The topological one-way waveguide mode of the acoustic wave has recently been demonstrated in various meta-structure systems. Here, we show that in a topological phononic crystal with a symmetry-broken acoustic unit cell, the topological state possesses not just a “spin-like” pseudospin mode but also real spin angular momentum. By rotating the double-square units, the band of the phononic crystal will become inverse and induce both topological phase transition and spin angular momentum reversal. As such, by putting two topologically different systems together, the spin angular momentum dependent one-way interface modes can be selectively excited by acoustic spin sources, exhibiting robust transport protected by tight spin-momentum locking. The spin angular momentum density distribution in the unit cell and edge states shows that in addition to the pseudospin, there is a strong correlation between the real spin angular momentum and topological properties in this acoustic system, producing the topologically selective acoustic torque. Revealing the real spin angular momentum and associated acoustic spin torque properties of these topological phononic and acoustic systems will give people a more general understanding about symmetric breaking wave systems and help people to explore more potential applications of acoustic spins in various topological systems.
REFERENCES
1.
K. V.
Klitzing
, G.
Dorda
, and M.
Pepper
, “New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance
,” Phys. Rev. Lett.
45
, 494
–497
(1980
). 2.
J.
Maciejko
, T. L.
Hughes
, and S.-C.
Zhang
, “The quantum spin Hall effect
,” Annu. Rev. Condens. Matter Phys.
2
, 31
–53
(2011
). 3.
C. L.
Kane
and E. J.
Mele
, “Quantum spin Hall effect in graphene
,” Phys. Rev. Lett.
95
, 226801
(2005
). 4.
B. A.
Bernevig
, T. L.
Hughes
, and S.-C.
Zhang
, “Quantum spin Hall effect and topological phase transition in HGTE quantum wells
,” Science
314
, 1757
–1761
(2006
). 5.
D.
Hsieh
, D.
Qian
, L.
Wray
, Y.
Xia
, Y. S.
Hor
, R. J.
Cava
, and M. Z.
Hasan
, “A topological Dirac insulator in a quantum spin Hall phase
,” Nature
452
, 970
–974
(2008
). 6.
M. Z.
Hasan
and C. L.
Kane
, “Colloquium: Topological insulators
,” Rev. Mod. Phys.
82
, 3045
–3067
(2010
). 7.
R.
Yu
, W.
Zhang
, H.-J.
Zhang
, S.-C.
Zhang
, X.
Dai
, and Z.
Fang
, “Quantized anomalous Hall effect in magnetic topological insulators
,” Science
329
, 61
–64
(2010
). 8.
X.-L.
Qi
and S.-C.
Zhang
, “Topological insulators and superconductors
,” Rev. Mod. Phys.
83
, 1057
–1110
(2011
). 9.
L.-H.
Wu
and X.
Hu
, “Scheme for achieving a topological photonic crystal by using dielectric material
,” Phys. Rev. Lett.
114
, 223901
(2015
). 10.
T.
Van Mechelen
and Z.
Jacob
, “Universal spin-momentum locking of evanescent waves
,” Optica
3
, 118
–126
(2016
). 11.
K. Y.
Bliokh
, D.
Smirnova
, and F.
Nori
, “Quantum spin Hall effect of light
,” Science
348
, 1448
–1451
(2015
). 12.
Z.-Q.
Yang
, Z.-K.
Shao
, H.-Z.
Chen
, X.-R.
Mao
, and R.-M.
Ma
, “Spin-momentum-locked edge mode for topological vortex lasing
,” Phys. Rev. Lett.
125
, 013903
(2020
). 13.
L.
Ye
, Y.
Yang
, Z.
Hong Hang
, C.
Qiu
, and Z.
Liu
, “Observation of valley-selective microwave transport in photonic crystals
,” Appl. Phys. Lett.
111
, 251107
(2017
). 14.
J.-W.
Dong
, X.-D.
Chen
, H.
Zhu
, Y.
Wang
, and X.
Zhang
, “Valley photonic crystals for control of spin and topology
,” Nat. Mater.
16
, 298
–302
(2017
). 15.
L.
Zhang
, J.
Ren
, J.-S.
Wang
, and B.
Li
, “Topological nature of the phonon Hall effect
,” Phys. Rev. Lett.
105
, 225901
(2010
). 16.
P.
Wang
, L.
Lu
, and K.
Bertoldi
, “Topological phononic crystals with one-way elastic edge waves
,” Phys. Rev. Lett.
115
, 104302
(2015
). 17.
R.
Fleury
, D. L.
Sounas
, C. F.
Sieck
, M. R.
Haberman
, and A.
Alù
, “Sound isolation and giant linear nonreciprocity in a compact acoustic circulator
,” Science
343
, 516
–519
(2014
). 18.
X.
Ni
, C.
He
, X.-C.
Sun
, X.
ping Liu
, M.-H.
Lu
, L.
Feng
, and Y.-F.
Chen
, “Topologically protected one-way edge mode in networks of acoustic resonators with circulating air flow
,” New J. Phys.
17
, 053016
(2015
). 19.
Z.
Yang
, F.
Gao
, X.
Shi
, X.
Lin
, Z.
Gao
, Y.
Chong
, and B.
Zhang
, “Topological acoustics
,” Phys. Rev. Lett.
114
, 114301
(2015
). 20.
A. B.
Khanikaev
, R.
Fleury
, S. H.
Mousavi
, and A.
Alù
, “Topologically robust sound propagation in an angular-momentum-biased graphene-like resonator lattice
,” Nat. Commun.
6
, 8260
(2015
). 21.
J.
Lu
, C.
Qiu
, M.
Ke
, and Z.
Liu
, “Valley vortex states in sonic crystals
,” Phys. Rev. Lett.
116
, 093901
(2016
). 22.
J.
Lu
, C.
Qiu
, L.
Ye
, X.
Fan
, M.
Ke
, F.
Zhang
, and Z.
Liu
, “Observation of topological valley transport of sound in sonic crystals
,” Nat. Phys.
13
, 369
–374
(2017
). 23.
C.
He
, S.-Y.
Yu
, H.
Ge
, H.
Wang
, Y.
Tian
, H.
Zhang
, X.-C.
Sun
, Y. B.
Chen
, J.
Zhou
, M.-H.
Lu
, and Y.-F.
Chen
, “Three-dimensional topological acoustic crystals with pseudospin-valley coupled saddle surface states
,” Nat. Commun.
9
, 4555
(2018
). 24.
Z.
Zhang
, Y.
Tian
, Y.
Wang
, S.
Gao
, Y.
Cheng
, X.
Liu
, and J.
Christensen
, “Directional acoustic antennas based on valley-Hall topological insulators
,” Adv. Mater.
30
, 1803229
(2018
). 25.
M.
Miniaci
, R. K.
Pal
, R.
Manna
, and M.
Ruzzene
, “Valley-based splitting of topologically protected helical waves in elastic plates
,” Phys. Rev. B
100
, 024304
(2019
). 26.
W.
Zhu
, Y.
Long
, H.
Chen
, and J.
Ren
, “Quantum valley Hall effects and spin-valley locking in topological Kane-Mele circuit networks
,” Phys. Rev. B
99
, 115410
(2019
). 27.
T.-W.
Liu
and F.
Semperlotti
, “Tunable acoustic valley-Hall edge states in reconfigurable phononic elastic waveguides
,” Phys. Rev. Appl.
9
, 014001
(2018
). 28.
M.
Yan
, J.
Lu
, F.
Li
, W.
Deng
, X.
Huang
, J.
Ma
, and Z.
Liu
, “On-chip valley topological materials for elastic wave manipulation
,” Nat. Mater.
17
, 993
–998
(2018
). 29.
R.
Süsstrunk
and S. D.
Huber
, “Observation of phononic helical edge states in a mechanical topological insulator
,” Science
349
, 47
(2015
). 30.
S. H.
Mousavi
, A. B.
Khanikaev
, and Z.
Wang
, “Topologically protected elastic waves in phononic metamaterials
,” Nat. Commun.
6
, 8682
(2015
). 31.
C.
He
, X.
Ni
, H.
Ge
, X.-C.
Sun
, Y.-B.
Chen
, M.-H.
Lu
, X.-P.
Liu
, and Y.-F.
Chen
, “Acoustic topological insulator and robust one-way sound transport
,” Nat. Phys.
12
, 1124
–1129
(2016
). 32.
Z.
Zhang
, Q.
Wei
, Y.
Cheng
, T.
Zhang
, D.
Wu
, and X.
Liu
, “Topological creation of acoustic pseudospin multipoles in a flow-free symmetry-broken metamaterial lattice
,” Phys. Rev. Lett.
118
, 084303
(2017
). 33.
Z.
Zhang
, Y.
Tian
, Y.
Cheng
, X.
Liu
, and J.
Christensen
, “Experimental verification of acoustic pseudospin multipoles in a symmetry-broken snowflakelike topological insulator
,” Phys. Rev. B
96
, 241306
(2017
). 34.
C.
Brendel
, V.
Peano
, O. J.
Painter
, and F.
Marquardt
, “Pseudomagnetic fields for sound at the nanoscale
,” Proc. Natl. Acad. Sci. U.S.A.
114
, E3390
–E3395
(2017
). 35.
S.-Y.
Yu
, C.
He
, Z.
Wang
, F.-K.
Liu
, X.-C.
Sun
, Z.
Li
, H.-Z.
Lu
, M.-H.
Lu
, X.-P.
Liu
, and Y.-F.
Chen
, “Elastic pseudospin transport for integratable topological phononic circuits
,” Nat. Commun.
9
, 3072
(2018
). 36.
M.
Miniaci
, R. K.
Pal
, B.
Morvan
, and M.
Ruzzene
, “Experimental observation of topologically protected helical edge modes in patterned elastic plates
,” Phys. Rev. X
8
, 031074
(2018
).37.
Z. K.
Lin
, S. Q.
Wu
, H. X.
Wang
, and J. H.
Jiang
, “Higher-order topological spin Hall effect of sound
,” Chin. Phys. Lett.
37
, 074302
(2020
). 38.
Y.
Long
, J.
Ren
, and H.
Chen
, “Intrinsic spin of elastic waves
,” Proc. Natl. Acad. Sci. U.S.A.
115
, 9951
–9955
(2018
). 39.
C.
Shi
, R.
Zhao
, Y.
Long
, S.
Yang
, Y.
Wang
, H.
Chen
, J.
Ren
, and X.
Zhang
, “Observation of acoustic spin
,” Natl. Sci. Rev.
6
, 707
–712
(2019
). 40.
K. Y.
Bliokh
and F.
Nori
, “Spin and orbital angular momenta of acoustic beams
,” Phys. Rev. B
99
, 174310
(2019
). 41.
I. D.
Toftul
, K. Y.
Bliokh
, M. I.
Petrov
, and F.
Nori
, “Acoustic radiation force and torque on small particles as measures of the canonical momentum and spin densities
,” Phys. Rev. Lett.
123
, 183901
(2019
). 42.
Y.
Long
, D.
Zhang
, C.
Yang
, J.
Ge
, H.
Chen
, and J.
Ren
, “Realization of acoustic spin transport in metasurface waveguides
,” Nat. Commun.
11
, 4716
(2020
). 43.
Y.
Long
, H.
Ge
, D.
Zhang
, X.
Xu
, J.
Ren
, M.-H.
Lu
, M.
Bao
, H.
Chen
, and Y.-F.
Chen
, “Symmetry selective directionality in near-field acoustics
,” Natl. Sci. Rev.
7
, 1024
–1035
(2020
). 44.
W.
Zhu
, S.
Hou
, Y.
Long
, H.
Chen
, and J.
Ren
, “Simulating quantum spin Hall effect in the topological Lieb lattice of a linear circuit network
,” Phys. Rev. B
97
, 075310
(2018
). 45.
S.-Q.
Shen
, W.-Y.
Shan
, and H.-Z.
Lu
, “Topological insulator and the Dirac equation
,” Spin
01
, 33
–44
(2011
). 46.
M.-H.
Lu
, L.
Feng
, and Y.-F.
Chen
, “Phononic crystals and acoustic metamaterials
,” Mater. Today
12
, 34
–42
(2009
). 47.
B.
Assouar
, B.
Liang
, Y.
Wu
, Y.
Li
, J.-C.
Cheng
, and Y.
Jing
, “Acoustic metasurface
,” Nat. Rev. Mater.
3
, 460
–472
(2018
). 48.
Z.
Zhang
, Y.
Tian
, Y.
Cheng
, Q.
Wei
, X.
Liu
, and J.
Christensen
, “Topological acoustic delay line
,” Phys. Rev. Appl.
9
, 034032
(2018
). 49.
T.
Liu
, S.
Liang
, F.
Chen
, and J.
Zhu
, “Inherent losses induced absorptive acoustic rainbow trapping with a gradient metasurface
,” J. Appl. Phys.
123
, 091702
(2018
). 50.
H.
Fan
, B.
Xia
, L.
Tong
, S.
Zheng
, and D.
Yu
, “Elastic higher-order topological insulator with topologically protected corner states
,” Phys. Rev. Lett.
122
, 204301
(2019
). 51.
T.
Liu
, F.
Chen
, S.
Liang
, H.
Gao
, and J.
Zhu
, “Subwavelength sound focusing and imaging via gradient metasurface-enabled spoof surface acoustic wave modulation
,” Phys. Rev. Appl.
11
, 034061
(2019
). 52.
J.-P.
Xia
, D.
Jia
, H.-X.
Sun
, S.-Q.
Yuan
, Y.
Ge
, Q.-R.
Si
, and X.-J.
Liu
, “Programmable coding acoustic topological insulator
,” Adv. Mater.
30
, 1805002
(2018
). © 2021 Author(s).
2021
Author(s)
You do not currently have access to this content.