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Thouless,D.J.et.al.Phys.Rev.Lett.49,405(1982);Klitzing,K.V.,Dorda,G.&Pepper,M.Phys.Rev.Lett.45,494(1980);Bernevig,B.A.,Hughes,T.L.&Zhang,S.-C.Science314,1757(2006);Hasan,Z.&Kane,C.L.Rev.Mod.Phys.82,3045(2010).Lindner,N.H.et.al.NaturePhys.7,NanjingPhotonicspinPhotonicIntegerQuantumHallF.D.M.Haldaneetal.PRL.100,013904Z.Wangetal.PRL.100,Z.Wangetal.Nature461,Photonictopologicaledgestates:

PhotonicFloquettopologicalM.Rechtsman,A.Szemeitetal.Nature496,196(2013).GermanyPhotonicspinhalleffectatM.Hafezietal.Nat.Phys.7,907-912M.Hafezietal.Nat.Photon.7,1001-1005 XBYin,X.Zhangetal,Science339,NanjingChernphononiccrystals：IQHEof Acoustic R.Fleuryetal.Science343,516X.Nietal.NewJ.Phys.17,053016

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PRL,114127401arXiv:1601.01311KramersdegeneracyNanjingPointgroup:622/6mm(or422Zhao,J.etal..PRB77,075126(2008);PLA372,486Elastic5700Kgm-C33=162C44=43e14=1.512Cm-5000Kgm-C33=269.5C44=45.3m15=550NA-m-5350Kgm-C33=215.75C44=44.15Huang,J.H.&Kuo,W.-S.J.Appl.Phys.81,1378-1386(1997).;Pan,E.Z.angew.Math.Phys.53,815-838 NanjingD(z)(

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