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拓扑学与物理的结合是近几十年物理学蓬勃发展的一个新领域，它不仅活跃在量子场理论以及高能物理中，更广泛地存在于凝聚态物理体系中，包括量子（反常、自旋）霍尔效应和拓扑绝缘体（超导体）等.声子是凝聚态体系中热输运的主要载体；最近由于各种声子器件的发现，声子学得到了广泛的关注.本文介绍了声子的拓扑性质以及声子的霍尔效应现象，分别评述了在破坏时间反演对称、破坏空间反演对称、以及同时破坏时间和空间反演对称三种情况下所产生的声子霍尔效应、声子谷霍尔效应等相关物理研究进展.最后对拓扑学在其他声学体系中的应用做了简单介绍，并进一步讨论了其未来的发展方向.The combination of topology and physics is a new field of physics development in recent decades. It is not only active in quantum field theory and high energy physics, but also widely exists in condensed matter physics, including quantum (anomalous, spin) Hall effect and topological insulators (superconductors) etc. Phonon, as the main carrier of heat transport in the crystal, recently, due to the discovery of various phonon devices, phonons has been widely concerned by scientist. In this paper, we introduce the topological properties of phonons and the phonon hall effect. We have reviewed the related physical research progress of phonon hall effect, phonon valley hall effect and so on, which are generated by breaking the time reversal symmetry, spatial inversion symmetry, both breaking the time and spatial inversion symmetry. Finally, the application of topology in other acoustic systems is briefly introduced, and the future development direction is discussed too.
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Keywords:
- topology /
- Berry phase /
- Berry curvature /
- phonon Hall effect
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[2] Wilczek F, Shapere A 1989 Geometric Phases Phys. 5 05857
[3] Prabhakar S, Melnik R, Bonilla L L 2014 Phys. Rev. B 89 245310
[4] Thouless D J, Kohmoto M, Nightingale M P, den Nijs M 1982 Phys. Rev. Lett. 49 405
[5] Karplus R, Luttinger J M 1954 Phys. Rev. 95 1154
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[15] Zhang L, Ren J, Wang J S, Li B W 2010 Phys. Rev. Lett. 105 225901
[16] Qin T, Zhou J, Shi J 2012 Phys. Rev. B 86 104305
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[18] Zhang L 2016 New J. Phys. 18 103039
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[25] Holz A 1972 Nuovo Cimento B 9 83
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[27] Kronig R L 1939 Physica 6 33
[28] van Vleck J H 1940 Phys. Rev. 57 426
[29] Wang L and Li B 2007 Phys. Rev. Lett. 99 177208
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[32] Onose Y, Ideue T, Katsura H, Shiomi Y, Nagaosa N, Tokura Y 2010 Science 329 297
[33] Xiao D, Yao W, Niu Q 2007 Phys. Rev. Lett. 99 236809
[34] Zeng H L, Cui X D 2016 Acta Phys. Sin. 45 505
[35] Chang M C, Niu Q 1996 Phys. Rev. B 53 7010
[36] Xiao D, Chang M C, Niu Q 2010 Rev. Mod. Phys. 82 1959
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[38] Gorbachev R V, Song S J C, Yu G L, Kretinin A V, Withers F, Cao Y, Mishchenko A, Grigorieva I V, Novoselov K S, Levitov L S, Geim A K 2014 Science 346 448
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[40] Hirschberger M, Chisnell R, Young S, Lee N P 2015 Phys. Rev. Lett. 115 106603
[41] Heinonen O, Taylor P L, Girvin S M 1984 Phys. Rev. B 30 3016
[42] Xu X D, Yao W, Xiao D, Heinz T F 2014 Nature Phys. 10 343
[43] Rycerz A, Tworzydlo J, Beenakker C W J 2007 Europhys. Lett. 79 57003
[44] Lu J Y, Qiu C Y, Ye L P, Fan X Y, Ke M Z, Zhang F, Liu Z Y 2016 Nature Phys. 13 369
[45] Lu J Y, Qiu C Y, Ke M Z, Liu Z Y 2016 Phys. Rev. Lett. 116 093901
[46] Kane C L, Lubensky T C 2013 arXiv preprint arXiv:1308.0554
[47] Ssstrunk R, Huber S D 2015 Science 349 47
[48] Wang P, Lu L, Bertoldi K 2015 Phys. Rev. Lett. 115 104302
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[1] Berry M V 1984 Math. Phys. Sci. 392 45
[2] Wilczek F, Shapere A 1989 Geometric Phases Phys. 5 05857
[3] Prabhakar S, Melnik R, Bonilla L L 2014 Phys. Rev. B 89 245310
[4] Thouless D J, Kohmoto M, Nightingale M P, den Nijs M 1982 Phys. Rev. Lett. 49 405
[5] Karplus R, Luttinger J M 1954 Phys. Rev. 95 1154
[6] Zeng C, Yao Y, Niu Q, Weitering H H 2006 Phys. Rev. Lett. 96 037204
[7] Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045
[8] Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057
[9] Li B, Wang L, Casati G 2004 Phys. Rev. Lett. 93 184301
[10] Chang C W, Okawa D, Majumdar A, Zettl A 2006 Science 314 1121
[11] Li B, Wang L, Casati G 2006 Appl. Phys. Lett. 88 143501
[12] Rikken G L J A, Strohm C, Wyder P 2002 Phys. Rev. Lett. 89 133005
[13] Inyushkin A V, Taldenkov A N 2007 JETP Lett. 86 379
[14] Sheng L, Sheng D N, Ting C S 2006 Phys. Rev. Lett. 96 155901
[15] Zhang L, Ren J, Wang J S, Li B W 2010 Phys. Rev. Lett. 105 225901
[16] Qin T, Zhou J, Shi J 2012 Phys. Rev. B 86 104305
[17] Zhang L, Niu Q 2015 Phys. Rev. Lett. 115 115502
[18] Zhang L 2016 New J. Phys. 18 103039
[19] Liu Y, Xu Y, Duan W 2017 arXiv preprint arXiv:1707.07142
[20] Zhou J H 2012 Ph. D. Dissertation (Beijing: Institute of Theoretical Physics, Chinese Academy of Sciences) (in Chinese) [周建辉 2012 博士学位论文 (北京: 中国科学院 理论物理研究所)]
[21] Nagaosa N, Sinova J, Onoda S, MacDonald A H, Ong N P 2010 Rev. Modern Phys. 82 1539
[22] Kagan Y, Maksimov L A 2008 Phys. Rev. Lett. 100 145902
[23] Wang J S, Zhang L 2009 Phys. Rev. B 80 012301
[24] Zhang L 2011 Ph. D. Dissertation (Singapore: National University of Singapore)
[25] Holz A 1972 Nuovo Cimento B 9 83
[26] Strohm C, Rikken G, Wyder P 2005 Phys. Rev. Lett. 95 155901
[27] Kronig R L 1939 Physica 6 33
[28] van Vleck J H 1940 Phys. Rev. 57 426
[29] Wang L and Li B 2007 Phys. Rev. Lett. 99 177208
[30] Zhang L, Ren J, Wang J S, Li B W 2011 J. Phys. Condens. Matter 23 305402
[31] Zhang L, Wang J S, Li B 2009 New J. Phys. 11 113038
[32] Onose Y, Ideue T, Katsura H, Shiomi Y, Nagaosa N, Tokura Y 2010 Science 329 297
[33] Xiao D, Yao W, Niu Q 2007 Phys. Rev. Lett. 99 236809
[34] Zeng H L, Cui X D 2016 Acta Phys. Sin. 45 505
[35] Chang M C, Niu Q 1996 Phys. Rev. B 53 7010
[36] Xiao D, Chang M C, Niu Q 2010 Rev. Mod. Phys. 82 1959
[37] Mak K F, McGill K L, Park J, McEuen P L 2014 Science 344 1489
[38] Gorbachev R V, Song S J C, Yu G L, Kretinin A V, Withers F, Cao Y, Mishchenko A, Grigorieva I V, Novoselov K S, Levitov L S, Geim A K 2014 Science 346 448
[39] Cao T, Wang G, Han W P, Ye H Q, Zhu C R, Shi J R, Niu Q, Tan P H, Wang E, Liu B L, Feng J 2012 Nat. Commun. 3 887
[40] Hirschberger M, Chisnell R, Young S, Lee N P 2015 Phys. Rev. Lett. 115 106603
[41] Heinonen O, Taylor P L, Girvin S M 1984 Phys. Rev. B 30 3016
[42] Xu X D, Yao W, Xiao D, Heinz T F 2014 Nature Phys. 10 343
[43] Rycerz A, Tworzydlo J, Beenakker C W J 2007 Europhys. Lett. 79 57003
[44] Lu J Y, Qiu C Y, Ye L P, Fan X Y, Ke M Z, Zhang F, Liu Z Y 2016 Nature Phys. 13 369
[45] Lu J Y, Qiu C Y, Ke M Z, Liu Z Y 2016 Phys. Rev. Lett. 116 093901
[46] Kane C L, Lubensky T C 2013 arXiv preprint arXiv:1308.0554
[47] Ssstrunk R, Huber S D 2015 Science 349 47
[48] Wang P, Lu L, Bertoldi K 2015 Phys. Rev. Lett. 115 104302
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