Zhenyu; Zhao, Degang; Luo, Jinlong Applied Physics Letters, Vol. 116, Issue 1 https://doi.org/10.1063/1.5135948	journal	January 2020
Topological mechanics of gyroscopic metamaterials Nash, Lisa M.; Kleckner, Dustin; Read, Alismari Proceedings of the National Academy of Sciences, Vol. 112, Issue 47 https://doi.org/10.1073/pnas.1507413112	journal	November 2015
Classification of topological phonons in linear mechanical metamaterials Süsstrunk, Roman; Huber, Sebastian D. Proceedings of the National Academy of Sciences, Vol. 113, Issue 33 https://doi.org/10.1073/pnas.1605462113	journal	August 2016
Pseudomagnetic fields for sound at the nanoscale Brendel, Christian; Peano, Vittorio; Painter, Oskar J. Proceedings of the National Academy of Sciences, Vol. 114, Issue 17 https://doi.org/10.1073/pnas.1615503114	journal	April 2017
Soft self-assembly of Weyl materials for light and sound Fruchart, Michel; Jeon, Seung-Yeol; Hur, Kahyun Proceedings of the National Academy of Sciences, Vol. 115, Issue 16 https://doi.org/10.1073/pnas.1720828115	journal	April 2018
Intrinsic spin of elastic waves Long, Yang; Ren, Jie; Chen, Hong Proceedings of the National Academy of Sciences, Vol. 115, Issue 40 https://doi.org/10.1073/pnas.1808534115	journal	September 2018
Guided transition waves in multistable mechanical metamaterials Jin, Lishuai; Khajehtourian, Romik; Mueller, Jochen Proceedings of the National Academy of Sciences, Vol. 117, Issue 5 https://doi.org/10.1073/pnas.1913228117	journal	January 2020
Observation of topological edge states of acoustic metamaterials at subwavelength scale Dai, Hongqing; Jiao, Junrui; Xia, Baizhan Journal of Physics D: Applied Physics, Vol. 51, Issue 17 https://doi.org/10.1088/1361-6463/aab504	journal	April 2018
Polarization-dependent and valley-protected Lamb waves in asymmetric pillared phononic crystals Wang, Wei; Bonello, Bernard; Djafari-Rouhani, Bahram Journal of Physics D: Applied Physics, Vol. 52, Issue 50 https://doi.org/10.1088/1361-6463/ab43f9	journal	September 2019
Elastic phononic plates with first-order and second-order topological phases Tong, Liang; Fan, Haiyan; Xia, Baizhan Journal of Physics D: Applied Physics, Vol. 53, Issue 11 https://doi.org/10.1088/1361-6463/ab6055	journal	January 2020
Topologically protected edge states for out-of-plane and in-plane bulk elastic waves Huo, Shao-Yong; Chen, Jiu-Jiu; Huang, Hong-Bo Journal of Physics: Condensed Matter, Vol. 30, Issue 14 https://doi.org/10.1088/1361-648x/aab22a	journal	March 2018
Topological chiral phonons in center-stacked bilayer triangle lattices Xu, Xifang; Zhang, Wei; Wang, Jiaojiao Journal of Physics: Condensed Matter, Vol. 30, Issue 22 https://doi.org/10.1088/1361-648x/aabf5e	journal	May 2018
Topologically protected edge transport of sound in coupled cavities of a modified honeycomb lattice Geng, Zhi-Guo; Peng, Yu-Gui; Shen, Ya-Xi Journal of Physics: Condensed Matter, Vol. 30, Issue 34 https://doi.org/10.1088/1361-648x/aad398	journal	July 2018
Evidence for hidden order in a nonlinear model elastic system Deymier, P. A.; Runge, K. Journal of Physics: Condensed Matter, Vol. 31, Issue 10 https://doi.org/10.1088/1361-648x/aafcfe	journal	January 2019
Mirror-symmetry induced topological valley transport along programmable boundaries in a hexagonal sonic crystal Geng, Zhi-Guo; Peng, Yu-Gui; Li, Peng-Qi Journal of Physics: Condensed Matter, Vol. 31, Issue 24 https://doi.org/10.1088/1361-648x/ab0fcc	journal	April 2019
Topological phase transition with p orbitals in the exciton-polariton honeycomb lattice Zhang, Chuanyi; Wang, Yuanxu; Zhang, Weifeng Journal of Physics: Condensed Matter, Vol. 31, Issue 33 https://doi.org/10.1088/1361-648x/ab2289	journal	June 2019
Phononic topological states in 1D quasicrystals Silva, J. R. M.; Vasconcelos, M. S.; Anselmo, D. H. A. L. Journal of Physics: Condensed Matter, Vol. 31, Issue 50 https://doi.org/10.1088/1361-648x/ab312a	journal	September 2019
Two-dimensionally confined topological edge states in photonic crystals Barik, Sabyasachi; Miyake, Hirokazu; DeGottardi, Wade New Journal of Physics, Vol. 18, Issue 11 https://doi.org/10.1088/1367-2630/18/11/113013	journal	November 2016
Edge waves in plates with resonators: an elastic analogue of the quantum valley Hall effect Pal, Raj Kumar; Ruzzene, Massimo New Journal of Physics, Vol. 19, Issue 2 https://doi.org/10.1088/1367-2630/aa56a2	journal	February 2017
Edge states of mechanical diamond and its topological origin Takahashi, Yuta; Kariyado, Toshikaze; Hatsugai, Yasuhiro New Journal of Physics, Vol. 19, Issue 3 https://doi.org/10.1088/1367-2630/aa5edb	journal	March 2017
Topological acoustic polaritons: robust sound manipulation at the subwavelength scale Yves, Simon; Fleury, Romain; Lemoult, Fabrice New Journal of Physics, Vol. 19, Issue 7 https://doi.org/10.1088/1367-2630/aa66f8	journal	July 2017
Topological edge states in acoustic Kagome lattices Ni, Xiang; Gorlach, Maxim A.; Alu, Andrea New Journal of Physics, Vol. 19, Issue 5 https://doi.org/10.1088/1367-2630/aa6996	journal	May 2017
Directional mechanical response in the bulk of topological metamaterials Rocklin, D. Zeb New Journal of Physics, Vol. 19, Issue 6 https://doi.org/10.1088/1367-2630/aa7155	journal	June 2017
L lines, C points and Chern numbers: understanding band structure topology using polarization fields Fösel, Thomas; Peano, Vittorio; Marquardt, Florian New Journal of Physics, Vol. 19, Issue 11 https://doi.org/10.1088/1367-2630/aa8a9f	journal	November 2017
Topological helical edge states in water waves over a topographical bottom Wu, Shiqiao; Wu, Ying; Mei, Jun New Journal of Physics, Vol. 20, Issue 2 https://doi.org/10.1088/1367-2630/aa9cdb	journal	February 2018
Fracturing of topological Maxwell lattices Zhang, Leyou; Mao, Xiaoming New Journal of Physics, Vol. 20, Issue 6 https://doi.org/10.1088/1367-2630/aac765	journal	June 2018
Acoustic topological insulator by honeycomb sonic crystals with direct and indirect band gaps Jia, Ding; Sun, Hong-xiang; Xia, Jian-ping New Journal of Physics, Vol. 20, Issue 9 https://doi.org/10.1088/1367-2630/aae104	journal	September 2018
Dark state, zero-index and topology in phononic metamaterials with negative mass and negative coupling Zhang, Danmei; Ren, Jie; Zhou, Tianxiong New Journal of Physics, Vol. 21, Issue 9 https://doi.org/10.1088/1367-2630/ab3f6d	journal	September 2019
Acoustic graphene network loaded with Helmholtz resonators: a first-principle modeling, Dirac cones, edge and interface waves Zheng, Li-Yang; Achilleos, Vassos; Chen, Ze-Guo New Journal of Physics, Vol. 22, Issue 1 https://doi.org/10.1088/1367-2630/ab60f1	journal	January 2020
Nonreciprocal wave propagation and parametric amplification of bulk elastic waves in nonlinear anisotropic materials Zakeri, Mahsa; Keller, Scott M.; Wang, Yuanxun Ethan New Journal of Physics, Vol. 22, Issue 2 https://doi.org/10.1088/1367-2630/ab61d9	journal	February 2020
Acoustic topological devices based on emulating and multiplexing of pseudospin and valley indices Gao, Meng; Wu, Shiqiao; Mei, Jun New Journal of Physics, Vol. 22, Issue 1 https://doi.org/10.1088/1367-2630/ab6633	journal	January 2020
Topology of triple-point metals Winkler, Georg W.; Singh, Sobhit; Soluyanov, Alexey A. Chinese Physics B, Vol. 28, Issue 7 https://doi.org/10.1088/1674-1056/28/7/077303	journal	July 2019
Magnonic analogs of topological Dirac semimetals Owerre, S. A. Journal of Physics Communications, Vol. 1, Issue 2 https://doi.org/10.1088/2399-6528/aa86d1	journal	September 2017
Gyro-elastic beams for the vibration reduction of long flexural systems Carta, G.; Jones, I. S.; Movchan, N. V. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 473, Issue 2203 https://doi.org/10.1098/rspa.2017.0136	journal	July 2017
Dispersion and topological characteristics of permutative polyatomic phononic crystals Al Ba'ba'a, H.; Nouh, M.; Singh, T. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 475, Issue 2226 https://doi.org/10.1098/rspa.2019.0022	journal	June 2019
One-way interfacial waves in a flexural plate with chiral double resonators Carta, G.; Colquitt, D. J.; Movchan, A. B. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 378, Issue 2162 https://doi.org/10.1098/rsta.2019.0350	journal	November 2019
Double-Weyl Phonons in Transition-Metal Monosilicides Zhang, Tiantian; Song, Zhida; Alexandradinata, A. Physical Review Letters, Vol. 120, Issue 1 https://doi.org/10.1103/PhysRevLett.120.016401	journal	January 2018
Chiral Voltage Propagation and Calibration in a Topolectrical Chern Circuit Hofmann, Tobias; Helbig, Tobias; Lee, Ching Hua Physical Review Letters, Vol. 122, Issue 24 https://doi.org/10.1103/PhysRevLett.122.247702	journal	June 2019
Dynamically generated synthetic electric fields for photons Zapletal, Petr; Walter, Stefan; Marquardt, Florian Physical Review A, Vol. 100, Issue 2 https://doi.org/10.1103/physreva.100.023804	journal	August 2019
Topological two-body bound states in the interacting Haldane model Salerno, Grazia; Di Liberto, Marco; Menotti, Chiara Physical Review A, Vol. 97, Issue 1 https://doi.org/10.1103/physreva.97.013637	journal	January 2018
Experimental Evidence of Robust Acoustic Valley Hall Edge States in a Nonresonant Topological Elastic Waveguide Liu, Ting-Wei; Semperlotti, Fabio Physical Review Applied, Vol. 11, Issue 1 https://doi.org/10.1103/physrevapplied.11.014040	journal	January 2019
Mechanical Quantum Hall Effect in Time-Modulated Elastic Materials Chen, H.; Yao, L. Y.; Nassar, H. Physical Review Applied, Vol. 11, Issue 4 https://doi.org/10.1103/physrevapplied.11.044029	journal	April 2019
Nonreciprocal Wave Propagation in a Continuum-Based Metamaterial with Space-Time Modulated Resonators Chen, Yangyang; Li, Xiaopeng; Nassar, Hussein Physical Review Applied, Vol. 11, Issue 6 https://doi.org/10.1103/physrevapplied.11.064052	journal	June 2019
Observation of Edge Waves in a Two-Dimensional Su-Schrieffer-Heeger Acoustic Network Zheng, Li-Yang; Achilleos, Vassos; Richoux, Olivier Physical Review Applied, Vol. 12, Issue 3 https://doi.org/10.1103/physrevapplied.12.034014	journal	September 2019
Tunable Nonlinear Topological Insulator for Acoustic Waves Darabi, Amir; Leamy, Michael J. Physical Review Applied, Vol. 12, Issue 4 https://doi.org/10.1103/physrevapplied.12.044030	journal	October 2019
Collective Resonances of a Chain of Coupled Phononic Microresonators Wang, Ting-Ting; Bargiel, Sylwester; Lardet-Vieudrin, Franck Physical Review Applied, Vol. 13, Issue 1 https://doi.org/10.1103/physrevapplied.13.014022	journal	January 2020
Tunable Topological Phononic Crystals Chen, Ze-Guo; Wu, Ying Physical Review Applied, Vol. 5, Issue 5 https://doi.org/10.1103/physrevapplied.5.054021	journal	May 2016
Tunable Acoustic Valley–Hall Edge States in Reconfigurable Phononic Elastic Waveguides Liu, Ting-Wei; Semperlotti, Fabio Physical Review Applied, Vol. 9, Issue 1 https://doi.org/10.1103/physrevapplied.9.014001	journal	January 2018
Sonic valley-Chern insulators Gao, Penglin; Zhang, Zhiwang; Christensen, Johan Physical Review B, Vol. 101, Issue 2 https://doi.org/10.1103/physrevb.101.020301	journal	January 2020
Phononic Weyl nodal straight lines in MgB 2 Li, Jiangxu; Xie, Qing; Liu, Jiaxi Physical Review B, Vol. 101, Issue 2 https://doi.org/10.1103/physrevb.101.024301	journal	January 2020
Unidirectional transport in electronic and photonic Weyl materials by Dirac mass engineering Bi, Ren; Wang, Zhong Physical Review B, Vol. 92, Issue 24 https://doi.org/10.1103/physrevb.92.241109	journal	December 2015
Floquet topological system based on frequency-modulated classical coupled harmonic oscillators Salerno, Grazia; Ozawa, Tomoki; Price, Hannah M. Physical Review B, Vol. 93, Issue 8 https://doi.org/10.1103/physrevb.93.085105	journal	February 2016
Transport and localization in a topological phononic lattice with correlated disorder Ong, Zhun-Yong; Lee, Ching Hua Physical Review B, Vol. 94, Issue 13 https://doi.org/10.1103/physrevb.94.134203	journal	October 2016
Quasilossless acoustic transmission in an arbitrary pathway of a network Dai, Hongqing; Liu, Tingting; Xia, Baizhan Physical Review B, Vol. 95, Issue 5 https://doi.org/10.1103/physrevb.95.054109	journal	February 2017
Observation of acoustic valley vortex states and valley-chirality locked beam splitting Ye, Liping; Qiu, Chunyin; Lu, Jiuyang Physical Review B, Vol. 95, Issue 17 https://doi.org/10.1103/physrevb.95.174106	journal	May 2017
Anharmonic interatomic force constants and thermal conductivity from Grüneisen parameters: An application to graphene Lee, Ching Hua; Gan, Chee Kwan Physical Review B, Vol. 96, Issue 3 https://doi.org/10.1103/physrevb.96.035105	journal	July 2017
Model for topological phononics and phonon diode Liu, Yizhou; Xu, Yong; Zhang, Shou-Cheng Physical Review B, Vol. 96, Issue 6 https://doi.org/10.1103/physrevb.96.064106	journal	August 2017
Tailoring phonon band structures with broken symmetry by shaping spatiotemporal modulations of stiffness in a one-dimensional elastic waveguide Deymier, Pierre A.; Gole, Vitthal; Lucas, Pierre Physical Review B, Vol. 96, Issue 6 https://doi.org/10.1103/physrevb.96.064304	journal	August 2017
Line nodes, Dirac points, and Lifshitz transition in two-dimensional nonsymmorphic photonic crystals Lin, Jun Yu; Hu, Nai Chao; Chen, You Jian Physical Review B, Vol. 96, Issue 7 https://doi.org/10.1103/physrevb.96.075438	journal	August 2017
Topological phononic insulator with robust pseudospin-dependent transport Xia, Bai-Zhan; Liu, Ting-Ting; Huang, Guo-Liang Physical Review B, Vol. 96, Issue 9 https://doi.org/10.1103/physrevb.96.094106	journal	September 2017
Robust edge states in amorphous gyromagnetic photonic lattices Mansha, Shampy; Chong, Y. D. Physical Review B, Vol. 96, Issue 12 https://doi.org/10.1103/physrevb.96.121405	journal	September 2017
Experimental verification of acoustic pseudospin multipoles in a symmetry-broken snowflakelike topological insulator Zhang, Zhiwang; Tian, Ye; Cheng, Ying Physical Review B, Vol. 96, Issue 24 https://doi.org/10.1103/physrevb.96.241306	journal	December 2017
Snowflake phononic topological insulator at the nanoscale Brendel, Christian; Peano, Vittorio; Painter, Oskar Physical Review B, Vol. 97, Issue 2 https://doi.org/10.1103/physrevb.97.020102	journal	January 2018
Coexistent three-component and two-component Weyl phonons in TiS, ZrSe, and HfTe Li, Jiangxu; Xie, Qing; Ullah, Sami Physical Review B, Vol. 97, Issue 5 https://doi.org/10.1103/physrevb.97.054305	journal	February 2018
Subwavelength and directional control of flexural waves in zone-folding induced topological plates Chaunsali, Rajesh; Chen, Chun-Wei; Yang, Jinkyu Physical Review B, Vol. 97, Issue 5 https://doi.org/10.1103/physrevb.97.054307	journal	February 2018
Quasitopological rotational waves in mechanical granular graphene Zheng, Li-Yang; Theocharis, Georgios; Tournat, Vincent Physical Review B, Vol. 97, Issue 6 https://doi.org/10.1103/physrevb.97.060101	journal	February 2018
Simulating quantum spin Hall effect in the topological Lieb lattice of a linear circuit network Zhu, Weiwei; Hou, Shanshan; Long, Yang Physical Review B, Vol. 97, Issue 7 https://doi.org/10.1103/physrevb.97.075310	journal	February 2018
Realization of a topological phase transition in a gyroscopic lattice Mitchell, Noah P.; Nash, Lisa M.; Irvine, William T. M. Physical Review B, Vol. 97, Issue 10 https://doi.org/10.1103/physrevb.97.100302	journal	March 2018
Observation of valleylike edge states of sound at a momentum away from the high-symmetry points Xia, Bai-Zhan; Zheng, Sheng-Jie; Liu, Ting-Ting Physical Review B, Vol. 97, Issue 15 https://doi.org/10.1103/physrevb.97.155124	journal	April 2018
Topological interface modes in local resonant acoustic systems Zhao, Degang; Xiao, Meng; Ling, C. W. Physical Review B, Vol. 98, Issue 1 https://doi.org/10.1103/physrevb.98.014110	journal	July 2018
Tunable band topology in gyroscopic lattices Mitchell, Noah P.; Nash, Lisa M.; Irvine, William T. M. Physical Review B, Vol. 98, Issue 17 https://doi.org/10.1103/physrevb.98.174301	journal	November 2018
Weyl points of mechanical diamond Takahashi, Yuta; Kariyado, Toshikaze; Hatsugai, Yasuhiro Physical Review B, Vol. 99, Issue 2 https://doi.org/10.1103/physrevb.99.024102	journal	January 2019
Kink-antikink asymmetry and impurity interactions in topological mechanical chains Zhou, Yujie; Chen, Bryan Gin-ge; Upadhyaya, Nitin Physical Review E, Vol. 95, Issue 2 https://doi.org/10.1103/physreve.95.022202	journal	February 2017
Nonreciprocal wave phenomena in spring-mass chains with effective stiffness modulation induced by geometric nonlinearity Wallen, S. P.; Haberman, M. R. Physical Review E, Vol. 99, Issue 1 https://doi.org/10.1103/physreve.99.013001	journal	January 2019
Disorder and Metal-Insulator Transitions in Weyl Semimetals Chen, Chui-Zhen; Song, Juntao; Jiang, Hua Physical Review Letters, Vol. 115, Issue 24 https://doi.org/10.1103/physrevlett.115.246603	journal	December 2015
Experimental Observation of Large Chern Numbers in Photonic Crystals Skirlo, Scott A.; Lu, Ling; Igarashi, Yuichi Physical Review Letters, Vol. 115, Issue 25 https://doi.org/10.1103/physrevlett.115.253901	journal	December 2015
Valley Vortex States in Sonic Crystals Lu, Jiuyang; Qiu, Chunyin; Ke, Manzhu Physical Review Letters, Vol. 116, Issue 9 https://doi.org/10.1103/physrevlett.116.093901	journal	February 2016
Topological Mechanics of Origami and Kirigami Chen, Bryan Gin-ge; Liu, Bin; Evans, Arthur A. Physical Review Letters, Vol. 116, Issue 13 https://doi.org/10.1103/physrevlett.116.135501	journal	March 2016
Mechanical Weyl Modes in Topological Maxwell Lattices Rocklin, D. Zeb; Chen, Bryan Gin–ge; Falk, Martin Physical Review Letters, Vol. 116, Issue 13 https://doi.org/10.1103/physrevlett.116.135503	journal	April 2016
Non-Abelian Braiding of Light Iadecola, Thomas; Schuster, Thomas; Chamon, Claudio Physical Review Letters, Vol. 117, Issue 7 https://doi.org/10.1103/physrevlett.117.073901	journal	August 2016
Infrared Topological Plasmons in Graphene Jin, Dafei; Christensen, Thomas; Soljačić, Marin Physical Review Letters, Vol. 118, Issue 24 https://doi.org/10.1103/physrevlett.118.245301	journal	June 2017
Circular Phonon Dichroism in Weyl Semimetals Liu, Donghao; Shi, Junren Physical Review Letters, Vol. 119, Issue 7 https://doi.org/10.1103/physrevlett.119.075301	journal	August 2017
Chiral Edge Mode in the Coupled Dynamics of Magnetic Solitons in a Honeycomb Lattice Kim, Se Kwon; Tserkovnyak, Yaroslav Physical Review Letters, Vol. 119, Issue 7 https://doi.org/10.1103/physrevlett.119.077204	journal	August 2017
Sonic Landau Levels and Synthetic Gauge Fields in Mechanical Metamaterials Abbaszadeh, Hamed; Souslov, Anton; Paulose, Jayson Physical Review Letters, Vol. 119, Issue 19 https://doi.org/10.1103/physrevlett.119.195502	journal	November 2017
Pseudospins and Topological Effects of Phonons in a Kekulé Lattice Liu, Yizhou; Lian, Chao-Sheng; Li, Yang Physical Review Letters, Vol. 119, Issue 25 https://doi.org/10.1103/physrevlett.119.255901	journal	December 2017
Topological Edge Floppy Modes in Disordered Fiber Networks Zhou, Di; Zhang, Leyou; Mao, Xiaoming Physical Review Letters, Vol. 120, Issue 6 https://doi.org/10.1103/physrevlett.120.068003	journal	February 2018
Valley Topological Phases in Bilayer Sonic Crystals Lu, Jiuyang; Qiu, Chunyin; Deng, Weiyin Physical Review Letters, Vol. 120, Issue 11 https://doi.org/10.1103/physrevlett.120.116802	journal	March 2018
Valley Physics in Non-Hermitian Artificial Acoustic Boron Nitride Wang, Mudi; Ye, Liping; Christensen, J. Physical Review Letters, Vol. 120, Issue 24 https://doi.org/10.1103/physrevlett.120.246601	journal	June 2018
Observation of Double Weyl Phonons in Parity-Breaking FeSi Miao, H.; Zhang, T. T.; Wang, L. Physical Review Letters, Vol. 121, Issue 3 https://doi.org/10.1103/physrevlett.121.035302	journal	July 2018
Edge Modes and Asymmetric Wave Transport in Topological Lattices: Experimental Characterization at Finite Frequencies Ma, Jihong; Zhou, Di; Sun, Kai Physical Review Letters, Vol. 121, Issue 9 https://doi.org/10.1103/physrevlett.121.094301	journal	August 2018
Observation of Nonreciprocal Wave Propagation in a Dynamic Phononic Lattice Wang, Yifan; Yousefzadeh, Behrooz; Chen, Hui Physical Review Letters, Vol. 121, Issue 19 https://doi.org/10.1103/physrevlett.121.194301	journal	November 2018
Topological Fano Resonances Zangeneh-Nejad, Farzad; Fleury, Romain Physical Review Letters, Vol. 122, Issue 1 https://doi.org/10.1103/physrevlett.122.014301	journal	January 2019
Experimental Demonstration of Acoustic Chern Insulators Ding, Yujiang; Peng, Yugui; Zhu, Yifan Physical Review Letters, Vol. 122, Issue 1 https://doi.org/10.1103/physrevlett.122.014302	journal	January 2019
Topological Waves in Fluids with Odd Viscosity Souslov, Anton; Dasbiswas, Kinjal; Fruchart, Michel Physical Review Letters, Vol. 122, Issue 12 https://doi.org/10.1103/physrevlett.122.128001	journal	March 2019
Topological Insulators by Topology Optimization Christiansen, Rasmus E.; Wang, Fengwen; Sigmund, Ole Physical Review Letters, Vol. 122, Issue 23 https://doi.org/10.1103/physrevlett.122.234502	journal	June 2019
Edge States and Topological Pumping in Spatially Modulated Elastic Lattices Rosa, Matheus I. N.; Pal, Raj Kumar; Arruda, José R. F. Physical Review Letters, Vol. 123, Issue 3 https://doi.org/10.1103/physrevlett.123.034301	journal	July 2019
Klein-Gordon Representation of Acoustic Waves and Topological Origin of Surface Acoustic Modes Bliokh, Konstantin Y.; Nori, Franco Physical Review Letters, Vol. 123, Issue 5 https://doi.org/10.1103/physrevlett.123.054301	journal	August 2019
Gradient-Index Granular Crystals: From Boomerang Motion to Asymmetric Transmission of Waves Kim, Eunho; Chaunsali, Rajesh; Yang, Jinkyu Physical Review Letters, Vol. 123, Issue 21 https://doi.org/10.1103/physrevlett.123.214301	journal	November 2019
Phononic Helical Nodal Lines with PT Protection in MoB 2 Zhang, T. T.; Miao, H.; Wang, Q. Physical Review Letters, Vol. 123, Issue 24 https://doi.org/10.1103/physrevlett.123.245302	journal	December 2019
Inverse design of discrete mechanical metamaterials Ronellenfitsch, Henrik; Stoop, Norbert; Yu, Josephine Physical Review Materials, Vol. 3, Issue 9 https://doi.org/10.1103/physrevmaterials.3.095201	journal	September 2019
Simulation of topological phases with color center arrays in phononic crystals Li, Xiao-Xiao; Li, Bo; Li, Peng-Bo Physical Review Research, Vol. 2, Issue 1 https://doi.org/10.1103/physrevresearch.2.013121	journal	February 2020
Fragile topologically protected perfect reflection for acoustic waves Ji, Chang-Yin; Zhang, Yongyou; Liao, Yunhong Physical Review Research, Vol. 2, Issue 1 https://doi.org/10.1103/physrevresearch.2.013131	journal	February 2020
Geared Topological Metamaterials with Tunable Mechanical Stability Meeussen, Anne S.; Paulose, Jayson; Vitelli, Vincenzo Physical Review X, Vol. 6, Issue 4 https://doi.org/10.1103/physrevx.6.041029	journal	November 2016
Experimental Observation of Topologically Protected Helical Edge Modes in Patterned Elastic Plates Miniaci, M.; Pal, R. K.; Morvan, B. Physical Review X, Vol. 8, Issue 3 https://doi.org/10.1103/physrevx.8.031074	journal	September 2018
Topological Boundary Floppy Modes in Quasicrystals Zhou, Di; Zhang, Leyou; Mao, Xiaoming Physical Review X, Vol. 9, Issue 2 https://doi.org/10.1103/physrevx.9.021054	journal	June 2019
Modulating Band Gap Structure by Parametric Excitations Yang, Xiao-Dong; Cui, Qing-Dian; Qian, Ying-Jing Journal of Applied Mechanics, Vol. 85, Issue 6 https://doi.org/10.1115/1.4039755	journal	April 2018
Acoustic metamaterials: From local resonances to broad horizons Ma, Guancong; Sheng, Ping Science Advances, Vol. 2, Issue 2 https://doi.org/10.1126/sciadv.1501595	journal	February 2016
Topological insulator laser: Theory Harari, Gal; Bandres, Miguel A.; Lumer, Yaakov Science, Vol. 359, Issue 6381 https://doi.org/10.1126/science.aar4003	journal	February 2018
Su-Schrieffer-Heeger Model Inspired Acoustic Interface States and Edge States Li, Xin; Meng, Yan; Wu, Xiaoxiao Unpublished https://doi.org/10.13140/rg.2.2.17556.35202	text	January 2018
Tunable topological bandgaps and frequencies in a pre-stressed soft phononic crystal Nguyen, B. H.; Park, H. S.; Zhuang, X. Unpublished https://doi.org/10.13140/rg.2.2.29307.77605	text	January 2018
Robust Edge States in Amorphous Gyromagnetic Photonic Lattices Mansha, Shampy; Chong, Y. D. CLEO: Applications and Technology, Conference on Lasers and Electro-Optics https://doi.org/10.1364/cleo_at.2017.jtu5a.41	conference	January 2017
First-principle calculation of Chern number in gyrotropic photonic crystals Zhao, Ran; Xie, Guo-Da; Chen, Menglin L. N. Optics Express, Vol. 28, Issue 4 https://doi.org/10.1364/oe.380077	journal	January 2020
Recent Advances in Non-Traditional Elastic Wave Manipulation by Macroscopic Artificial Structures Park, Jeonghoon; Lee, Dongwoo; Rho, Junsuk Applied Sciences, Vol. 10, Issue 2 https://doi.org/10.3390/app10020547	journal	January 2020
Doppler-Based Acoustic Gyrator Zangeneh-Nejad, Farzad; Fleury, Romain Applied Sciences, Vol. 8, Issue 7 https://doi.org/10.3390/app8071083	journal	July 2018
Three-Dimensional Topological States of Phonons with Tunable Pseudospin Physics Liu, Yizhou; Xu, Yong; Duan, Wenhui Research, Vol. 2019 https://doi.org/10.34133/2019/5173580	journal	July 2019
Topological mechanics of gyroscopic metamaterials Nash, Lisa M.; Kleckner, Dustin; Read, Alismari arXiv https://doi.org/10.48550/arxiv.1504.03362	text	January 2015
Experimental Observation of Large Chern numbers in Photonic Crystals Skirlo, Scott A.; Lu, Ling; Yan, Qinghui arXiv https://doi.org/10.48550/arxiv.1504.04399	text	January 2015
Topological boundary modes in jammed matter Sussman, Daniel M.; Stenull, Olaf; Lubensky, T. C. arXiv https://doi.org/10.48550/arxiv.1512.04480	text	January 2015
Pseudo-time-reversal symmetry and topological edge states in two-dimensional acoustic crystals Mei, Jun; Chen, Ze-Guo; Wu, Ying arXiv https://doi.org/10.48550/arxiv.1606.02944	text	January 2016
Model for Topological Phononics and Phonon Diode Liu, Yizhou; Xu, Yong; Zhang, Shou-Cheng arXiv https://doi.org/10.48550/arxiv.1606.08013	text	January 2016
Sonic Landau-level lasing and synthetic gauge fields in mechanical metamaterials Abbaszadeh, Hamed; Souslov, Anton; Paulose, Jayson arXiv https://doi.org/10.48550/arxiv.1610.06406	text	January 2016
Directional mechanical response in the bulk of topological metamaterials Rocklin, D. Zeb arXiv https://doi.org/10.48550/arxiv.1612.00084	text	January 2016
Edge states of mechanical diamond and its topological origin Takahashi, Yuta; Kariyado, Toshikaze; Hatsugai, Yasuhiro arXiv https://doi.org/10.48550/arxiv.1612.02614	text	January 2016
Chiral edge mode in the coupled dynamics of magnetic solitons in a honeycomb lattice Kim, Se Kwon; Tserkovnyak, Yaroslav arXiv https://doi.org/10.48550/arxiv.1706.04187	text	January 2017
Topological edge floppy modes in disordered fiber networks Zhou, Di; Zhang, Leyou; Mao, Xiaoming arXiv https://doi.org/10.48550/arxiv.1708.03935	text	January 2017
Subwavelength and directional control of flexural waves in zone-folding induced topological plates Chaunsali, Rajesh; Chen, Chun-Wei; Yang, Jinkyu arXiv https://doi.org/10.48550/arxiv.1708.07994	text	January 2017
Soft self-assembly of Weyl materials for light and sound Fruchart, Michel; Jeon, Seung-Yeol; Hur, Kahyun arXiv https://doi.org/10.48550/arxiv.1711.11019	text	January 2017
Topological nodal states in circuit lattice Luo, Kaifa; Yu, Rui; Weng, Hongming arXiv https://doi.org/10.48550/arxiv.1801.05581	text	January 2018
Observation of nonreciprocal wave propagation in a dynamic phononic lattice Wang, Yifan; Yousefzadeh, Behrooz; Chen, Hui arXiv https://doi.org/10.48550/arxiv.1803.11503	text	January 2018
Valley-projected edge modes observed in underwater sonic crystals Shen, Yuanyuan; Qiu, Chunyin; Cai, Xiangxi arXiv https://doi.org/10.48550/arxiv.1807.10887	text	January 2018
Prethermalization and nonreciprocal phonon transport in a levitated optomechanical array Liu, Shengyan; Yin, Zhang-qi; Li, Tongcang arXiv https://doi.org/10.48550/arxiv.1810.00163	text	January 2018
Klein-Gordon representation of acoustic waves and topological origin of surface acoustic modes Bliokh, Konstantin Y.; Nori, Franco arXiv https://doi.org/10.48550/arxiv.1902.03614	text	January 2019
Mechanical analogue of a Majorana bound state Chen, Chun-Wei; Lera, Natalia; Chaunsali, Rajesh arXiv https://doi.org/10.48550/arxiv.1905.03510	text	January 2019
Simulation of topological phases with color center arrays in phononic crystals Li, Xiao-Xiao; Li, Bo; Li, Peng-Bo arXiv https://doi.org/10.48550/arxiv.2001.01397	text	January 2020