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Topological phase is a new degree of freedom to describe the state of matter in condensed matter physics. One could predict the existence of the interface state between two topological different phononic crystals. The band structures of phononic crystal depend on the characteristics of their composite and their combination, such as geometry, filling fraction, and stiffness. However, after the phononic crystal is fabricated out, it is relatively difficult to tune their band structure and its topology. In order to broaden the application scope of phononic crystals, different kinds of tunable phononic crystals have been proposed. One method to achieve this tunability is to introduce nonlinearity into the phononic crystals. Granular crystals is one type of tunable nonlinear material, whose nonlinearity stems from nonlinear Hertzian contact. By changing the static precompression, the dispersion of granular crystals can be tuned. In this paper, by combining topology with nonlinear we create a new type of interface state switch without changing the experimental setup. Based on the Su-Schrieffer-Heeger (SSH) model–an example of a one dimensional (1D) topological insulator, we present a 1D nonlinear granular crystal, to realize the topological transition by precompression. First, we construct a 1D mechanical structure, which is made up of nonlinear granular crystal and linear phononic crystal. The 1D nonlinear granular crystal is simplified as a “mass-spring” model with tunable elastic constant and invariable elastic constant. By calculating the band topology–the Zak phase, we found that the Zak phase of the two bands can switch from π to 0. There exist a critical precompression F0, when F F0 the Zak phase of the band is π, when F > F0 the Zak phase is 0. The granular crystal vary from nontrivial bandgap to trivial one as precompression gradually increase. This effect enables us to design interface state switch at the interface between granular crystals with trivial and nontrivial band gap. Furthermore, when F F0, we find that the localization of interface state decreases as the applied precompression increases. Thus, we investigate existence of the interface state under different precompression and found that the interface state can be controlled freely. We anticipate these results to enable the creation of novel tunable acoustic devices.
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Keywords:
- interface state /
- tunability /
- topological phase transition /
- granular crystal
[1] Ma G C, Sheng P 2016 Sci. Adv 2 e1501595
[2] Yang S X, Page J H, Liu Z Y, Cowan M L, Chan C T, Sheng P 2004 Phys. Rev. Lett. 93 024301
[3] Wu F G, Liu Z Y, Liu Y Y 2002 Phys. Rev. E 66 046628
[4] Wu L Y, Yang W P, Chen L W 2008 Phys. Lett. A 372 2701
[5] Matar O B, Robillard J F, Vasseur J O, Hennion A C H, Deymier P A, Pernod P, Preobrazhensky V 2012 J. Appl. Phys. 111 054901
[6] Boechler N, Theocharis G, Daraio C 2011 Nat. Mater. 10 665
[7] Porter M A, Kevrekidis P G, Daraio C 2015 Phys. Today 68 44
[8] Li F, Ngo D, Yang J Y, Daraio C 2012 Appl. Phys. Lett.101 171903
[9] Garcia M S, Lydon J, Daraio C 2016 Phys. Rev. E 93 010901
[10] Sinev I S, Mukhin I S, Slobozhanyuk A P, Poddubny A N, Miroshnichenko A E, Samuseva A K, Kivshar Y S 2015 Nanoscale 7 11904
[11] Weimann S, Kremer M, Plotnik Y, Lumer Y, Nolte S, Makris K G, Segev M, Rechtsman M C, Szameit A 2017 Nat. Mater. 10 4811
[12] Xiao M, Ma G C, Yang Z Y, Sheng P, Zhang Z Q, Chan C T 2015 Nat. Phys. 11 240
[13] Xiao Y X, Ma G C, Zhang Z Q, Chan C T 2017 Phys. Rev. Lett. 118 166803
[14] Kane C L, Lubensky T C 2014 Nat. Phys. 10 2835
[15] Theocharis G, Boechler N, Daraio C 2013 Nonlinear Phononic Periodic Structures and Granular Crystals (Berlin Heidelberg: Springer) p217
[16] Huang K, Han R Q 1988 Solid State Physics (Beijing: Higher Education Press) p93 (in Chinese) [黄昆 著, 韩汝琦 改编 1988 固体物理学 (北京: 高等教育出版社) 第 93 页]
[17] Berry M V 1984 Proc. R. Soc. Lond. A 392 45
[18] Zak J 1989 Phys. Rev. Lett. 62 2747
[19] Xiao M, Zhang Z Q, Chan C T 2014 Phys. Rev. X 4 021017
[20] Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057
[21] Chen X, Gu Z C, Liu Z X, Wen X G 2013 Phys. Rev. B 87 155114
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[1] Ma G C, Sheng P 2016 Sci. Adv 2 e1501595
[2] Yang S X, Page J H, Liu Z Y, Cowan M L, Chan C T, Sheng P 2004 Phys. Rev. Lett. 93 024301
[3] Wu F G, Liu Z Y, Liu Y Y 2002 Phys. Rev. E 66 046628
[4] Wu L Y, Yang W P, Chen L W 2008 Phys. Lett. A 372 2701
[5] Matar O B, Robillard J F, Vasseur J O, Hennion A C H, Deymier P A, Pernod P, Preobrazhensky V 2012 J. Appl. Phys. 111 054901
[6] Boechler N, Theocharis G, Daraio C 2011 Nat. Mater. 10 665
[7] Porter M A, Kevrekidis P G, Daraio C 2015 Phys. Today 68 44
[8] Li F, Ngo D, Yang J Y, Daraio C 2012 Appl. Phys. Lett.101 171903
[9] Garcia M S, Lydon J, Daraio C 2016 Phys. Rev. E 93 010901
[10] Sinev I S, Mukhin I S, Slobozhanyuk A P, Poddubny A N, Miroshnichenko A E, Samuseva A K, Kivshar Y S 2015 Nanoscale 7 11904
[11] Weimann S, Kremer M, Plotnik Y, Lumer Y, Nolte S, Makris K G, Segev M, Rechtsman M C, Szameit A 2017 Nat. Mater. 10 4811
[12] Xiao M, Ma G C, Yang Z Y, Sheng P, Zhang Z Q, Chan C T 2015 Nat. Phys. 11 240
[13] Xiao Y X, Ma G C, Zhang Z Q, Chan C T 2017 Phys. Rev. Lett. 118 166803
[14] Kane C L, Lubensky T C 2014 Nat. Phys. 10 2835
[15] Theocharis G, Boechler N, Daraio C 2013 Nonlinear Phononic Periodic Structures and Granular Crystals (Berlin Heidelberg: Springer) p217
[16] Huang K, Han R Q 1988 Solid State Physics (Beijing: Higher Education Press) p93 (in Chinese) [黄昆 著, 韩汝琦 改编 1988 固体物理学 (北京: 高等教育出版社) 第 93 页]
[17] Berry M V 1984 Proc. R. Soc. Lond. A 392 45
[18] Zak J 1989 Phys. Rev. Lett. 62 2747
[19] Xiao M, Zhang Z Q, Chan C T 2014 Phys. Rev. X 4 021017
[20] Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057
[21] Chen X, Gu Z C, Liu Z X, Wen X G 2013 Phys. Rev. B 87 155114
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