| CONDENSED MATTER: STRUCTURE, MECHANICAL AND THERMAL PROPERTIES |
|
|
|
|
From Elastic Spin to Phonon Spin: Symmetry and Fundamental Relations |
| Jie Ren* |
| Center for Phononics and Thermal Energy Science, China-EU Joint Lab on Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China |
|
| Cite this article: |
|
Jie Ren 2022 Chin. Phys. Lett. 39 126301 |
|
|
|
|
Abstract This work is mainly based on postgraduate lectures at Tongji University since 2020 spring. We firstly revisit the elastic spin and orbital angular momentum [Proc. Natl. Acad. Sci. USA 115, 9951 (2018)] but more general for anisotropic systems by applying Noether's theorem to the elastic Lagrangian and by applying the symmetry argument in the field theory. Then, fundamental relations between elastic energy flux and elastic spin are uncovered. In particular cases, the wave spin is closely related to the vorticity of energy flux and momentum. Secondly, we move forward from the elastic spin to revisit the phonon spin [Fizika Tverdogo Tela 3, 2160 (1961)] by applying the second quantization to elastic fields. We show that the uncovered phonon spin, a polarized elastic-vibration quanta, is generally not restricted to transverse phonon modes, but applying to general phonon modes, such as the longitudinal phonon modes, surface phonon modes, and hybridized phonon modes, regarded as a consequence of mode interferences. The elastic spin and phonon spin originate from the local rotating of the field polarization in time domain, not the local circulation (vorticity) of displacement or velocity in space domain. It is hopeful that the present results could advance the fundamental understanding of phonon spin and elastic spin, and promote the spin phononics for hybrid quantum sensing and technology with multiple degrees of freedom.
|
|
|
Received: 10 November 2022
Published: 05 December 2022
|
|
| PACS: |
63.20.-e
|
(Phonons in crystal lattices)
|
| |
62.30.+d
|
(Mechanical and elastic waves; vibrations)
|
| |
47.10.ab
|
(Conservation laws and constitutive relations)
|
| |
11.30.-j
|
(Symmetry and conservation laws)
|
| |
03.70.+k
|
(Theory of quantized fields)
|
|
|
|
|
|
| [1] | Belinfante F 1940 Physica 7 449 |
| [2] | Soper D E 2008 Classical Field Theory (New York: Courier Dover Publications) |
| [3] | Noether E 1918 Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen (Mathematisch-Physikalische Klasse) pp 235–257 |
| [4] | Voronskii and Svirskii 1961 Fizika Tverdogo Tela 3 2160 |
| [5] | Voronskii and Svirskii 1962 Sov. Phys.: Solid State 3 1568 |
| [6] | Levine A T 1962 IL Nuovo Cimento 26 190 |
| [7] | Goerbig M O 2011 Rev. Mod. Phys. 83 1193 |
| [8] | Zhang L and Niu Q 2014 Phys. Rev. Lett. 112 085503 |
| [9] | Nakane J J and Kohno H 2018 Phys. Rev. B 97 174403 |
| [10] | Alud B A 1973 Acoustic Fields and Waves in Solids (New York: John Wiley & Sons) vol I |
| [11] | Long Y, Ren J, and Chen H 2018 arXiv:1801.03907 [cond-mat.mes-hall] |
| [12] | Long Y, Ren J, and Chen H 2018 arXiv:1801.05790 [physics.app-ph] |
| [13] | Long Y, Ren J, and Chen H 2018 Proc. Natl. Acad. Sci. USA 115 9951 |
| [14] | Yuan W, Yang C, Zhang D, Long Y, Pan Y, Zhong Z, Chen H, Zhao J, and Ren J 2021 Nat. Commun. 12 6954 |
| [15] | Li S, Kim I, Iwamoto S, Zang J, and Yang J 2019 Phys. Rev. B 100 195102 |
| [16] | Geilen M, Kohl F, Nicoloiu A, Müller A, Hillebrands B, and Pirro P 2020 Appl. Phys. Lett. 117 213501 |
| [17] | Nieves M, Carta G, Pagneux V, and Brun M 2020 Int. J. Eng. Sci. 156 103365 |
| [18] | Chaplain G J, De Ponti J M, and Craster R V 2022 Phys. Rev. Lett. 128 064301 |
| [19] | Bliokh K Y 2022 Phys. Rev. Lett. 129 204303 |
| [20] | Deymier P A, Runge K, Vasseur J O, Hladky A C, and Lucas P 2018 J. Phys. B 51 135301 |
| [21] | Zhang X, Bauer G E W, and Yu T 2020 Phys. Rev. Lett. 125 077203 |
| [22] | Zhao C, Li Y, Zhang Z, Vogel M, Pearson J E, Wang J, Zhang W, Novosad V, Liu Q, and Hoffmann A 2020 Phys. Rev. Appl. 13 054032 |
| [23] | Sato T, Yu W, Streib S, and Bauer G E W 2021 Phys. Rev. B 104 014403 |
| [24] | Sasaki R, Nii Y, and Onose Y 2021 Nat. Commun. 12 2599 |
| [25] | Sonner M M, Khosravi F, Janker L, Rudolph D, Koblmüller G, Jacob Z, and Krenner H J 2021 Sci. Adv. 7 eabf7414 |
| [26] | Smirnov A, Zaitsev B, Teplykh A, Nedospasov I, Golovanov E, Qian Z H, Wang B, and Kuznetsova I 2021 Sensors 21 2238 |
| [27] | Shi C, Zhao R, Long Y, Yang S, Wang Y, Chen H, Ren J, and Zhang X 2019 Natl. Sci. Rev. 6 707 |
| [28] | Bliokh K Y and Nori F 2019 Phys. Rev. B 99 174310 |
| [29] | Bliokh K Y and Nori F 2019 Phys. Rev. B 99 020301 |
| [30] | Rondón I and Leykam D 2019 J. Phys.: Condens. Matter 32 104001 |
| [31] | Toftul I D, Bliokh K Y, Petrov M I, and Nori F 2019 Phys. Rev. Lett. 123 183901 |
| [32] | Yang C, Tan Y T, Chen H, and Ren J 2021 J. Appl. Phys. 129 135106 |
| [33] | Long Y, Ge H, Zhang D, Xu X, Ren J, Lu M H, Bao M, Chen H, and Chen Y F 2020 Natl. Sci. Rev. 7 1024 |
| [34] | Wei L and Rodriguez-Fortuno F J 2020 New J. Phys. 22 083016 |
| [35] | Long Y, Zhang D, Yang C, Ge J, Chen H, and Ren J 2020 Nat. Commun. 11 4716 |
| [36] | Landau L D and Lifshitz E M 1970 Theory of Elasticity 2nd edn (Pergamon Press) |
| [37] | Laude V and Beugnot J C 2015 New J. Phys. 17 125003 |
| [38] | Misner C W, Thorne K S, Wheeler J A, and Kaiser D I 2017 Gravitation (Princeton University Press) |
| [39] | Jones W L 1973 J. Fluid Mech. 58 737 |
| [40] | Bliokh K Y, Punzmann H, Xia H, Nori F, and Shats M 2022 Sci. Adv. 8 eabm1295 |
| [41] | Golat S, Lim E A, and Rodríguez-Fortuño F J 2020 Phys. Rev. D 101 084046 |
| [42] | Xin S, Long Y, and Ren J 2021 New J. Phys. 23 043035 |
| [43] | Messiah A 1999 Quantum Mechanics (Dover Publications) |
| [44] | Zhang L and Niu Q 2015 Phys. Rev. Lett. 115 115502 |
| [45] | Liu Y, Lian C S, Li Y, Xu Y, and Duan W 2017 Phys. Rev. Lett. 119 255901 |
| [46] | Goldstein H 2002 Classical Mechanics (Addison-Wesley Longman) |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
