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In traditional physics, phonon is widely regarded as being linearly polarized, which means that phonon carries zero angular momentum. Thus the angular momentum of lattice related to mechanical rotation only reflects the lattice rigid-body motion. Recently, in a magnetic system with time reversal symmetry broken by spin-phonon interaction, one found that the phonon angular momentum is nonzero and an odd function of magnetization. At zero temperature, phonon was reported to have a zero-point angular momentum and zero-point energy. Thus the gyromagnetic ratio obtained through the Einstein-de Haas effect needs correcting by considering the nonzero phonon angular momentum. As is well known, if phonon has nonzero angular momentum, which means that phonon can have rotation, it can be right-handed or left-handed, that is, the phonon is chiral. Actually, we can define the polarization of phonon to represent the phonon chirality, which comes from the circular vibration of sublattices. When the phonon polarization is larger (less) than zero, the phonon is right (left)-handed. In non-magnetic honeycomb AB lattices, with inversion symmetrybrocken, the chiral phonons are found to be of valley contrasting circular polarization and concentrated in Brillouin-zone corners. At valleys, there is a three-fold rotational symmetry endowing phonons with quantized pseudo angular momentum. Then conversation of pseudo angular momentum, which determines the selection rules in phonon-involved intervalley scattering of electrons, must be satisfied. Chiral valley phonons can be measured by polarized infrared absorption or emission. In addition, since the phonon Berry curvature is reported to be nonzero at valley, it can distort phonon transport under a strain gradient, which can act as an effective magnetic field. Thus, a valley phonon Hall effect is theoretically predicted, which is probably a method of measuring chiral valley phonons. In consideration of phonons angular momentum and chiral phonons, photon helicity changed by phonons at Gamma point will be explained reasonably. In conclusion, chiral phonons are present in systems that break time reversal or spatial inversion symmetries. In a magnetic system, where time reversal symmetry is broken, phonons generally carry a nonzero angular momentum, which can influence the classic Einstein-de Haas effect. In a nonequilibrium system, the phonon Hall effect can be observed due to the chiral phonons. In a non-magnetic crystal, with inversion symmetry brocken, phonons in the Brillouin-zone center and corners are chiral and have a quantized pseudo angular momentum, providing an alternative to valleytronics in insulators. We believe that the findings of the phonon angular momentum and the chiral phonons together with phonon pseudoangular momentum, selection rules, and valley phonon Hall effect will lead to the relevant exploration and new development of phonon related subject in condensed matter physics.
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Keywords:
- phonon angular momentum /
- chiral phonons /
- conversation of pseudoangular momentum /
- valley phonon Hall effect
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[1] Einstein A, de Haas W J 1915 Verh. Dtsch. Phys. Ges. 17 152
[2] Leduc M A 1887 J. Phys. 6 378
[3] Strohm C, Rikken G, Wyder P 2005 Phys. Rev. Lett. 95 155901
[4] Inyushkin A V, Taldenkov A N 2007 JETP Lett. 86 379
[5] Sheng L, Sheng D N, Ting C S 2006 Phys. Rev. Lett. 96 155901
[6] Kagan Y, Maksimov L A 2008 Phys. Rev. Lett. 100 145902
[7] Qin T, Niu Q, Shi J R 2011 Phys. Rev. Lett. 107 236601
[8] Zhang L 2011 Ph. D. Dissertation (Singapore: National University of Singapore)
[9] Zhang L F, Niu Q 2014 Phys. Rev. Lett. 112 085503
[10] Ray T, Ray D K 1967 Phys. Rev. 164 420
[11] Ioselevich A S, Capellmann H 1995 Phys. Rev. B 51 11446
[12] Qin T, Zhou J, Shi J R 2012 Phys. Rev. B 86 104305
[13] Walton D 1967 Phys. Rev. Lett. 19 305
[14] Reck R A, Fry D L 1969 Phys. Rev. 184 492
[15] Xiao D, Yao W, Niu Q 2007 Phys. Rev. Lett. 99 236809
[16] Zeng H L, Cui X D 2016 Wuli 45 505 (in Chinese) [曾华凌, 崔晓冬 2016 物理 45 505]
[17] Zeng H L, Dai J F, Yao W, Xiao D, Cui X D 2012 Nat. Nanotech. 7 490
[18] Chen S Y, Zheng C X, Fuhrer M S, Yan J 2015 Nano Lett. 15 2526
[19] Zhang L F, Niu Q 2015 Phys. Rev. Lett. 115 115502
[20] Chen S Y, Wu Q, Mishra C, Kang J, Zhang H, Cho K, Cai W, Balandin A A, Ruoff R S 2012 Nat. Mater. 11 203
[21] Zhou S Y, Gweon G H, Fedorov A V, First P N, de Heer W A, Lee D H, Guinea F, Castro Neto A H, Lanzara A 2007 Nat. Mater. 6 770
[22] Kim G, Jang A R, Jeong H Y, Lee Z, Kang D J, Shin H S 2013 Nano Lett. 13 1834
[23] Saito R, Jorio A, Souza Filho A G, Dresselhaus G, Dresselhaus M S, Pimenta M A 2001 Phys. Rev. Lett. 88 027401
[24] Malarda L M, Pimentaa M A, Dresselhaus G, Dresselhaus M S 2009 Phys. Rep. 473 51
[25] 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
[26] Wu F, Qu F, MacDonald A H 2015 Phys. Rev. B 91 075310
[27] Chang M C, Niu Q 1996 Phys. Rev. B 53 7010
[28] Xiao D, Chang M C, Niu Q 2010 Rev. Mod. Phys. 82 1959
[29] Mak K F, McGill K L, Park J, McEuen P L 2014 Science 344 1489
[30] 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
[31] Sheng L, Sheng D N, Ting C S 2006 Phys. Rev. Lett. 96 155901
[32] Tian Y, Shen S P, Cong J Z, Chai Y S, Yan L Q, Wang S G, Sun Y 2016 J. Am. Chem. Soc. 138 782
[33] Goldstein T, Chen S Y, Tong J, Xiao D, Ramasubramaniam A, Yan J 2016 Sci. Rep. 6 28024
[34] Lu J Y, Qiu C Y, Ke M Z, Liu Z Y 2016 Phys. Rev. Lett. 116 093901
[35] Zhu H, et al. 2018 Science 359 6375
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